%
% CCA Bibliography on
% Constructivity, Computability and Complexity in Analysis
%
% http://cca-net.de/
%
% Last updated on 5 May 2023
%
% (c) 2000-2023 Vasco Brattka
%
@article{AAFHS99,
author = {Aps{\={\i}}tis, Kalvis and Arikawa, Setsuo and Freivalds, R{\=u}si{\c{n}}{\v{s}} and Hirowatari, Eiju and Smith, Carl H.},
title = {On the inductive inference of recursive real-valued functions},
journal = {Theoretical Computer Science},
volume = {219},
year = {1999},
pages = {3--17},
}
@incollection{AB14,
author = {Avigad, Jeremy and Brattka, Vasco},
title = {Computability and analysis: the legacy of {A}lan {T}uring},
editor = {Downey, Rod},
booktitle = {Turing's Legacy: Developments from Turing's Ideas in Logic},
series = {Lecture Notes in Logic},
volume = {42},
publisher = {Cambridge University Press},
address = {Cambridge, UK},
year = {2014},
pages = {1--47},
doi = {10.1017/CBO9781107338579.002},
}
@incollection{ABC+17,
author = {Ambaram, T{\^a}nia and Beggs, Edwin and Costa, Jos{\'e} F{\'e}lix and Po{\c{c}}as, Diogo and Tucker, John V},
title = {An analogue-digital model of computation: {T}uring machines with physical oracles},
booktitle = {Advances in Unconventional Computing},
publisher = {Springer},
year = {2017},
pages = {73--115},
}
@article{Abe68,
author = {Aberth, Oliver},
title = {Analysis in the Computable Number Field},
journal = {Journal of the Association for Computing Machinery},
volume = {15},
year = {1968},
pages = {275--299},
}
@article{Abe69,
author = {Aberth, Oliver},
title = {A Chain of Inclusion Relations in Computable Analysis},
journal = {Proceedings of the American Mathematical Society},
volume = {22},
year = {1969},
pages = {539--548},
}
@inproceedings{Abe70,
author = {Aberth, Oliver},
title = {Computable analysis and differential equations},
editor = {Kino, A. and Myhill, J. and Vesley, R.E.},
booktitle = {Intuitionism and Proof Theory},
series = {Studies in Logic and the Foundations of Mathematics},
publisher = {North-Holland},
address = {Amsterdam},
year = {1970},
pages = {47--52},
note = {Proc. of the Summer Conf. at Buffalo N.Y. 1968},
}
@article{Abe71,
author = {Aberth, Oliver},
title = {The failure in computable analysis of a classical existence theorem for differential equations},
journal = {Proceedings of the American Mathematical Society},
volume = {30},
year = {1971},
pages = {151--156},
}
@book{Abe80,
author = {Aberth, Oliver},
title = {Computable Analysis},
publisher = {McGraw-Hill},
address = {New York},
year = {1980},
}
@proceedings{ABEH13,
title = {Special Issue for the Conference Computability and Complexity in Analysis ({CCA} 2011)},
editor = {Archibald, Margaret and Brattka, Vasco and Escard{\'o}, Mart{\'\i}n and Hertling, Peter},
series = {Logical Methods in Computer Science},
year = {2013},
note = {Cape Town, South Africa, January 31-February 4, 2011},
doi = {10.2168/LMCS-CCA:2011},
}
@article{ABH08,
author = {Archibald, Margaret and Brattka, Vasco and Heuberger, Clemens},
title = {Randomness with respect to the Signed-Digit Representation},
journal = {Fundamenta Informaticae},
volume = {83},
number = {1--2},
year = {2008},
pages = {1--19},
}
@inproceedings{ABHK04,
author = {Akama, Yohji and Berardi, Stefano and Hayashi, Susumu and Kohlenbach, Ulrich},
title = {An arithmetical hierarchy of the law of excluded middle and related principles},
booktitle = {Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science (LICS 2004)},
publisher = {IEEE Computer Society Press},
year = {2004},
pages = {192--201},
doi = {10.1109/LICS.2004.1319613},
}
@article{ABS14,
author = {Allen, Kelty and Bienvenu, Laurent and Slaman, Theodore A.},
title = {On zeros of {M}artin-{L}\"of random {B}rownian motion},
journal = {Journal of Logic and Analysis},
volume = {6},
year = {2014},
pages = {Paper 9, 34},
doi = {10.4115/jla.2014.6.9},
}
@article{AD02,
author = {van Atten, Mark and van Dalen, Dirk},
title = {Arguments for the Continuity Principle},
journal = {Bulletin of Symbolic Logic},
volume = {8},
number = {3},
year = {2002},
pages = {329--347},
}
@phdthesis{AdA20,
author = {Angl{\`e}s d'Auriac, Paul-Elliot},
title = {Infinite Computations in Algorithmic Randomness and Reverse Mathematics},
school = {Universit{\'e} Paris-Est},
year = {2020},
}
@article{ADK21,
author = {Angl{\`e}s d'Auriac, Paul-Elliot and Kihara, Takayuki},
title = {A Comparison of Various Analytic Choice Principles},
journal = {The Journal of Symbolic Logic},
volume = {86},
number = {4},
year = {2021},
pages = {1452--1485},
doi = {10.1017/jsl.2021.37},
}
@article{Adl69,
author = {Adler, Andrew},
title = {Some recursively unsolvable problems in analysis},
journal = {Proceedings of the American Mathematical Society},
volume = {22},
year = {1969},
pages = {523--526},
}
@inproceedings{ADM08,
author = {Andreev, Valentin V. and Daniel, Dale and McNicholl, Timothy H.},
title = {Technical Report: Computation on the Extended Complex Plane and Conformal Mapping of Multiply-connected Domains},
editor = {Brattka, Vasco and Dillhage, Ruth and Grubba, Tanja and Klutsch, Angela},
booktitle = {{CCA} 2008, Fifth International Conference on Computability and Complexity in Analysis},
series = {Electronic Notes in Theoretical Computer Science},
volume = {221},
publisher = {Elsevier},
year = {2008},
pages = {127--139},
note = {{CCA} 2008, Fifth International Conference, Hagen, Germany, August 21--24, 2008},
}
@article{ADR12,
author = {Avigad, Jeremy and Dean, Edward T. and Rute, Jason},
title = {Algorithmic randomness, reverse mathematics, and the dominated convergence theorem},
journal = {Annals of Pure and Applied Logic},
volume = {163},
number = {12},
year = {2012},
pages = {1854--1864},
doi = {10.1016/j.apal.2012.05.010},
}
@article{ADR12a,
author = {Avigad, Jeremy and Dean, Edward T. and Rute, Jason},
title = {A metastable dominated convergence theorem},
journal = {J. Log. Anal.},
volume = {4},
year = {2012},
pages = {Paper 3, 19},
doi = {10.4115/jla.2012.4.3},
}
@inproceedings{AFR11,
author = {Ackerman, Nathanael L. and Freer, Cameron E. and Roy, Daniel M.},
title = {Noncomputable conditional distributions},
booktitle = {26th {A}nnual {IEEE} {S}ymposium on {L}ogic in {C}omputer {S}cience---{LICS} 2011},
publisher = {IEEE Computer Soc., Los Alamitos, CA},
year = {2011},
pages = {107--116},
}
@article{AFR17,
author = {Ackerman, Nathanael L. and Freer, Cameron E. and Roy, Daniel M.},
title = {On computability and disintegration},
journal = {Mathematical Structures in Computer Science},
volume = {27},
number = {8},
publisher = {Cambridge University Press},
year = {2017},
pages = {1287--1314},
doi = {10.1017/S0960129516000098},
}
@article{AFR19,
author = {Ackerman, Nathanael L. and Freer, Cameron E. and Roy, Daniel M.},
title = {On the Computability of Conditional Probability},
journal = {Journal of the ACM},
volume = {66},
number = {3},
publisher = {ACM},
address = {New York, NY, USA},
year = {2019},
month = jun,
pages = {23:1--23:40},
doi = {10.1145/3321699},
}
@article{AGT10,
author = {Avigad, Jeremy and Gerhardy, Philipp and Towsner, Henry},
title = {Local stability of ergodic averages},
journal = {Transactions of the American Mathematical Society},
volume = {362},
year = {2010},
pages = {261--288},
doi = {10.1090/S0002-9947-09-04814-4},
}
@inproceedings{AH22a,
author = {Amir, Djamel Eddine and Hoyrup, Mathieu},
title = {Computability of Finite Simplicial Complexes},
editor = {Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
booktitle = {49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
volume = {229},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
year = {2022},
pages = {111:1--111:16},
doi = {10.4230/LIPIcs.ICALP.2022.111},
}
@inproceedings{AI05,
author = {Akama, Yohji and Iizuka, Shinji},
title = {Real number representations of graph-directed {IFS} attractors},
editor = {Grubba, Tanja and Hertling, Peter and Tsuiki, Hideki and Weihrauch, Klaus},
booktitle = {Computability and Complexity in Analysis},
series = {Informatik Berichte},
volume = {326},
publisher = {FernUniversit\"at in Hagen},
year = {2005},
month = jul,
pages = {3--24},
note = {Proccedings, Second International Conference, CCA 2005, Kyoto, Japan, August 25--29, 2005},
}
@article{Aka04,
author = {Akama, Yohji},
title = {Limiting partial combinatory algebras},
journal = {Theoretical Computer Science},
volume = {311},
year = {2004},
pages = {199--220},
}
@article{AM10,
author = {Andreev, Valentin V. and McNicholl, Timothy H.},
title = {Computing Interpolating Sequences},
journal = {Theory of Computing Systems},
volume = {46},
number = {2},
year = {2010},
pages = {340--350},
doi = {10.1007/s00224-008-9140-z},
}
@article{AM11,
author = {Andreev, Valentin V. and McNicholl, Timothy H.},
title = {Estimating the error in the {K}oebe construction},
journal = {Computational Methods and Function Theory},
volume = {11},
number = {2},
year = {2011},
pages = {707--724},
doi = {10.1007/BF03321883},
}
@article{AM12,
author = {Andreev, Valentin V. and McNicholl, Timothy H.},
title = {Computing conformal maps of finitely connected domains onto canonical slit domains},
journal = {Theory of Computing Systems},
volume = {50},
number = {2},
year = {2012},
pages = {354--369},
doi = {10.1007/s00224-010-9305-4},
}
@incollection{AM21,
author = {Andreev, Valentin V. and McNicholl, Timothy H.},
title = {Computable Complex Analysis},
editor = {Brattka, Vasco and Hertling, Peter},
booktitle = {Handbook of Computability and Complexity in Analysis},
series = {Theory and Applications of Computability},
publisher = {Springer},
address = {Cham},
year = {2021},
pages = {101--140},
doi = {10.1007/978-3-030-59234-9_4},
}
@article{AMBJL13,
author = {Ariza-Ruiz, David and Martol Briseid, Eyvind and Jim{\'e}nez-Melado, Antonio and L{\'o}pez-Acedo, Genaro},
title = {Rate of convergence under weak contractiveness conditions},
journal = {Fixed Point Theory},
volume = {14},
number = {1},
year = {2013},
pages = {11--27},
}
@article{Anb10,
author = {Anberr{\'e}e, Thomas},
title = {Semantical proofs of correctness for programs performing non-deterministic tests on real numbers},
journal = {Math. Structures Comput. Sci.},
volume = {20},
number = {5},
year = {2010},
pages = {723--751},
doi = {10.1017/S0960129510000186},
}
@article{Anb13,
author = {Anberr{\'e}e, Thomas},
title = {First-order universality for real programs},
journal = {J. Logic Comput.},
volume = {23},
number = {4},
year = {2013},
pages = {729--751},
doi = {10.1093/logcom/exr044},
}
@article{AP11,
author = {Ali-Akbari, Mahdi and Pourmahdian, Massoud},
title = {Computational Models of Certain Hyperspaces of Quasi-metric Spaces},
journal = {Logical Methods in Computer Science},
volume = {7},
year = {2011},
pages = {4:1, 25},
doi = {10.2168/LMCS-7(4:1)2011},
}
@article{AR12,
author = {Ardeshir, Mohammad and Ramezanian, Rasoul},
title = {On the constructive notion of closure maps},
journal = {MLQ Math. Log. Q.},
volume = {58},
number = {4-5},
year = {2012},
pages = {348--355},
doi = {10.1002/malq.201110040},
}
@article{AR15,
author = {Avigad, Jeremy and Rute, Jason},
title = {Oscillation and the mean ergodic theorem for uniformly convex {B}anach spaces},
journal = {Ergodic Theory and Dynamical Systems},
volume = {35},
number = {4},
year = {2015},
pages = {1009--1027},
doi = {10.1017/etds.2013.90},
}
@article{AS06,
author = {Avigad, Jeremy and Simic, Ksenija},
title = {Fundamental notions of analysis in subsystems of second-order arithmetic},
journal = {Annals of Pure and Applied Logic},
volume = {139},
year = {2006},
pages = {138--184},
}
@incollection{AS21,
author = {Alaev, Pavel and Selivanov, Victor},
title = {Complexity issues for the iterated {$h$}-preorders},
booktitle = {Descriptional complexity of formal systems},
series = {Lecture Notes in Comput. Sci.},
volume = {13037},
publisher = {Springer, Cham},
year = {2021},
pages = {1--12},
doi = {10.1007/978-3-030-93489-7\_1},
}
@article{AS21a,
author = {Alaev, P. E. and Selivanov, V. L.},
title = {Fields of algebraic numbers computable in polynomial time. {II}},
journal = {Algebra and Logic},
volume = {60},
number = {6},
year = {2021},
pages = {349--359},
}
@inproceedings{Avi05,
author = {Avigad, Jeremy},
title = {Weak theories of nonstandard arithmetic and analysis},
editor = {Simpson, Stephen},
booktitle = {Reverse Mathematics 2001},
series = {Lecture Notes in Logic},
publisher = {Association for Symbolic Logic},
address = {La Jolla},
year = {2005},
pages = {19--46},
}
@article{Avi09,
author = {Avigad, Jeremy},
title = {The metamathematics of ergodic theory},
journal = {Annals of Pure and Applied Logic},
volume = {157},
number = {2-3},
year = {2009},
pages = {64--76},
doi = {10.1016/j.apal.2008.09.001},
}
@article{Avi12,
author = {Avigad, Jeremy},
title = {Inverting the {F}urstenberg correspondence},
journal = {Discrete Contin. Dyn. Syst.},
volume = {32},
number = {10},
year = {2012},
pages = {3421--3431},
doi = {10.3934/dcds.2012.32.3421},
}
@article{Avi12a,
author = {Avigad, Jeremy},
title = {Uncomputably noisy ergodic limits},
journal = {Notre Dame Journal of Formal Logic},
volume = {53},
number = {3},
year = {2012},
pages = {347--350},
doi = {10.1215/00294527-1716757},
}
@article{AWZ00,
author = {Ambos-Spies, Klaus and Weihrauch, Klaus and Zheng, Xizhong},
title = {Weakly Computable Real Numbers},
journal = {Journal of Complexity},
volume = {16},
number = {4},
year = {2000},
pages = {676--690},
}
@phdthesis{Axo10,
author = {Logan M. Axon},
title = {Algorithmically random closed sets and probability},
school = {Department of Mathematics, University of Notre Dame},
year = {2010},
note = {{Ph.D.} thesis},
}
@article{Axo15,
author = {Axon, Logan M.},
title = {Martin-{L}{\"o}f Randomness in Spaces of Closed Sets},
journal = {The Journal of Symbolic Logic},
volume = {80},
number = {2},
year = {2015},
pages = {359--383},
doi = {10.1017/jsl.2014.76},
}
@article{Axo18,
author = {Axon, Logan},
title = {{M}artin-{L}{\"o}f random generalized {P}oisson processes},
journal = {Annals of Pure and Applied Logic},
volume = {169},
number = {4},
year = {2018},
pages = {261--276},
doi = {10.1016/j.apal.2017.12.003},
}
@inproceedings{AZ19,
author = {Ambos-Spies, Klaus and Zheng, Xizhong},
title = {On the Differences and Sums of Strongly Computably Enumerable Real Numbers},
editor = {Manea, Florin and Martin, Barnaby and Paulusma, Dani{\"e}l and Primiero, Giuseppe},
booktitle = {Computing with Foresight and Industry},
series = {Lecture Notes in Computer Science},
volume = {11558},
publisher = {Springer},
address = {Cham},
year = {2019},
pages = {310--322},
note = {15th Conference on Computability in Europe, CiE 2019, Durham, UK, July 15-19, 2019},
doi = {10.1007/978-3-030-22996-2_27},
}
@article{AZ19a,
author = {Armstrong, Mark and Zucker, Jeffery},
title = {Notions of semicomputability in topological algebras over the reals},
journal = {Computability},
volume = {8},
number = {1},
year = {2019},
pages = {1--26},
doi = {10.3233/com-180087},
}
@article{BA99,
author = {Bedregal, Benjam{\'{\i}}n Ren{\'{e}} Callejas and Aci{\'{o}}ly, Benedito Melo},
title = {Effectively Given Continuous Domains: A Computable Interval Analysis},
journal = {Electronic Journal on Mathematics of Computation},
volume = {0},
year = {1999},
}
@article{Bae83,
author = {Baez, J.C.},
title = {Recursivity in quantum mechanics},
journal = {Transactions of the American Mathematical Society},
volume = {280},
year = {1983},
pages = {339--350},
}
@article{Bai85,
author = {Baigger, G{\"u}nter},
title = {Die {N}ichtkonstruktivit{\"a}t des {B}rouwerschen {F}ixpunktsatzes},
journal = {Archive for Mathematical Logic},
volume = {25},
year = {1985},
pages = {183--188},
}
@article{Bai99,
author = {Baire, R.},
title = {Sur les fonctions des variables reeles},
journal = {Annali di matematica pura ed applicata},
series = {3},
volume = {3},
year = {1899},
pages = {1--123},
}
@inproceedings{Bar02,
author = {Barmpalias, George},
title = {On $0'$-computable Reals},
editor = {Brattka, Vasco and Schr{\"{o}}der, Matthias and Weihrauch, Klaus},
booktitle = {{CCA} 2002 Computability and Complexity in Analysis},
series = {Electronic Notes in Theoretical Computer Science},
volume = {66},
publisher = {Elsevier},
address = {Amsterdam},
year = {2002},
note = {5th International Workshop, {CCA} 2002, M{\'{a}}laga, Spain, July 12--13, 2002},
}
@article{Bar03,
author = {Barmpalias, George},
title = {A transfinite hierarchy of reals},
journal = {Mathematical Logic Quarterly},
volume = {49},
number = {2},
year = {2003},
pages = {163--172},
}
@article{Bar03a,
author = {Barmpalias, George},
title = {The approximation structure of a computably approximable real},
journal = {The Journal of Symbolic Logic},
volume = {68},
number = {3},
year = {2003},
pages = {885--922},
}
@article{Bar04,
author = {Barmpalias, George},
title = {Approximation representations for reals and their wtt-degrees},
journal = {Mathematical Logic Quarterly},
volume = {50},
number = {4,5},
year = {2004},
pages = {370--380},
}
@phdthesis{Bar04a,
author = {Barmpalias, Georgios},
title = {Computability and Applications to Analysis},
school = {University of Leeds, School of Mathematics},
address = {Leeds},
year = {2004},
}
@article{Bar04b,
author = {Barmpalias, George},
title = {Approximation representations for $\Delta_2$ reals},
journal = {Archive for Mathematical Logic},
volume = {43},
number = {8},
year = {2004},
pages = {947--964},
}
@article{Bar05,
author = {Baroni, Marian Alexandru},
title = {Constructive Suprema},
journal = {Journal of Universal Computer Science},
volume = {11},
number = {12},
year = {2005},
pages = {1865--1877},
}
@article{Bar06,
author = {Barmpalias, George},
title = {Random non-cupping revisited},
journal = {Journal of Complexity},
volume = {22},
number = {6},
year = {2006},
pages = {850--857},
}
@inproceedings{Bar09,
author = {Baroni, Marian Alexandru},
title = {Towards a good constructive definition of order completeness},
booktitle = {Proceedings of the {S}ixth {C}ongress of {R}omanian {M}athematicians. {V}ol. 1},
publisher = {Ed. Acad. Rom\^ane, Bucharest},
year = {2009},
pages = {547--550},
}
@incollection{Bar20,
author = {Barmpalias, George},
title = {Aspects of {C}haitin's {O}mega},
editor = {Franklin, Johanna N.Y. and Porter, Christopher P.},
booktitle = {Algorithmic Randomness: Progress and Prospects},
series = {Lecture Notes in Logic},
volume = {50},
publisher = {Cambridge University Press},
year = {2020},
pages = {175--205},
doi = {10.1017/9781108781718.007},
}
@inproceedings{Bat08,
author = {Batra, Prashant},
title = {Newton's method and the Computational Complexity of the Fundamental Theorem of Algebra},
editor = {Dillhage, Ruth and Grubba, Tanja and Sorbi, Andrea and Weihrauch, Klaus and Zhong, Ning},
booktitle = {Proceedings of the Fourth International Conference on Computability and Complexity in Analysis ({CCA} 2007)},
series = {Electronic Notes in Theoretical Computer Science},
volume = {202},
publisher = {Elsevier},
year = {2008},
pages = {201--218},
note = {{CCA} 2007, Siena, Italy, June 16--18, 2007},
}
@phdthesis{Bau00,
author = {Bauer, Andrej},
title = {The Realizability Approach to Computable Analysis and Topology},
school = {School of Computer Science, Carnegie Mellon University},
address = {Pittsburgh},
year = {2000},
}
@inproceedings{Bau01,
author = {Bauer, Andrej},
title = {A Relationship between Equilogical Spaces and Type Two Effectivity},
editor = {Brooks, Stephen and Mislove, Michael},
booktitle = {Seventeenth Conference on the Mathematical Foundations of Programming Semantics},
series = {Electronic Notes in Theoretical Computer Science},
volume = {45},
publisher = {Elsevier},
address = {Amsterdam},
year = {2001},
note = {{MFPS} 2001, Aarhus, Denmark May 23--26, 2001},
}
@article{Bau02,
author = {Bauer, Andrej},
title = {A Relationship between Equilogical Spaces and Type Two Effectivity},
journal = {Mathematical Logic Quarterly},
volume = {48},
number = {Suppl. 1},
year = {2002},
pages = {1--15},
}
@article{Bau15,
author = {Bauer, Andrej},
title = {An injection from the {B}aire space to natural numbers},
journal = {Mathematical Structures in Computer Science},
volume = {25},
year = {2015},
month = {10},
pages = {1484--1489},
doi = {10.1017/S0960129513000406},
}
@article{Bau17,
author = {Bauer, Andrej},
title = {Five Stages of Accepting Constructive Mathematics},
journal = {Bulletin of Symbolic Logic},
volume = {54},
number = {3},
year = {2017},
pages = {481--498},
doi = {10.1090/bull/1556},
}
@article{Bau17a,
author = {Bauer, Andrej},
title = {On fixed-point theorems in synthetic computability},
journal = {Tbilisi Mathematical Journal},
volume = {10},
number = {3},
year = {2017},
pages = {167--181},
doi = {10.1515/tmj-2017-0107},
}
@article{Bau22,
author = {Bauer, Andrej},
title = {Instance reducibility and {W}eihrauch degrees},
journal = {Logical Methods in Computer Science},
volume = {18},
number = {3},
year = {2022},
month = Aug,
pages = {20:1--20:18},
doi = {10.46298/lmcs-18(3:20)2022},
}
@article{BB06,
author = {Berger, Josef and Bridges, Douglas S.},
title = {A bizarre property equivalent to the {$\Pi^0_1$}--fan theorem},
journal = {Logic Journal of the IGPL},
volume = {14},
year = {2006},
pages = {867--871},
}
@article{BB07,
author = {Berger, Josef and Bridges, Douglas S.},
title = {A fan-theoretic equivalent of the antithesis of {S}pecker's theorem},
journal = {Indagationes Mathematicae},
volume = {18},
number = {2},
year = {2007},
pages = {195--202},
}
@inproceedings{BB08,
author = {Baroni, M. A. and Bridges, D. S.},
title = {Continuity Properties of Preference Relations},
editor = {Dillhage, Ruth and Grubba, Tanja and Sorbi, Andrea and Weihrauch, Klaus and Zhong, Ning},
booktitle = {Proceedings of the Fourth International Conference on Computability and Complexity in Analysis ({CCA} 2007)},
series = {Electronic Notes in Theoretical Computer Science},
volume = {202},
publisher = {Elsevier},
year = {2008},
pages = {19--25},
note = {{CCA} 2007, Siena, Italy, June 16--18, 2007},
}
@article{BB08a,
author = {Berger, Josef and Bridges, Douglas S.},
title = {The anti-{S}pecker property, a {H}eine-{B}orel property},
journal = {Archive for Mathematical Logic},
volume = {46},
number = {7--8},
year = {2008},
pages = {583--592},
}
@article{BB08b,
author = {Baroni, Marian A. and Bridges, Douglas S.},
title = {Continuity properties of preference relations},
journal = {Mathematical Logic Quarterly},
volume = {54},
number = {5},
year = {2008},
pages = {454--459},
}
@article{BB08d,
author = {Berger, Josef and Bridges, Douglas S.},
title = {The fan theorem and positive-valued uniformly continuous functions on compact intervals},
journal = {New Zealand Journal of Mathematics},
volume = {38},
year = {2008},
pages = {129--135},
}
@inproceedings{BB09,
author = {Binder, Ilia and Braverman, Mark},
title = {The complexity of simulating {B}rownian motion},
booktitle = {Proceedings of the {T}wentieth {A}nnual {ACM}-{SIAM} {S}ymposium on {D}iscrete {A}lgorithms},
publisher = {SIAM},
address = {Philadelphia, PA},
year = {2009},
pages = {58--67},
}
@inproceedings{BB09a,
author = {Binder, Ilia and Braverman, Mark},
title = {The Complexity of Simulating {B}rownian Motion},
booktitle = {Proceedings of the Twentieth Annual ACM-SIAM Symposium on Discrete Algorithms},
series = {SODA '09},
publisher = {Society for Industrial and Applied Mathematics},
address = {Philadelphia, PA, USA},
year = {2009},
pages = {58--67},
}
@article{BB10,
author = {Berger, Josef and Bridges, Douglas S.},
title = {A constructive study of {L}andau's summability theorem},
journal = {J.UCS},
volume = {16},
number = {18},
year = {2010},
pages = {2523--2534},
}
@article{BB12,
author = {Binder, Ilia and Braverman, Mark},
title = {The rate of convergence of the walk on spheres algorithm},
journal = {Geom. Funct. Anal.},
volume = {22},
number = {3},
year = {2012},
pages = {558--587},
doi = {10.1007/s00039-012-0161-z},
}
@article{BB17,
author = {Beros, Achilles and Beros, Konstantinos},
title = {Normal Numbers and Limit Computable {C}antor Series},
journal = {Notre Dame Journal of Formal Logic},
volume = {58},
number = {2},
year = {2017},
month = {March},
pages = {215--220},
doi = {10.1215/00294527-2017-0004},
}
@inproceedings{BB22,
author = {Blanc, Manon and Bournez, Olivier},
title = {A Characterization of Polynomial Time Computable Functions from the Integers to the Reals Using Discrete Ordinary Differential Equations},
editor = {Durand-Lose, J{\'e}r{\^o}me and Vaszil, Gy{\"o}rgy},
booktitle = {Machines, Computations, and Universality},
series = {Lecture Notes in Computer Science},
volume = {13419},
publisher = {Springer},
address = {Cham},
year = {2022},
pages = {58--74},
doi = {10.1007/978-3-031-13502-6_4},
}
@book{BB85,
author = {Bishop, Errett and Bridges, Douglas S.},
title = {Constructive Analysis},
series = {Grundlehren der Mathematischen Wissenschaften},
volume = {279},
publisher = {Springer},
address = {Berlin},
year = {1985},
}
@article{BBC+07,
author = {Barmpalias, George and Brodhead, Paul and Cenzer, Douglas and Dashti, Seyyed and Weber, Rebecca},
title = {Algorithmic Randomness of Closed Sets},
journal = {Journal of Logic and Computation},
volume = {17},
number = {6},
publisher = {Oxford University Press},
address = {Oxford, UK},
year = {2007},
pages = {1041--1062},
}
@article{BBCRW08,
author = {Barmpalias, George and Brodhead, Paul and Cenzer, Douglas and Remmel, Jeffrey B. and Weber, Rebecca},
title = {Algorithmic randomness of continuous functions},
journal = {Archive for Mathematical Logic},
volume = {46},
number = {7--8},
year = {2008},
pages = {533--546},
}
@proceedings{BBF+17,
title = {Preface to the special issue: Continuity, Computability, Constructivity: From Logic to Algorithms 2014},
editor = {Bauer, Andrej and Berger, Ulrich and Fouch{\'e}, Willem and Spreen, Dieter and Tsuiki, Hideki and Ziegler, Martin},
series = {The Journal of Logic \& Analysis},
volume = {9},
year = {2017},
doi = {10.4115/jla.2017.9.c0},
}
@article{BBGMV04,
author = {Benci, V. and Bonanno, C. and Galatolo, S. and Menconi, G. and Virgilio, M.},
title = {Dynamical systems and computable information},
journal = {Discrete and Continuous Dynamical Systems B},
volume = {4},
number = {4},
year = {2004},
pages = {935--960},
}
@proceedings{BBH01,
title = {Computability and Complexity in Analysis},
editor = {Blanck, Jens and Brattka, Vasco and Hertling, Peter},
series = {Lecture Notes in Computer Science},
volume = {2064},
publisher = {Springer},
address = {Berlin},
year = {2001},
note = {4th International Workshop, CCA 2000, Swansea, UK, September 17-19, 2000. Selected Papers},
doi = {10.1007/3-540-45335-0},
}
@proceedings{BBMS12,
title = {Continuity, Computability, Constructivity: From Logic to Algorithms},
editor = {Berger, Ulrich and Brattka, Vasco and Morozov, Andrei S. and Spreen, Dieter},
series = {Annals of Pure and Applied Logic},
volume = {163},
number = {8},
publisher = {Elsevier},
address = {Amsterdam},
year = {2012},
doi = {10.1016/j.apal.2011.12.019},
}
@article{BBP12,
author = {Brattka, Vasco and de Brecht, Matthew and Pauly, Arno},
title = {Closed Choice and a Uniform Low Basis Theorem},
journal = {Annals of Pure and Applied Logic},
volume = {163},
year = {2012},
pages = {986--1008},
doi = {10.1016/j.apal.2011.12.020},
}
@article{BBP12a,
author = {Berger, Josef and Bridges, Douglas S. and Palmgren, Erik},
title = {Double sequences, almost {C}auchyness and {BD}-{N}},
journal = {Log. J. IGPL},
volume = {20},
number = {1},
year = {2012},
pages = {349--354},
doi = {10.1093/jigpal/jzr045},
}
@article{BBRY11,
author = {Binder, Ilia and Braverman, Mark and Rojas, Cristobal and Yampolsky, Michael},
title = {Computability of {B}rolin-{L}yubich measure},
journal = {Comm. Math. Phys.},
volume = {308},
number = {3},
year = {2011},
pages = {743--771},
doi = {10.1007/s00220-011-1363-1},
}
@proceedings{BBS+15,
title = {Computing with Infinite Data: Topological and Logical Foundations Part 1},
editor = {Berger, Ulrich and Brattka, Vasco and Selivanov, Victor and Spreen, Dieter and Tsuiki, Hideki},
series = {Mathematical Structures in Computer Science},
volume = {25},
number = {7},
publisher = {Cambridge University Press},
address = {Cambridge},
year = {2015},
doi = {10.1017/S0960129513000364},
}
@proceedings{BBS+15a,
title = {Computing with Infinite Data: Topological and Logical Foundations Part 2},
editor = {Berger, Ulrich and Brattka, Vasco and Selivanov, Victor and Spreen, Dieter and Tsuiki, Hideki},
series = {Mathematical Structures in Computer Science},
volume = {25},
number = {8},
publisher = {Cambridge University Press},
address = {Cambridge},
year = {2015},
doi = {10.1017/S0960129513000364},
}
@article{BBS04,
author = {Bauer, Andrej and Birkedal, Lars and Scott, Dana S.},
title = {Equilogical spaces},
journal = {Theoretical Computer Science},
volume = {315},
year = {2004},
pages = {35--59},
}
@article{BBS06,
author = {Berger, Josef and Bridges, Douglas S. and Schuster, Peter},
title = {The fan theorem and unique existence of maxima},
journal = {The Journal of Symbolic Logic},
volume = {71},
number = {2},
year = {2006},
pages = {713--720},
}
@article{BBY06,
author = {Binder, I. and Braverman, Mark and Yampolsky, M.},
title = {On computational complexity of {S}iegel {J}ulia sets},
journal = {Comm. Math. Phys.},
volume = {264},
number = {2},
year = {2006},
pages = {317--334},
doi = {10.1007/s00220-006-1546-3},
}
@article{BBY07,
author = {Binder, I. and Braverman, M. and Yampolsky, M.},
title = {Filled {J}ulia sets with empty interior are computable},
journal = {Foundations of Computational Mathematics},
volume = {7},
number = {4},
year = {2007},
pages = {405--416},
doi = {10.1007/s10208-005-0210-1},
}
@article{BBY07a,
author = {Binder, Ilia and Braverman, Mark and Yampolsky, Michael},
title = {On the computational complexity of the {R}iemann mapping},
journal = {Arkiv f\"or Matematik},
volume = {45},
number = {2},
year = {2007},
pages = {221--239},
doi = {10.1007/s11512-007-0045-x},
}
@article{BBY12,
author = {Bonnot, Sylvain and Braverman, Mark and Yampolsky, Michael},
title = {Thurston equivalence to a rational map is decidable},
journal = {Mosc. Math. J.},
volume = {12},
number = {4},
year = {2012},
pages = {747--763, 884},
}
@article{BC06,
author = {Braverman, Mark and Cook, Stephen A.},
title = {Computing over the Reals: Foundations for Scientific Computing},
journal = {Notices of the AMS},
volume = {53},
number = {3},
year = {2006},
pages = {318--329},
}
@article{BC08,
author = {Brodhead, Paul and Cenzer, Douglas},
title = {Effectively closed sets and enumerations},
journal = {Archive for Mathematical Logic},
volume = {46},
number = {7--8},
year = {2008},
pages = {565--582},
}
@inproceedings{BC08a,
author = {Bournez, Olivier and Campagnolo, Manuel L.},
title = {A survey on continuous time computations},
booktitle = {New computational paradigms},
publisher = {Springer},
address = {New York},
year = {2008},
pages = {383--423},
doi = {10.1007/978-0-387-68546-5_17},
}
@book{BC72,
author = {Bishop, E. and Cheng, H.},
title = {Constructive {M}easure {T}heory},
publisher = {American Mathematical Society},
address = {Providence},
year = {1972},
}
@inproceedings{BC90,
author = {Boehm, Hans and Cartwright, Robert},
title = {Exact real arithmetic, formulating real numbers as functions},
editor = {Turner, D.},
booktitle = {Research topics in functional programming},
publisher = {Addison-Wesley},
year = {1990},
pages = {43--64},
}
@inproceedings{BCD06,
author = {Brodhead, Paul and Cenzer, Douglas and Dashti, Seyyed},
title = {Random Closed Sets},
editor = {Beckmann, A. and Berger, U. and L{\"o}we, B. and Tucker, J.V.},
booktitle = {Logical Approaches to Computational Barriers},
series = {Lecture Notes in Computer Science},
volume = {3988},
publisher = {Springer},
address = {Berlin},
year = {2006},
pages = {55--64},
note = {Second Conference on Computability in Europe, CiE 2006, Swansea, UK, June 30-July 5, 2006},
}
@article{BCG+17,
author = {Brattka, Vasco and Cettolo, Andrea and Gherardi, Guido and Marcone, Alberto and Schr{\"o}der, Matthias},
title = {Addendum to: ``{T}he {B}olzano-{W}eierstrass Theorem is the Jump of Weak {K}{\H{o}}nig's Lemma''},
journal = {Annals of Pure and Applied Logic},
volume = {168},
number = {8},
year = {2017},
pages = {1605--1608},
doi = {10.1016/j.apal.2017.04.004},
}
@inproceedings{BCGH06,
author = {Bournez, Olivier and Campagnolo, Manuel L. and Gra{\c{c}}a, Daniel S. and Hainry, Emmanuel},
title = {The general purpose analog computer and computable analysis are two equivalent paradigms of analog computation},
booktitle = {Theory and applications of models of computation},
series = {Lecture Notes in Comput. Sci.},
volume = {3959},
publisher = {Springer},
address = {Berlin},
year = {2006},
pages = {631--643},
doi = {10.1007/11750321_60},
}
@article{BCGH07,
author = {Bournez, Olivier and Campagnolo, Manuel L. and Gra{\c{c}}a, Daniel S. and Hainry, Emmanuel},
title = {Polynomial differential equations compute all real computable functions on computable compact intervals},
journal = {Journal of Complexity},
volume = {23},
number = {3},
year = {2007},
pages = {317--335},
}
@article{BCH21,
author = {Bienvenu, Laurent and Csima, Barbara F. and Harrison-Trainor, Matthew},
title = {Some questions of uniformity in algorithmic randomness},
journal = {The Journal of Symbolic Logic},
volume = {86},
number = {4},
year = {2021},
pages = {1612--1631},
doi = {10.1017/jsl.2021.58},
}
@inproceedings{BCJMR81,
author = {Bridges, Douglas S. and Calder, Allan and Julian, William and Mines, Ray and Richman, Fred},
title = {Locating metric complements in {R}$^n$},
editor = {Richman, F.},
booktitle = {Constructive Mathematics},
series = {Lecture Notes in Mathematics},
volume = {873},
year = {1981},
pages = {241--249},
note = {Proc. New Mexico State Univ. Conf., Aug. 11--15, 1980, Las Cruces, NM},
}
@article{BCJMR81a,
author = {Bridges, Douglas S. and Calder, Allan and Julian, William and Mines, Ray and Richman, Fred},
title = {Bounded linear mappings of finite rank},
journal = {Journal of Functional Analysis},
volume = {43},
number = {2},
year = {1981},
pages = {143--148},
}
@article{BCJMR82,
author = {Bridges, Douglas S. and Calder, Allan and Julian, William and Mines, Ray and Richman, Fred},
title = {Picard's theorem},
journal = {Transactions of the American Mathematical Society},
volume = {269},
number = {2},
year = {1982},
pages = {513--520},
}
@article{BCPS99,
author = {Bridges, D. S. and Calude, C. and Pavlov, B. and {\c{S}}tef{\u{a}}nescu, D.},
title = {The constructive implicit function theorem and applications in mechanics},
journal = {Chaos, Solitons and Fractals},
volume = {10},
number = {6},
year = {1999},
pages = {927--934},
}
@article{BCPT17,
author = {Beggs, Edwin and Costa, Jos{\'e} F{\'e}lix and Po{\c{c}}as, Diogo and Tucker, John V.},
title = {Computations with oracles that measure vanishing quantities},
journal = {Mathematical Structures in Computer Science},
volume = {27},
number = {8},
publisher = {Cambridge University Press},
year = {2017},
pages = {1315--1363},
doi = {10.1017/S0960129516000219},
}
@inproceedings{BCR07,
author = {Brodhead, Paul and Cenzer, Douglas and Remmel, Jeffrey B.},
title = {Random Continuous Functions},
editor = {Cenzer, Douglas and Dillhage, Ruth and Grubba, Tanja and Weihrauch, Klaus},
booktitle = {Proceedings of the Third International Conference on Computability and Complexity in Analysis},
series = {Electronic Notes in Theoretical Computer Science},
volume = {167},
publisher = {Elsevier},
address = {Amsterdam},
year = {2007},
note = {{CCA} 2006, Gainesville, Florida, USA, November 1--5, 2006},
}
@proceedings{BCR09,
title = {Computability and Complexity in Analysis},
editor = {Brattka, Vasco and Collins, Pieter and Rettinger, Robert},
series = {Journal of Universal Computer Science},
volume = {15},
number = {6},
publisher = {Graz University of Technology},
address = {Graz},
year = {2009},
note = {Selected Papers of the Fifth International Conference on Computability and Complexity in Analysis, August 21-24, 2008, Hagen, Germany},
doi = {10.3217/jucs-015-06},
}
@inproceedings{BCRW07,
author = {Barmpalias, George and Cenzer, Douglas and Remmel, Jeffrey B. and Weber, Rebecca},
title = {K-Trivial Closed Sets and Continuous Functions},
editor = {Cooper, S. Barry and L{\"o}we, Benedikt and Sorbi, Andrea},
booktitle = {Computation and Logic in the Real World},
series = {Lecture Notes in Computer Science},
volume = {4497},
publisher = {Springer},
address = {Berlin},
year = {2007},
pages = {135--145},
note = {Third Conference on Computability in Europe, CiE 2007, Siena, Italy, June 18-23, 2007},
}
@article{BCRW09,
author = {Barmpalias, George and Cenzer, Douglas and Remmel, Jeffrey B. and Weber, Rebecca},
title = {K-Triviality of Closed Sets and Continuous Functions},
journal = {Journal of Logic and Computation},
volume = {19},
number = {1},
year = {2009},
pages = {3--16},
}
@article{BCT14,
author = {Beggs, Edwin and Costa, Jos\'{e} F\'{e}lix and Tucker, J. V.},
title = {Three Forms of Physical Measurement and their Computability},
journal = {The Review of Symbolic Logic},
volume = {7},
number = {4},
year = {2014},
pages = {618--646},
doi = {10.1017/S1755020314000240},
}
@article{BCTW11,
author = {Brodhead, Paul and Cenzer, Douglas and Toska, Ferit and Wyman, Sebastian},
title = {Algorithmic randomness and capacity of closed sets},
journal = {Log. Methods Comput. Sci.},
volume = {7},
number = {3},
year = {2011},
pages = {3:16, 16},
}
@inproceedings{BCZ22,
author = {Brau{\ss}e, Franz and Collins, Pieter and Ziegler, Martin},
title = {Computer Science for Continuous Data},
editor = {Boulier, Fran{\c{c}}ois and England, Matthew and Sadykov, Timur M. and Vorozhtsov, Evgenii V.},
booktitle = {Computer Algebra in Scientific Computing},
publisher = {Springer},
address = {Cham},
year = {2022},
pages = {62--82},
doi = {10.1007/978-3-031-14788-3_5},
}
@article{BD00,
author = {Bridges, Douglas S. and Dediu, Lumini{\c{t}}a},
title = {The weak-operator sequential continuity of left multiplication},
journal = {Indagationes Mathematicae},
volume = {11},
number = {1},
year = {2000},
pages = {39--42},
}
@article{BD05,
author = {Brattka, Vasco and Dillhage, Ruth},
title = {Computability of the Spectrum of Self-Adjoint Operators},
journal = {Journal of Universal Computer Science},
volume = {11},
number = {12},
year = {2005},
pages = {1884--1900},
doi = {10.3217/jucs-011-12-1884},
}
@article{BD06a,
author = {Bridges, Douglas S. and Diener, Hannes},
title = {A constructive treatment of {U}rysohn's {L}emma in an apartness space},
journal = {Mathematical Logic Quarterly},
volume = {52},
number = {5},
year = {2006},
pages = {464--469},
}
@inproceedings{BD07,
author = {Brattka, Vasco and Dillhage, Ruth},
title = {On Computable Compact Operators on {B}anach Spaces},
editor = {Cenzer, Douglas and Dillhage, Ruth and Grubba, Tanja and Weihrauch, Klaus},
booktitle = {Proceedings of the Third International Conference on Computability and Complexity in Analysis},
series = {Electronic Notes in Theoretical Computer Science},
volume = {167},
publisher = {Elsevier},
address = {Amsterdam},
year = {2007},
pages = {365--386},
note = {{CCA} 2006, Gainesville, Florida, USA, November 1--5, 2006},
}
@article{BD07a,
author = {Brattka, Vasco and Dillhage, Ruth},
title = {On Computable Compact Operators on Computable {B}anach Spaces with Bases},
journal = {Mathematical Logic Quarterly},
volume = {53},
number = {4--5},
year = {2007},
pages = {345--364},
}
@article{BD07b,
author = {Bridges, Douglas S. and Diener, Hannes},
title = {The pseudocompactness of {$[0,1]$} is equivalent to the uniform continuity theorem},
journal = {The Journal of Symbolic Logic},
volume = {72},
number = {4},
year = {2007},
pages = {1379--1384},
doi = {10.2178/jsl/1203350793},
}
@article{BD10,
author = {Bridges, Douglas S. and Diener, Hannes},
title = {The anti-{S}pecker property, positivity, and total boundedness},
journal = {Mathematical Logic Quarterly},
volume = {56},
number = {4},
year = {2010},
pages = {434--441},
}
@article{BD10a,
author = {Brattka, Vasco and Dillhage, Ruth},
title = {Computability of finite-dimensional linear subspaces and best approximation},
journal = {Annals of Pure and Applied Logic},
volume = {162},
year = {2010},
pages = {182--193},
}
@incollection{BD19,
author = {Bournez, Olivier and Durand, Arnaud},
title = {Recursion schemes, discrete differential equations and characterization of polynomial time computations},
booktitle = {44th {I}nternational {S}ymposium on {M}athematical {F}oundations of {C}omputer {S}cience},
series = {LIPIcs. Leibniz Int. Proc. Inform.},
volume = {138},
publisher = {Schloss Dagstuhl. Leibniz-Zent. Inform., Wadern},
year = {2019},
pages = {Art. No. 23, 14},
}
@inproceedings{BD20,
author = {Boche, H. and Deppe, C.},
title = {Computability of the Zero-Error Capacity with {K}olmogorov Oracle},
booktitle = {2020 IEEE International Symposium on Information Theory (ISIT)},
year = {2020},
pages = {2020--2025},
doi = {10.1109/ISIT44484.2020.9173984},
}
@article{BD91,
author = {Bridges, Douglas S. and Demuth, Osvald},
title = {On the {L}ebesgue measurability of continuous functions in constructive analysis},
journal = {BAMS},
volume = {24},
number = {2},
year = {1991},
pages = {259--276},
}
@article{BD97,
author = {Bridges, Douglas S. and Dediu, Lumini{\c{t}}a},
title = {Paradise lost, or paradise regained?},
journal = {Bulletin of the European Association for Theoretical Computer Science},
volume = {63},
year = {1997},
pages = {141--155},
}
@article{BD98,
author = {Bridges, D. S. and Dudley Ward, N. F.},
title = {Constructing ultraweakly continuous functionals on ${B}({H})$},
journal = {Proceedings of the American Mathematical Society},
volume = {126},
number = {11},
year = {1998},
pages = {3347--3353},
}
@article{BD99,
author = {Bridges, Douglas S. and Dediu, Lumini{\c{t}}a},
title = {Weak continuity properties in constructive analysis},
journal = {Logic Journal of the IGPL. Interest Group in Pure and Applied Logics},
volume = {7},
number = {3},
year = {1999},
pages = {277--281},
}
@article{BD99a,
author = {Bridges, Douglas S. and Dediu, Lumini{\c{t}}a},
title = {Weak-operator continuity and the existence of adjoints},
journal = {Mathematical Logic Quarterly},
volume = {45},
number = {2},
year = {1999},
pages = {203--206},
}
@inproceedings{BDC01,
author = {Becher, Ver{\'o}nica and Daicz, Sergio and Chaitin, Gregory},
title = {A highly random number},
booktitle = {Combinatorics, computability and logic ({C}onstan{\c{t}}a, 2001)},
series = {Springer Ser. Discrete Math. Theor. Comput. Sci.},
publisher = {Springer},
address = {London},
year = {2001},
pages = {55--68},
}
@proceedings{BDGK08,
title = {Proceedings of the Fifth International Conference on Computability and Complexity in Analysis},
editor = {Brattka, Vasco and Dillhage, Ruth and Grubba, Tanja and Klutsch, Angela},
series = {Electronic Notes in Theoretical Computer Science},
volume = {221},
publisher = {Elsevier},
address = {Amsterdam},
year = {2008},
note = {{CCA} 2008, Hagen, Germany, August 21-24, 2008},
doi = {10.1016/j.entcs.2008.12.001},
}
@article{BDH+12,
author = {Bienvenu, Laurent and Day, Adam R. and Hoyrup, Mathieu and Mezhirov, Ilya and Shen, Alexander},
title = {A constructive version of {B}irkhoff's ergodic theorem for {M}artin-{L}\"of random points},
journal = {Information and Computation},
volume = {210},
year = {2012},
pages = {21--30},
doi = {10.1016/j.ic.2011.10.006},
}
@article{BDI03,
author = {Bridges, Douglas S. and van Dalen, Dirk and Ishihara, Hajime},
title = {Ishihara's proof technique in constructive analysis},
journal = {Indagationes Mathematicae},
volume = {14},
number = {2},
year = {2003},
pages = {163--168},
}
@proceedings{BDKL19,
title = {Special issue: {O}berwolfach Workshop on Computability Theory 2018},
editor = {Brattka, Vasco and Downey, Rod G. and Knight, Julia F. and Lempp, Steffen},
series = {Computability - The Journal of the Association CiE},
volume = {8},
number = {3, 4},
publisher = {IOS Press},
year = {2019},
pages = {193--415},
doi = {10.3233/COM-180103},
}
@article{BDM13,
author = {Bridges, D. S. and Dent, J. E. and McKubre-Jordens, M. N.},
title = {Two direct proofs that {LLPO} implies the detachable fan theorem},
journal = {Log. J. IGPL},
volume = {21},
number = {5},
year = {2013},
pages = {830--835},
doi = {10.1093/jigpal/jzt003},
}
@article{BDM14,
author = {Bridges, Douglas S. and Dent, James and McKubre-Jordens, Maarten},
title = {Constructive connections between anti-{S}pecker, positivity, and fan-theoretic properties},
journal = {New Zealand J. Math.},
volume = {44},
year = {2014},
pages = {21--33},
}
@article{BDM16,
author = {Bridges, Douglas S. and Dent, James and McKubre-Jordens, Maarten},
title = {{Z}-stability in Constructive Analysis},
journal = {Logical Methods in Computer Science},
volume = {12},
number = {3},
year = {2016},
month = Sep,
doi = {10.2168/LMCS-12(3:10)2016},
}
@proceedings{BDMP20,
title = {Special issue: Dagstuhl Seminar on Measuring the Complexity of Computational Content 2018},
editor = {Brattka, Vasco and Dzhafarov, Damir and Marcone, Alberto and Pauly, Arno},
series = {Computability - The Journal of the Association CiE},
volume = {9},
number = {3, 4},
publisher = {IOS Press},
year = {2020},
pages = {167--341},
doi = {10.3233/COM-208001},
}
@inproceedings{BDMS10,
author = {Bienvenu, Laurent and Day, Adam and Mezhirov, Ilya and Shen, Alexander},
title = {Ergodic-type Characterizations of Algorithmic Randomness},
editor = {Fernando Ferreira and Benedikt L{\"o}we and Elvira Mayordomo and Lu\'{\i}s Mendes Gomes},
booktitle = {CiE 2010},
series = {Lecture Notes in Computer Science},
volume = {6158},
publisher = {Springer},
address = {Berlin},
year = {2010},
pages = {49--58},
}
@inproceedings{BDN16,
author = {Bournez, Olivier and Dershowitz, Nachum and N\'{e}ron, Pierre},
title = {Axiomatizing Analog Algorithms},
editor = {Beckmann, Arnold and Bienvenu, Laurent and Jonoska, Nata\v{s}a},
booktitle = {Pursuit of the Universal},
series = {Lecture Notes in Computer Science},
volume = {9709},
publisher = {Springer},
address = {Switzerland},
year = {2016},
pages = {215--224},
note = {12th Conference on Computability in Europe, CiE 2016, Paris, France, June 27 - July 1, 2016},
doi = {10.1007/978-3-319-40189-8_22},
}
@proceedings{BDS14,
title = {Logic, Computation, Hierarchies},
editor = {Brattka, Vasco and Diener, Hannes and Spreen, Dieter},
series = {Ontos Mathematical Logic},
volume = {4},
publisher = {Walter de Gruyter},
address = {Boston},
year = {2014},
doi = {10.1515/9781614518044},
}
@article{BDWY22,
author = {Burr, Michael and Das, Suddhasattwa and Wolf, Christian and Yang, Yun},
title = {Computability of topological pressure on compact shift spaces beyond finite type},
journal = {Nonlinearity},
volume = {35},
number = {8},
publisher = {IOP Publishing},
year = {2022},
month = {jun},
pages = {4250--4282},
doi = {10.1088/1361-6544/ac7702},
}
@article{BE17,
author = {Bilokon, Paul and Edalat, Abbas},
title = {A domain-theoretic approach to {B}rownian motion and general continuous stochastic processes},
journal = {Theoretical Computer Science},
volume = {691},
year = {2017},
pages = {10--26},
doi = {10.1016/j.tcs.2017.07.016},
}
@inproceedings{Bec12,
author = {Becher, Ver{\'o}nica},
title = {Turing's normal numbers: towards randomness},
editor = {Cooper, S. Barry and Dawar, Anuj and L{\"o}we, Benedikt},
booktitle = {How the World Computes},
series = {Lecture Notes in Computer Science},
volume = {7318},
publisher = {Springer},
address = {Heidelberg},
year = {2012},
pages = {35--45},
}
@incollection{Bee05,
author = {Beeson, Michael},
title = {Constructivity, Computability, and the Continuum},
editor = {Sica, Giandomenico},
booktitle = {Essays on the Foundations of Mathematics and Logic},
series = {Advanced Studies in Mathematics and Logic},
volume = {2},
publisher = {Polimetrica},
address = {Milano},
year = {2005},
pages = {9--37},
}
@inproceedings{Bee80,
author = {Beeson, M.J.},
title = {Problematic principles in constructive mathematics},
booktitle = {Logic Colloquium '80},
series = {Studies in Logic and the Foundations of Mathematics},
volume = {108},
publisher = {North-Holland},
address = {Amsterdam},
year = {1980},
pages = {11--55},
}
@book{Bee85,
author = {Beeson, Michael J.},
title = {Foundations of {C}onstructive {M}athematics},
series = {A Series of Modern Surveys in Mathematics},
publisher = {Springer},
address = {Berlin},
year = {1985},
}
@article{Ber05,
author = {Berger, Josef},
title = {Exact calculation of inverse functions},
journal = {Mathematical Logic Quarterly},
volume = {51},
number = {2},
year = {2005},
pages = {201--205},
}
@article{Ber05a,
author = {Berger, Josef},
title = {Constructive Equivalents of the Uniform Continuity Theorem},
journal = {Journal of Universal Computer Science},
volume = {11},
number = {12},
year = {2005},
pages = {1878--1883},
}
@inproceedings{Ber05b,
author = {Berger, Josef},
title = {The fan theorem and uniform continuity},
editor = {Cooper, S. Barry and L{\"o}we, Benedikt and Torenvliet, Leen},
booktitle = {New Computational Paradigms},
series = {Lecture Notes in Computer Science},
volume = {3526},
publisher = {Springer-Verlag},
address = {Berlin, Heidelberg},
year = {2005},
pages = {18--22},
note = {{P}roceedings of the First International Conference on Computability in Europe, CiE 2005},
doi = {10.1007/11494645_3},
}
@inproceedings{Ber06,
author = {Berger, Josef},
title = {The Logical Strength of the Uniform Continuity Theorem},
editor = {Beckmann, A. and Berger, U. and L{\"o}we, B. and Tucker, J.V.},
booktitle = {Logical Approaches to Computational Barriers},
series = {Lecture Notes in Computer Science},
volume = {3988},
publisher = {Springer},
address = {Berlin},
year = {2006},
pages = {35--39},
note = {Second Conference on Computability in Europe, CiE 2006, Swansea, UK, June 30-July 5, 2006},
}
@inproceedings{Ber06a,
author = {Berger, Josef},
title = {The logical strength of the uniform continuity theorem},
editor = {Beckmann, Arnold and Berger, Ulrich and L{\"{o}}we, Benedikt and Tucker, John V.},
booktitle = {Logical Approaches to Computational Barriers},
series = {Lecture Notes in Computer Science},
volume = {3988},
publisher = {Springer},
address = {Berlin/Heidelberg},
year = {2006},
pages = {35--39},
}
@article{Ber07,
author = {Bertot, Yves},
title = {Affine functions and series with co-inductive real numbers},
journal = {Mathematical Structures in Computer Science},
volume = {17},
year = {2007},
pages = {37--63},
}
@inproceedings{Ber07a,
author = {Berger, Josef},
title = {Weak {K}\"{o}nig's lemma implies the fan theorem for c-bars},
booktitle = {Computation and Logic in the Real World},
year = {2007},
pages = {86--88},
note = {{CiE} 2007, Quaderni del Dipartimento di Scienze Matematiche e Informatiche ``Roberto Magari''},
}
@article{Ber08,
author = {Berger, Josef},
title = {The weak {K}{\"o}nig lemma and uniform continuity},
journal = {Journal of Symbolic Logic},
volume = {73},
number = {3},
year = {2008},
pages = {933--939},
doi = {10.2178/jsl/1230396756},
}
@article{Ber09,
author = {Berger, Josef},
title = {A decomposition of {B}rouwer's fan theorem},
journal = {Journal of Logic and Analysis},
volume = {1},
year = {2009},
pages = {Paper 6, 8},
doi = {10.4115/jla.2009.1.6},
}
@inproceedings{Ber10,
author = {Berger, J.},
title = {A separation result for varieties of {B}rouwer's fan theorem},
booktitle = {10th {A}sian {L}ogic {C}onference},
publisher = {World Sci. Publ., Hackensack, NJ},
year = {2010},
pages = {85--92},
doi = {10.1142/9789814293020_0003},
}
@article{Ber11,
author = {Berger, Ulrich},
title = {From coinductive proofs to exact real arithmetic: theory and applications},
journal = {Log. Methods Comput. Sci.},
volume = {7},
number = {1},
year = {2011},
pages = {1:8, 24},
doi = {10.2168/LMCS-7(1:8)2011},
}
@article{Ber12,
author = {Berger, Josef},
title = {Aligning the weak {K}{\"o}nig lemma, the uniform continuity theorem, and {B}rouwer's fan theorem},
journal = {Annals of Pure and Applied Logic},
volume = {163},
number = {8},
year = {2012},
pages = {981--985},
doi = {10.1016/j.apal.2011.12.021},
}
@article{Ber16,
author = {Berger, Josef},
title = {Dickson's lemma and {H}igman's lemma are equivalent},
journal = {South American Journal of Logic},
volume = {2},
number = {1},
year = {2016},
pages = {35--39},
}
@inproceedings{BES02,
author = {Bauer, Andrej and Escard{\'{o}}, Mart{\'{\i}}n H{\"{o}}tzel and Simpson, Alex},
title = {Comparing Functional Paradigms for Exact Real-Number Computation},
editor = {Widmayer, Peter and Triguero, Francisco and Morales, Rafael and Hennessy, Matthew and Eidenbenz, Stephan and Conejo, Ricardo},
booktitle = {Automata, Languages and Programming},
series = {Lecture Notes in Computer Science},
volume = {2380},
publisher = {Springer},
address = {Berlin},
year = {2002},
pages = {488--500},
note = {29th International Colloquium, ICALP, M{\'{a}}laga, Spain, July 8--13, 2002},
}
@article{BF02,
author = {Becher, Ver{\'{o}}nica and Figueira, Santiago},
title = {An example of a computable absolutely normal number},
journal = {Theoretical Computer Science},
volume = {270},
year = {2002},
pages = {947--958},
}
@article{BF05,
author = {Becher, Ver{\'o}nica and Figueira, Santiago},
title = {Kolmogorov complexity for possibly infinite computations},
journal = {Journal of Logic, Language and Information},
volume = {14},
number = {2},
year = {2005},
pages = {133--148},
doi = {10.1007/s10849-005-2255-6},
}
@proceedings{BFM07,
title = {Real Numbers},
editor = {Brattka, Vasco and Frougny, Christiane and M{\"u}ller, Norbert},
series = {Theoretical Informatics and Applications},
volume = {41},
number = {1},
publisher = {EDP Sciences},
address = {Les Ulis},
year = {2007},
note = {Selected Papers of the 6th conference on Real Numbers and Computers, Dagstuhl, Germany, November 15-17, 2004},
doi = {10.1051/ita:2007001},
}
@article{BFP07,
author = {Becher, Ver{\'{o}}nica and Figueira, Santiago and Picchi, Rafael},
title = {{T}uring's unpublished algorithm for normal numbers},
journal = {Theoretical Computer Science},
volume = {377},
number = {1--3},
year = {2007},
pages = {126--138},
}
@article{BG04,
author = {Becher, Ver{\'{o}}nica and Grigorieff, Serge},
title = {Recursion and topology on $2^{\leq\omega}$ for possibly infinite computations},
journal = {Theoretical Computer Science},
volume = {322},
number = {1},
year = {2004},
pages = {85--136},
}
@article{BG05,
author = {Becher, Ver{\'o}nica and Grigorieff, Serge},
title = {Random reals and possibly infinite computations. {I}. {R}andomness in {$\emptyset'$}},
journal = {Journal of Symbolic Logic},
volume = {70},
number = {3},
year = {2005},
pages = {891--913},
doi = {10.2178/jsl/1122038919},
}
@inproceedings{BG07,
author = {Brattka, Vasco and Gherardi, Guido},
title = {Borel Complexity of Topological Operations on Computable Metric Spaces},
editor = {Cooper, S. Barry and L{\"o}we, Benedikt and Sorbi, Andrea},
booktitle = {Computation and Logic in the Real World},
series = {Lecture Notes in Computer Science},
volume = {4497},
publisher = {Springer},
address = {Berlin},
year = {2007},
pages = {83--97},
note = {Third Conference on Computability in Europe, CiE 2007, Siena, Italy, June 18-23, 2007},
}
@article{BG09,
author = {Brattka, Vasco and Gherardi, Guido},
title = {Borel Complexity of Topological Operations on Computable Metric Spaces},
journal = {Journal of Logic and Computation},
volume = {19},
number = {1},
year = {2009},
pages = {45--76},
}
@article{BG09a,
author = {Becher, Ver{\'o}nica and Grigorieff, Serge},
title = {From index sets to randomness in {$\emptyset^n$}: random reals and possibly infinite computations. {II}},
journal = {Journal of Symbolic Logic},
volume = {74},
number = {1},
year = {2009},
pages = {124--156},
doi = {10.2178/jsl/1231082305},
}
@inproceedings{BG09c,
author = {Brattka, Vasco and Gherardi, Guido},
title = {Weihrauch Degrees, Omniscience Principles and Weak Computability},
editor = {Bauer, Andrej and Hertling, Peter and Ko, Ker-I},
booktitle = {{CCA} 2009, Proceedings of the Sixth International Conference on Computability and Complexity in Analysis},
publisher = {Leibniz-Zentrum f\"ur Informatik},
address = {Schloss Dagstuhl, Germany},
year = {2009},
pages = {83--94},
}
@inproceedings{BG09d,
author = {Brattka, Vasco and Gherardi, Guido},
title = {Effective Choice and Boundedness Principles in Computable Analysis},
editor = {Bauer, Andrej and Hertling, Peter and Ko, Ker-I},
booktitle = {{CCA} 2009, Proceedings of the Sixth International Conference on Computability and Complexity in Analysis},
publisher = {Leibniz-Zentrum f\"ur Informatik},
address = {Schloss Dagstuhl, Germany},
year = {2009},
pages = {95--106},
}
@article{BG11,
author = {Brattka, Vasco and Gherardi, Guido},
title = {Weihrauch Degrees, Omniscience Principles and Weak Computability},
journal = {The Journal of Symbolic Logic},
volume = {76},
number = {1},
year = {2011},
pages = {143--176},
doi = {10.2178/jsl/1294170993},
}
@article{BG11a,
author = {Brattka, Vasco and Gherardi, Guido},
title = {Effective Choice and Boundedness Principles in Computable Analysis},
journal = {The Bulletin of Symbolic Logic},
volume = {17},
number = {1},
year = {2011},
pages = {73--117},
doi = {10.2178/bsl/1294186663},
}
@article{BG15,
author = {Becher, Ver{\'o}nica and Grigorieff, Serge},
title = {{B}orel and {H}ausdorff hierarchies in topological spaces of {C}hoquet games and their effectivization},
journal = {Mathematical Structures in Computer Science},
volume = {25},
year = {2015},
month = {10},
pages = {1490--1519},
doi = {10.1017/S096012951300025X},
}
@article{BG15a,
author = {Becher, Ver{\'o}nica and Grigorieff, Serge},
title = {{W}adge hardness in {S}cott spaces and its effectivization},
journal = {Mathematical Structures in Computer Science},
volume = {25},
year = {2015},
month = {10},
pages = {1520--1545},
doi = {10.1017/S0960129513000248},
}
@article{BG20,
author = {Brattka, Vasco and Gherardi, Guido},
title = {Weihrauch Goes {B}rouwerian},
journal = {The Journal of Symbolic Logic},
volume = {85},
number = {4},
year = {2020},
pages = {1614--1653},
doi = {10.1017/jsl.2020.76},
}
@article{BG21a,
author = {Brattka, Vasco and Gherardi, Guido},
title = {Completion of Choice},
journal = {Annals of Pure and Applied Logic},
volume = {172},
number = {3},
year = {2021},
pages = {102914},
doi = {10.1016/j.apal.2020.102914},
}
@article{BGH+11,
author = {Bienvenu, Laurent and G{\'a}cs, Peter and Hoyrup, Mathieu and Rojas, Crist\'obal and Shen, Alexander},
title = {Algorithmic tests and randomness with respect to a class of measures},
journal = {Proceedings of the Steklov Institute of Mathematics},
volume = {274},
number = {1},
publisher = {Steklov Institute of Mathematics},
year = {2011},
month = Nov,
pages = {34-89},
doi = {10.1134/S0081543811060058},
}
@inproceedings{BGH10,
author = {Bournez, Olivier and Gra{\c{c}}a, Daniel S. and Hainry, Emmanuel},
title = {Robust computations with dynamical systems},
booktitle = {Mathematical foundations of computer science 2010},
series = {Lecture Notes in Comput. Sci.},
volume = {6281},
publisher = {Springer},
address = {Berlin},
year = {2010},
pages = {198--208},
doi = {10.1007/978-3-642-15155-2_19},
}
@article{BGH13a,
author = {Bournez, Olivier and Gra{\c{c}}a, Daniel S. and Hainry, Emmanuel},
title = {Computation with perturbed dynamical systems},
journal = {J. Comput. System Sci.},
volume = {79},
number = {5},
year = {2013},
pages = {714--724},
doi = {10.1016/j.jcss.2013.01.025},
}
@inproceedings{BGH15,
author = {Brattka, Vasco and Gherardi, Guido and H{\"o}lzl, Rupert},
title = {Las {V}egas Computability and Algorithmic Randomness},
editor = {Mayr, Ernst W. and Ollinger, Nicolas},
booktitle = {32nd International Symposium on Theoretical Aspects of Computer Science ({STACS} 2015)},
series = {Leibniz International Proceedings in Informatics ({LIPI}cs)},
volume = {30},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
year = {2015},
pages = {130--142},
doi = {10.4230/LIPIcs.STACS.2015.130},
}
@article{BGH15a,
author = {Brattka, Vasco and Gherardi, Guido and H{\"o}lzl, Rupert},
title = {Probabilistic Computability and Choice},
journal = {Information and Computation},
volume = {242},
year = {2015},
pages = {249--286},
doi = {10.1016/j.ic.2015.03.005},
}
@incollection{BGHP17,
author = {Brattka, Vasco and Gherardi, Guido and H\"olzl, Rupert and Pauly, Arno},
title = {The {V}itali Covering Theorem in the {W}eihrauch Lattice},
editor = {Day, Adam and Fellows, Michael and Greenberg, Noam and Khoussainov, Bakhadyr and Melnikov, Alexander and Rosamond, Frances},
booktitle = {Computability and Complexity: Essays Dedicated to Rodney G. Downey on the Occasion of His 60th Birthday},
series = {Lecture Notes in Computer Science},
volume = {10010},
publisher = {Springer},
address = {Cham},
year = {2017},
pages = {188--200},
doi = {10.1007/978-3-319-50062-1_14},
}
@article{BGI04,
author = {Bonanno, Claudio and Galatolo, Stefano and Isola, Stefano},
title = {Recurrence and algorithmic information},
journal = {Nonlinearity},
volume = {17},
number = {3},
year = {2004},
pages = {1057--1074},
}
@proceedings{BGKS22,
title = {Special issue: Oberwolfach Workshop on Computability Theory 2021},
editor = {Brattka, Vasco and Greenberg, Noam and Kalimullin, Iskander and Soskova, Mariya},
series = {Computability - The Journal of the Association CiE},
volume = {11},
number = {3, 4},
publisher = {IOS Press},
year = {2022},
pages = {163--358},
doi = {10.3233/COM-220950},
}
@article{BGM12,
author = {Brattka, Vasco and Gherardi, Guido and Marcone, Alberto},
title = {The {B}olzano-{W}eierstrass Theorem is the Jump of Weak {K}{\H{o}}nig's Lemma},
journal = {Annals of Pure and Applied Logic},
volume = {163},
year = {2012},
pages = {623--655},
doi = {10.1016/j.apal.2011.10.006},
}
@inproceedings{BGP11,
author = {Bournez, Olivier and Gra{\c{c}}a, Daniel S. and Pouly, Amaury},
title = {Solving analytic differential equations in polynomial time over unbounded domains},
editor = {Murlak, F. and Sankowski, P.},
booktitle = {Mathematical Foundations of Computer Science 2011},
series = {Lecture Notes in Computer Science},
volume = {6907},
publisher = {Springer},
address = {Heidelberg},
year = {2011},
pages = {170--181},
doi = {10.1007/978-3-642-22993-0_18},
}
@inproceedings{BGP12,
author = {Bournez, Olivier and Gra\c{c}a, Daniel S. and Pouly, Amaury},
title = {On the complexity of solving initial value problems},
editor = {van der Hoeven, Joris and van Hoeij, Mark},
booktitle = {I{SSAC} 2012---{P}roceedings of the 37th {I}nternational {S}ymposium on {S}ymbolic and {A}lgebraic {C}omputation},
publisher = {ACM},
address = {New York},
year = {2012},
pages = {115--121},
doi = {10.1145/2442829.2442849},
}
@incollection{BGP13,
author = {Bournez, Olivier and Gra\c{c}a, Daniel S. and Pouly, Amaury},
title = {Turing machines can be efficiently simulated by the general purpose analog computer},
booktitle = {Theory and applications of models of computation},
series = {Lecture Notes in Comput. Sci.},
volume = {7876},
publisher = {Springer},
address = {Heidelberg},
year = {2013},
pages = {169--180},
doi = {10.1007/978-3-642-38236-9_16},
}
@inproceedings{BGP16,
author = {Bournez, Olivier and Gra\c{c}a, Daniel S. and Pouly, Amaury},
title = {Rigorous numerical computation of polynomial differential equations over unbounded domains},
editor = {Kotsireas, Ilias S. and Rump, Siegfried M. and Yap, Chee K.},
booktitle = {Mathematical aspects of computer and information sciences},
series = {Lecture Notes in Computer Science},
volume = {9582},
publisher = {Springer},
address = {Cham},
year = {2016},
pages = {469--473},
note = {6th International Conference, {MACIS} 2015, Berlin, Germany, November 11--13, 2015, Revised Selected Papers},
doi = {10.1007/978-3-319-32859-1_40},
}
@article{BGP16a,
author = {Bournez, Olivier and Gra\c{c}a, Daniel and Pouly, Amaury},
title = {Computing with polynomial ordinary differential equations},
journal = {Journal of Complexity},
volume = {36},
year = {2016},
pages = {106--140},
doi = {10.1016/j.jco.2016.05.002},
}
@inproceedings{BGP16b,
author = {Bournez, Olivier and Gra\c{c}a, Daniel S. and Pouly, Amaury},
title = {Polynomial time corresponds to solutions of polynomial ordinary differential equations of polynomial length: the general purpose analog computer and computable analysis are two efficiently equivalent models of computations},
editor = {Chatzigiannakis, Ioannis and Mitzenmacher, Michael and Rabani, Yuval and Sangiorgi, Davide},
booktitle = {43rd {I}nternational {C}olloquium on {A}utomata, {L}anguages, and {P}rogramming},
series = {LIPIcs. Leibniz Int. Proc. Inform.},
volume = {55},
publisher = {Schloss Dagstuhl. Leibniz-Zent. Inform.},
address = {Dagstuhl, Germany},
year = {2016},
pages = {Art. No. 109, 15},
}
@article{BGP17a,
author = {Bournez, Olivier and Gra\c{c}a, Daniel S. and Pouly, Amaury},
title = {Polynomial time corresponds to solutions of polynomial ordinary differential equations of polynomial length},
journal = {Journal of the ACM},
volume = {64},
number = {6},
year = {2017},
pages = {Art. 38, 76},
doi = {10.1145/3127496},
}
@article{BGP17b,
author = {Bournez, Olivier and Gra\c{c}a, Daniel and Pouly, Amaury},
title = {On the functions generated by the general purpose analog computer},
journal = {Information and Computation},
volume = {257},
year = {2017},
pages = {34--57},
doi = {10.1016/j.ic.2017.09.015},
}
@incollection{BGP21,
author = {Brattka, Vasco and Gherardi, Guido and Pauly, Arno},
title = {Weihrauch Complexity in Computable Analysis},
editor = {Brattka, Vasco and Hertling, Peter},
booktitle = {Handbook of Computability and Complexity in Analysis},
series = {Theory and Applications of Computability},
publisher = {Springer},
address = {Cham},
year = {2021},
pages = {367--417},
doi = {10.1007/978-3-030-59234-9_11},
}
@incollection{BGPZ13,
author = {Bournez, Olivier and Gra\c{c}a, Daniel S. and Pouly, Amaury and Zhong, Ning},
title = {Computability and computational complexity of the evolution of nonlinear dynamical systems},
booktitle = {The nature of computation},
series = {Lecture Notes in Comput. Sci.},
volume = {7921},
publisher = {Springer},
address = {Heidelberg},
year = {2013},
pages = {12--21},
doi = {10.1007/978-3-642-39053-1_2},
}
@inproceedings{BGR12,
author = {Braverman, Mark and Grigo, Alexander and Rojas, Cristobal},
title = {Noise vs Computational Intractability in Dynamics},
booktitle = {Proceedings of the 3rd Innovations in Theoretical Computer Science Conference},
series = {ITCS '12},
publisher = {ACM},
address = {New York, NY, USA},
year = {2012},
pages = {128--141},
doi = {10.1145/2090236.2090247},
}
@article{BGRY22,
author = {Binder, Ilia and Glucksam, Adi and Rojas, Cristobal and Yampolsky, Michael},
title = {Computability in harmonic analysis},
journal = {Foundations of Computational Mathematics},
volume = {22},
number = {3},
year = {2022},
pages = {849--873},
doi = {10.1007/s10208-021-09524-w},
}
@inproceedings{BGZ11,
author = {Buescu, J. and Gra{\c{c}}a, D. S. and Zhong, N.},
title = {Computability and dynamical systems},
booktitle = {Dynamics, games and science. {I}},
series = {Springer Proc. Math.},
volume = {1},
publisher = {Springer},
address = {Heidelberg},
year = {2011},
pages = {169--181},
doi = {10.1007/978-3-642-11456-4_11},
}
@article{BH00a,
author = {Bridges, Douglas S. and Havea, Robin},
title = {A constructive analysis of a proof that the numerical range is convex},
journal = {London Math. Soc. Journal of Mathematics and Computation},
volume = {3},
year = {2000},
pages = {191--206},
}
@article{BH01,
author = {Bridges, Douglas S. and Havea, Robin},
title = {A constructive version of the spectral mapping theorem},
journal = {Mathematical Logic Quarterly},
volume = {47},
number = {3},
year = {2001},
pages = {299--304},
}
@article{BH02,
author = {Brattka, Vasco and Hertling, Peter},
title = {Topological properties of real number representations},
journal = {Theoretical Computer Science},
volume = {284},
number = {2},
year = {2002},
pages = {241--257},
doi = {10.1016/S0304-3975(01)00066-4},
}
@article{BH05,
author = {Bournez, Olivier and Hainry, Emmanuel},
title = {Elementarily computable functions over the real numbers and $R$-sub-recursive functions},
journal = {Theoretical Computer Science},
volume = {348},
year = {2005},
pages = {130--147},
}
@article{BH06,
author = {Bournez, Olivier and Hainry, Emmanuel},
title = {Recursive Analysis Characterized as a Class of Real Recursive Functions},
journal = {Fundamenta Informaticae},
volume = {74},
number = {4},
year = {2006},
pages = {409--433},
}
@article{BH07,
author = {Bridges, Douglas S. and Havea, Robin},
title = {Powers of a {H}ermitian element},
journal = {New Zealand J. Math.},
volume = {36},
year = {2007},
pages = {1--10},
}
@article{BH08,
author = {Bridges, Douglas S. and Havea, Robin S.},
title = {Constructive notions of maximality for ideals},
journal = {Journal of Universal Computer Science},
volume = {14},
number = {22},
year = {2008},
pages = {3648--3657},
}
@article{BH09,
author = {Bridges, Douglas S. and Havea, Robin S.},
title = {Constructing square roots in a {B}anach algebra},
journal = {Scientiae Mathematicae Japonicae},
volume = {70},
number = {3},
year = {2009},
pages = {355--366},
}
@article{BH10,
author = {Bienvenu, Laurent and Hoyrup, Mathieu},
title = {Une br\`eve introduction \`a la th\'eorie effective de l'al\'eatoire},
journal = {Gaz. Math.},
number = {123},
year = {2010},
pages = {35--47},
}
@article{BH10a,
author = {Bridges, Douglas S. and Hendtlass, Matthew},
title = {Continuous homomorphisms of {${R}$} onto a compact group},
journal = {Mathematical Logic Quarterly},
volume = {56},
number = {2},
year = {2010},
pages = {191--197},
doi = {10.1002/malq.200810048},
}
@article{BH10b,
author = {Bridges, Douglas S. and Hendtlass, Matthew},
title = {Continuous isomorphisms from {$R$} onto a complete abelian group},
journal = {J. Symbolic Logic},
volume = {75},
number = {3},
year = {2010},
pages = {930--944},
doi = {10.2178/jsl/1278682208},
}
@inproceedings{BH12,
author = {Bridges, Douglas S. and Havea, Robin S.},
title = {Square roots and powers in constructive {B}anach algebra theory},
editor = {Cooper, S. Barry and Dawar, Anuj and L{\"o}we, Benedikt},
booktitle = {How the World Computes},
series = {Lecture Notes in Computer Science},
volume = {7318},
publisher = {Springer},
address = {Heidelberg},
year = {2012},
pages = {68--77},
}
@article{BH13,
author = {Becher, Ver{\'o}nica and Heiber, Pablo Ariel},
title = {Normal numbers and finite automata},
journal = {Theoret. Comput. Sci.},
volume = {477},
year = {2013},
pages = {109--116},
doi = {10.1016/j.tcs.2013.01.019},
}
@article{BH15,
author = {Bosserhoff, Volker and Hertling, Peter},
title = {Effective subsets under homeomorphisms of {$R^n$}},
journal = {Information and Computation},
volume = {245},
year = {2015},
pages = {197--212},
doi = {10.1016/j.ic.2015.09.001},
}
@proceedings{BH21,
title = {Handbook of Computability and Complexity in Analysis},
editor = {Brattka, Vasco and Hertling, Peter},
series = {Theory and Applications of Computability},
publisher = {Springer},
address = {Cham},
year = {2021},
doi = {10.1007/978-3-030-59234-9},
}
@article{BH98,
author = {Brattka, Vasco and Hertling, Peter},
title = {Feasible real random access machines},
journal = {Journal of Complexity},
volume = {14},
number = {4},
year = {1998},
pages = {490--526},
}
@inproceedings{BHK17,
author = {Brattka, Vasco and H{\"o}lzl, Rupert and Kuyper, Rutger},
title = {{M}onte {C}arlo Computability},
editor = {Vollmer, Heribert and Vall{\'e}e, Brigitte},
booktitle = {34th Symposium on Theoretical Aspects of Computer Science (STACS 2017)},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
volume = {66},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
year = {2017},
pages = {17:1--17:14},
doi = {10.4230/LIPIcs.STACS.2017.17},
}
@article{BHK17a,
author = {Brattka, Vasco and Hendtlass, Matthew and Kreuzer, Alexander P.},
title = {On the Uniform Computational Content of Computability Theory},
journal = {Theory of Computing Systems},
volume = {61},
number = {4},
year = {2017},
pages = {1376--1426},
doi = {10.1007/s00224-017-9798-1},
}
@article{BHK18,
author = {Brattka, Vasco and Hendtlass, Matthew and Kreuzer, Alexander P.},
title = {On the Uniform Computational Content of the {B}aire Category Theorem},
journal = {Notre Dame Journal of Formal Logic},
volume = {59},
number = {4},
year = {2018},
pages = {605--636},
doi = {10.1215/00294527-2018-0016},
}
@proceedings{BHKT06,
title = {Computability and Complexity in Analysis},
editor = {Brattka, Vasco and Hertling, Peter and Ko, Ker-I and Tsuiki, Hideki},
series = {Journal of Complexity},
volume = {522},
number = {6},
publisher = {Elsevier},
address = {Amsterdam},
year = {2006},
note = {Selected Papers of the International Conference CCA 2005, held in Kyoto, Japan, August 25--29, 2005},
doi = {10.1016/j.jco.2006.10.001},
}
@proceedings{BHKZ04,
title = {Special Issue Computability and Complexity in Analysis},
editor = {Brattka, Vasco and Hertling, Peter and Ko, Ker-I and Zhong, Ning},
series = {Mathematical Logic Quarterly},
volume = {50},
number = {4,5},
publisher = {Wiley-VCH},
address = {Weinheim},
year = {2004},
note = {Selected Papers of the International Conference CCA 2003, held in Cincinnati, Ohio, August 28--30, 2003},
doi = {10.1002/malq.200490000},
}
@inproceedings{BHMN12,
author = {Bienvenu, Laurent and H{\"o}lzl, Rupert and Miller, Joseph S. and Nies, Andr{\'e}},
title = {The {D}enjoy alternative for computable functions},
booktitle = {29th {I}nternational {S}ymposium on {T}heoretical {A}spects of {C}omputer {S}cience},
series = {LIPIcs. Leibniz Int. Proc. Inform.},
volume = {14},
publisher = {Schloss Dagstuhl. Leibniz-Zent. Inform., Wadern},
year = {2012},
pages = {543--554},
}
@article{BHMN14,
author = {Bienvenu, Laurent and H{\"o}lzl, Rupert and Miller, Joseph S. and Nies, Andr{\'e}},
title = {Denjoy, {D}emuth and density},
journal = {J. Math. Log.},
volume = {14},
number = {1},
year = {2014},
pages = {1450004, 35},
doi = {10.1142/S0219061314500044},
}
@article{BHP16,
author = {Bridges, Douglas S. and Hendtlass, Matthew and Palmgren, Erik},
title = {A constructive examination of rectifiability},
journal = {Journal of Logic and Analysis},
volume = {8},
year = {2016},
pages = {Paper No. 4, 17},
}
@article{BHS06,
author = {Bridges, Douglas S. and Havea, Robin and Schuster, Peter},
title = {Ideals in constructive {B}anach algebra theory},
journal = {Journal of Complexity},
volume = {22},
number = {6},
year = {2006},
pages = {729--737},
}
@article{BHS06a,
author = {Bridges, Douglas S. and Havea, Robin and Schuster, Peter},
title = {Constructive {B}anach algebra theory and the {N}ullstellensatz},
journal = {Publ. Math. Debrecen},
volume = {69},
number = {1,2},
year = {2006},
pages = {171--184},
}
@article{BHS13,
author = {Becher, Ver{\'o}nica and Heiber, Pablo Ariel and Slaman, Theodore A.},
title = {A polynomial-time algorithm for computing absolutely normal numbers},
journal = {Information and Computation},
volume = {232},
year = {2013},
pages = {1--9},
doi = {10.1016/j.ic.2013.08.013},
}
@article{BHS17,
author = {Bienvenu, Laurent and Hoyrup, Mathieu and Shen, Alexander},
title = {Layerwise Computability and Image Randomness},
journal = {Theory of Computing Systems},
volume = {61},
number = {4},
year = {2017},
pages = {1353--1375},
doi = {10.1007/s00224-017-9791-8},
}
@incollection{BHW08,
author = {Brattka, Vasco and Hertling, Peter and Weihrauch, Klaus},
title = {A Tutorial on Computable Analysis},
editor = {Cooper, S. Barry and L\"owe, Benedikt and Sorbi, Andrea},
booktitle = {New Computational Paradigms: Changing Conceptions of What Is Computable},
publisher = {Springer},
address = {New York},
year = {2008},
pages = {425--491},
}
@article{BHW21a,
author = {BeMent, Zach and Hirst, Jeffry and Wallace, Asuka},
title = {Reverse mathematics and {W}eihrauch analysis motivated by finite complexity theory},
journal = {Computability},
volume = {10},
number = {4},
year = {2021},
pages = {343--354},
doi = {10.3233/COM-210310},
}
@proceedings{BHYZ02,
title = {Selected Papers of the Dagstuhl Seminar on Computability and Complexity in Analysis 2001},
editor = {Brattka, Vasco and Hertling, Peter and Yasugi, Mariko and Zhong, Ning},
series = {Mathematical Logic Quarterly},
volume = {48 (Suppl. 1)},
publisher = {Wiley-VCH},
address = {Weinheim},
year = {2002},
doi = {10.1002/1521-3870(200210)48:1+3.0.CO;2-0},
}
@article{BI01,
author = {Bridges, Douglas S. and Ishihara, Hajime},
title = {Constructive closed range and open mapping theorems},
journal = {Indagationes Mathematicae},
volume = {11},
number = {4},
year = {2001},
pages = {509--516},
}
@inproceedings{BI01a,
author = {Bridges, Douglas S. and Ishihara, Hajime},
title = {Constructive unbounded operators},
editor = {Schuster, Peter and Berger, Ulrich and Osswald, Horst},
booktitle = {Reuniting the antipodes---constructive and nonstandard views of the continuum (Venice, 1999)},
series = {Synthese Library},
volume = {306},
publisher = {Kluwer Acad. Publ.},
address = {Dordrecht},
year = {2001},
pages = {25--37},
}
@article{BI05,
author = {Berger, Josef and Ishihara, Hajime},
title = {Brouwer's fan theorem and unique existence in constructive analysis},
journal = {Mathematical Logic Quarterly},
volume = {51},
number = {4},
year = {2005},
pages = {360--364},
}
@article{BI14,
author = {Burnik, Konrad and Iljazovi{\'c}, Zvonko},
title = {Computability of 1-manifolds},
journal = {Logical Methods in Computer Science},
volume = {10},
number = {2},
year = {2014},
pages = {2:8, 28},
doi = {10.2168/LMCS-10(2:8)2014},
}
@article{BI90,
author = {Bridges, Douglas S. and Ishihara, Hajime},
title = {Linear mappings are fairly well-behaved},
journal = {Archiv der Mathematik},
volume = {54},
number = {6},
year = {1990},
pages = {558--562},
}
@article{BI92,
author = {Bridges, Douglas S. and Ishihara, Hajime},
title = {Locating the range of an operator on a {H}ilbert space},
journal = {The Bulletin of the London Mathematical Society},
volume = {24},
number = {6},
year = {1992},
pages = {599--605},
}
@article{BI94,
author = {Bridges, Douglas S. and Ishihara, Hajime},
title = {Complements of intersections in constructive mathematics},
journal = {Mathematical Logic Quarterly},
volume = {40},
number = {1},
year = {1994},
pages = {35--43},
}
@article{BI94a,
author = {Bridges, Douglas S. and Ishihara, Hajime},
title = {Absolute continuity and the uniqueness of the constructive functional calculus},
journal = {Mathematical Logic Quarterly},
volume = {40},
number = {4},
year = {1994},
pages = {519--527},
}
@article{BI94b,
author = {Bridges, Douglas S. and Ishihara, Hajime},
title = {Erratum: ``{C}omplements of intersections in constructive mathematics''},
journal = {Mathematical Logic Quarterly},
volume = {40},
number = {4},
year = {1994},
pages = {570},
}
@article{BI96,
author = {Bridges, Douglas S. and Ishihara, Hajime},
title = {Spectra of selfadjoint operators in constructive analysis},
journal = {Indagationes Mathematicae},
volume = {7},
number = {1},
year = {1996},
pages = {11--35},
}
@article{BI98,
author = {Bridges, Douglas S. and Ishihara, Hajime},
title = {A definite constructive open mapping theorem?},
journal = {Mathematical Logic Quarterly},
volume = {44},
number = {4},
year = {1998},
pages = {545--552},
}
@article{BIKN19,
author = {Berger, Josef and Ishihara, Hajime and Kihara, Takayuki and Nemoto, Takako},
title = {The binary expansion and the intermediate value theorem in constructive reverse mathematics},
journal = {Archive for Mathematical Logic},
volume = {58},
number = {1-2},
year = {2019},
pages = {203--217},
doi = {10.1007/s00153-018-0627-2},
}
@article{Bil03,
author = {Billinge, Helen},
title = {Did Bishop Have a Philosophy of Mathematics?},
journal = {Philosophia Mathematica},
volume = {11},
number = {2},
year = {2003},
pages = {176--194},
doi = {10.1093/philmat/11.2.176},
}
@article{BIM13,
author = {Bridges, Douglas S. and Ishihara, Hajime and McKubre-Jordens, Maarten},
title = {Uniformly convex {B}anach spaces are reflexive---constructively},
journal = {Mathematical Logic Quarterly},
volume = {59},
number = {4-5},
year = {2013},
pages = {352--356},
doi = {10.1002/malq.201200093},
}
@article{BIMRSV07,
author = {Bridges, Douglas S. and Ishihara, Hajime and Mines, Ray and Richman, Fred and Schuster, Peter M. and V{\^{\i}}{\c{t}}{\u{a}}, Lumini{\c{t}}a},
title = {Almost locatedness in uniform spaces},
journal = {Czechoslovak Math. J.},
volume = {57},
number = {1},
year = {2007},
pages = {1--12},
}
@article{BIPS12,
author = {Berger, Josef and Ishihara, Hajime and Palmgren, Erik and Schuster, Peter},
title = {A predicative completion of a uniform space},
journal = {Annals of Pure and Applied Logic},
volume = {163},
number = {8},
year = {2012},
pages = {975--980},
doi = {10.1016/j.apal.2011.12.022},
}
@inproceedings{BIS02,
author = {Bridges, Douglas S. and Ishihara, Hajime and Schuster, Peter},
title = {Compactness and continuity, constructively revisited},
editor = {Bradfield, Julian},
booktitle = {Computer science logic},
series = {Lecture Notes in Computer Science},
volume = {2471},
publisher = {Springer},
year = {2002},
pages = {89--102},
}
@article{BIS03,
author = {Bridges, Douglas S. and Ishihara, Hajime and Spitters, Bas},
title = {Locating the range of an operator with an adjoint},
journal = {Indagationes Mathematicae},
volume = {13},
number = {4},
year = {2003},
pages = {433--440},
}
@article{BIS12,
author = {Berger, Josef and Ishihara, Hajime and Schuster, Peter},
title = {The weak {K}{\H{o}}nig lemma, {B}rouwer's {F}an theorem, de {M}organ's law, and dependent choice},
journal = {Reports on Mathematical Logic},
number = {47},
year = {2012},
pages = {63--86},
}
@inproceedings{Bis66,
author = {Bishop, Errett},
title = {Constructive {M}ethods in the {T}heory of {B}anach {A}lgebras},
editor = {Birtel, F.T.},
booktitle = {Function Algebras},
publisher = {Scott-Foresman},
address = {Chicago},
year = {1966},
pages = {343--345},
note = {Proc. Internat. Sympos. on Function Algebras, Tulane Univ., 1965},
}
@book{Bis67,
author = {Bishop, Errett},
title = {Foundations of Constructive Analysis},
publisher = {McGraw-Hill},
address = {New York},
year = {1967},
}
@article{Bis67a,
author = {Bishop, Errett},
title = {A constructive ergodic theorem},
journal = {J. Math. Mech.},
volume = {17},
year = {1967/1968},
pages = {631--639},
}
@article{Bis68,
author = {Bishop, Errett},
title = {The constructivization of abstract mathematical analysis},
journal = {Izdat. Mir},
year = {1968},
pages = {308--313},
note = {Proc. Internat. Congr. Math., Moscow, 1968},
}
@incollection{Bis70,
author = {Bishop, Errett},
title = {Mathematics as a numerical language},
editor = {Kino, A. and Myhill, J. and Vesley, R.E.},
booktitle = {Intuitionism and {P}roof {T}heory ({P}roc. {C}onf., {B}uffalo, {N}.{Y}., 1968)},
series = {Studies in Logic and the Foundations of Mathematics},
volume = {60},
publisher = {North-Holland, Amsterdam},
year = {1970},
pages = {53--71},
doi = {10.1016/S0049-237X(08)70740-7},
}
@article{BIS99,
author = {Bridges, Douglas S. and Ishihara, Hajime and Schuster, Peter},
title = {Sequential Compactness in Constructive Analysis},
journal = {\"{O}sterr. Akad. Wiss. Math.-Natur. Kl. Sitzungsber. II.},
volume = {208},
year = {1999},
pages = {159--163},
}
@article{BISV05,
author = {Bridges, Douglas S. and Ishihara, Hajime and Schuster, Peter and V{\^\i}{\c{t}}{\u{a}}, Lumini{\c{t}}a S.},
title = {Strong continuity implies uniform sequential continuity},
journal = {Archive for Mathematical Logic},
volume = {44},
number = {7},
year = {2005},
pages = {887--895},
}
@article{BISV08,
author = {Bridges, Douglas S. and Ishihara, Hajime and Schuster, Peter M. and V{\^{\i}}{\c{t}}{\u{a}}, Lumini{\c{t}}a},
title = {Apartness, compactness and nearness},
journal = {Theoretical Computer Science},
volume = {405},
number = {1-2},
year = {2008},
pages = {3--10},
doi = {10.1016/j.tcs.2008.06.019},
}
@proceedings{BISZ08,
title = {Computability and Complexity in Analysis},
editor = {Brattka, Vasco and Ishihara, Hajime and Schr{\"o}der, Matthias and Zhong, Ning},
series = {Journal of Universal Computer Science},
volume = {14},
number = {6},
publisher = {Graz University of Technology},
address = {Graz},
year = {2008},
note = {Selected Papers of the Fourth International Conference on Computability and Complexity in Analysis, June 16-18, 2007, Siena, Italy},
doi = {10.3217/jucs-014-06},
}
@proceedings{BISZ08a,
title = {Computability and Complexity in Analysis},
editor = {Brattka, Vasco and Ishihara, Hajime and Schr{\"o}der, Matthias and Zhong, Ning},
series = {Mathematical Logic Quarterly},
volume = {54},
number = {5},
publisher = {Wiley-VCH},
address = {Weinheim},
year = {2008},
note = {Selected Papers of the Fourth International Conference on Computability and Complexity in Analysis, June 16-18, 2007, Siena, Italy},
doi = {10.1002/malq.200810400},
}
@article{BIV04,
author = {Bridges, Douglas S. and Ishihara, Hajime and V{\^{\i}}{\c{t}}{\u{a}}, Lumini{\c{t}}a},
title = {Computing infima on convex sets, with applications in {H}ilbert spaces},
journal = {Proceedings of the American Mathematical Society},
volume = {132},
number = {9},
year = {2004},
pages = {2723--2732},
}
@article{BIV06,
author = {Bridges, Douglas S. and Ishihara, Hajime and V{\^{\i}}{\c{t}}{\u{a}}, Lumini{\c{t}}a},
title = {A new constructive version of {B}aire's Theorem},
journal = {Hokkaido Math. Journal},
volume = {35},
number = {1},
year = {2006},
pages = {107--118},
}
@inproceedings{BJL01,
author = {Breutzmann, Josef M. and Juedes, David W. and Lutz, Jack H.},
title = {Baire Category and Nowhere Differentiability for Feasible Real Functions},
editor = {Eades, Peter and Takaoka, Tadao},
booktitle = {Algorithms and Computation},
series = {Lecture Notes in Computer Science},
volume = {2223},
publisher = {Springer},
address = {Berlin},
year = {2001},
pages = {219--230},
note = {12th International Symposium, ISAAC 2001, Christchurch, New Zealand, December 19-21, 2001},
}
@article{BJL04,
author = {Breutzmann, Josef M. and Juedes, David W. and Lutz, Jack H.},
title = {Baire category and nowhere differentiability for feasible real functions},
journal = {Mathematical Logic Quarterly},
volume = {50},
number = {4,5},
year = {2004},
pages = {460--472},
}
@article{BJM89,
author = {Bridges, Douglas S. and Julian, William and Mines, Ray},
title = {A constructive treatment of open and unopen mapping theorems},
journal = {Zeitschrift f\"ur Mathematische Logik und Grundlagen der Mathematik},
volume = {35},
number = {1},
year = {1989},
pages = {29--43},
}
@article{BJRM92,
author = {Bridges, D.S. and Julian, W.H. and Richman, F. and Mines, R.},
title = {Extensions and fixed points of contractive maps in {R}$^n$},
journal = {J. Math. Anal. Appl.},
volume = {165},
year = {1992},
pages = {438--456},
}
@inproceedings{BK08,
author = {Bauer, Andrej and Kavkler, Iztok},
title = {Implementing real numbers with {RZ}},
editor = {Dillhage, Ruth and Grubba, Tanja and Sorbi, Andrea and Weihrauch, Klaus and Zhong, Ning},
booktitle = {Proceedings of the Fourth International Conference on Computability and Complexity in Analysis ({CCA} 2007)},
series = {Electronic Notes in Theoretical Computer Science},
volume = {202},
publisher = {Elsevier},
year = {2008},
pages = {365--384},
note = {{CCA} 2007, Siena, Italy, June 16--18, 2007},
}
@incollection{BK17,
author = {Bienvenu, Laurent and Kuyper, Rutger},
title = {Parallel and serial jumps of {W}eak {W}eak {K}{\"o}nig's {L}emma},
editor = {Day, Adam and Fellows, Michael and Greenberg, Noam and Khoussainov, Bakhadyr and Melnikov, Alexander and Rosamond, Frances},
booktitle = {Computability and Complexity: Essays Dedicated to Rodney G. Downey on the Occasion of His 60th Birthday},
series = {Lecture Notes in Computer Science},
volume = {10010},
publisher = {Springer},
address = {Cham},
year = {2017},
pages = {201--217},
doi = {10.1007/978-3-319-50062-1_15},
}
@incollection{BK98,
author = {Brattka, Vasco and Kalantari, Iraj},
title = {A Bibliography of Recursive Analysis and Recursive Topology},
editor = {Ershov, Yu. L. and Goncharov, S.S. and Nerode, A. and Remmel, J.B.},
booktitle = {Handbook of Recursive Mathematics},
series = {Studies in Logic and the Foundations of Mathematics},
volume = {138},
publisher = {Elsevier},
address = {Amsterdam},
year = {1998},
pages = {583--620},
note = {Volume 1, Recursive Model Theory},
}
@inproceedings{BKM16,
author = {Brau{\ss}e, Franz and Korovina, Margarita and M{\"u}ller, Norbert},
title = {Using {T}aylor models in exact real arithmetic},
editor = {Kotsireas, Ilias S. and Rump, Siegfried M. and Yap, Chee K.},
booktitle = {Mathematical aspects of computer and information sciences},
series = {Lecture Notes in Computer Science},
volume = {9582},
publisher = {Springer},
address = {Cham},
year = {2016},
pages = {474--488},
note = {6th International Conference, {MACIS} 2015, Berlin, Germany, November 11--13, 2015, Revised Selected Papers},
doi = {10.1007/978-3-319-32859-1_41},
}
@inproceedings{BL00,
author = {Burrows, Ashley and Lester, David},
title = {Exact Arithmetic and the {K}orteweg-de {V}ries Equation},
editor = {Blanck, Jens and Brattka, Vasco and Hertling, Peter and Weihrauch, Klaus},
booktitle = {Computability and Complexity in Analysis},
series = {Informatik Berichte},
volume = {272},
publisher = {FernUniversit\"at Hagen},
year = {2000},
month = sep,
pages = {23--41},
note = {CCA 2000 Workshop, Swansea, Wales, September 17--19, 2000},
}
@article{BL10,
author = {Bridges, Douglas S. and Loeb, Iris},
title = {Glueing continuous functions constructively},
journal = {Arch. Math. Logic},
volume = {49},
number = {5},
year = {2010},
pages = {603--616},
doi = {10.1007/s00153-010-0189-4},
}
@article{BL12,
author = {Bauer, Andrej and Le{\v{s}}nik, Davorin},
title = {Metric spaces in synthetic topology},
journal = {Ann. Pure Appl. Logic},
volume = {163},
number = {2},
year = {2012},
pages = {87--100},
doi = {10.1016/j.apal.2011.06.017},
}
@incollection{BL17,
author = {Barmpalias, George and Lewis-Pye, Andrew},
title = {A Note on the Differences of Computably Enumerable Reals},
editor = {Day, Adam and Fellows, Michael and Greenberg, Noam and Khoussainov, Bakhadyr and Melnikov, Alexander and Rosamond, Frances},
booktitle = {Computability and Complexity: Essays Dedicated to Rodney G. Downey on the Occasion of His 60th Birthday},
series = {Lecture Notes in Computer Science},
volume = {10010},
publisher = {Springer},
address = {Cham},
year = {2017},
pages = {623--632},
doi = {10.1007/978-3-319-50062-1_37},
}
@article{Bla00,
author = {Blanck, Jens},
title = {Domain representations of topological spaces},
journal = {Theoretical Computer Science},
volume = {247},
year = {2000},
pages = {229--255},
}
@inproceedings{Bla01,
author = {Blanck, Jens},
title = {Effectivity of Regular Spaces},
editor = {Blanck, Jens and Brattka, Vasco and Hertling, Peter},
booktitle = {Computability and Complexity in Analysis},
series = {Lecture Notes in Computer Science},
volume = {2064},
publisher = {Springer},
address = {Berlin},
year = {2001},
pages = {1--15},
note = {4th International Workshop, CCA 2000, Swansea, UK, September 2000},
}
@inproceedings{Bla01a,
author = {Blanck, Jens},
title = {Exact Real Arithmetic Systems: Results of Competition},
editor = {Blanck, Jens and Brattka, Vasco and Hertling, Peter},
booktitle = {Computability and Complexity in Analysis},
series = {Lecture Notes in Computer Science},
volume = {2064},
publisher = {Springer},
address = {Berlin},
year = {2001},
pages = {389--393},
note = {4th International Workshop, CCA 2000, Swansea, UK, September 2000},
}
@article{Bla02,
author = {Bl{\"a}ser, Markus},
title = {Uniform computational complexity of the derivatives of {$C^\infty$}-functions},
journal = {Theoretical Computer Science},
volume = {284},
number = {2},
year = {2002},
pages = {199--206},
}
@article{Bla05,
author = {Blanck, Jens},
title = {Efficient exact computation of iterated maps},
journal = {The Journal of Logic and Algebraic Programming},
volume = {64},
year = {2005},
pages = {41--59},
}
@article{Bla97,
author = {Blanck, Jens},
title = {Domain representability of metric spaces},
journal = {Annals of Pure and Applied Logic},
volume = {83},
year = {1997},
pages = {225--247},
}
@phdthesis{Bla97a,
author = {Blanck, Jens},
title = {Computability on topological spaces by effective domain representations},
school = {Uppsala University, Department of Mathematics},
address = {Uppsala, Sweden},
year = {1997},
}
@article{Bla99,
author = {Blanck, Jens},
title = {Effective domain representations of {$H(X)$}, the space of compact subsets},
journal = {Theoretical Computer Science},
volume = {219},
year = {1999},
pages = {19--48},
}
@inproceedings{BLP12a,
author = {Brattka, Vasco and Le Roux, St{\'e}phane and Pauly, Arno},
title = {On the Computational Content of the {B}rouwer {F}ixed {P}oint {T}heorem},
editor = {Cooper, S. Barry and Dawar, Anuj and L{\"o}we, Benedikt},
booktitle = {How the World Computes},
series = {Lecture Notes in Computer Science},
volume = {7318},
publisher = {Springer},
address = {Berlin},
year = {2012},
pages = {57--67},
note = {Turing Centenary Conference and 8th Conference on Computability in Europe, CiE 2012, Cambridge, UK, June 2012},
doi = {10.1007/978-3-642-30870-3_7},
}
@inproceedings{BLRMP16,
author = {Brattka, Vasco and Le Roux, St{\'e}phane and Miller, Joseph S. and Pauly, Arno},
title = {The {B}rouwer Fixed Point Theorem Revisited},
editor = {Beckmann, Arnold and Bienvenu, Laurent and Jonoska, Nata\v{s}a},
booktitle = {Pursuit of the Universal},
series = {Lecture Notes in Computer Science},
volume = {9709},
publisher = {Springer},
address = {Switzerland},
year = {2016},
pages = {58--67},
note = {12th Conference on Computability in Europe, CiE 2016, Paris, France, June 27 - July 1, 2016},
doi = {10.1007/978-3-319-40189-8_6},
}
@article{BLRMP19,
author = {Brattka, Vasco and Le Roux, St{\'e}phane and Miller, Joseph S. and Pauly, Arno},
title = {Connected Choice and the {B}rouwer Fixed Point Theorem},
journal = {Journal of Mathematical Logic},
volume = {19},
number = {1},
year = {2019},
pages = {1--46},
doi = {10.1142/S0219061319500041},
}
@article{BM00,
author = {Bridges, Douglas S. and Mahalanobis, Ayan},
title = {Sequential continuity of functions in constructive analysis},
journal = {Mathematical Logic Quarterly},
volume = {46},
number = {1},
year = {2000},
pages = {139--143},
}
@article{BM01,
author = {Bridges, Douglas S. and Mahalanobis, Ayan},
title = {Increasing, nondecreasing, and virtually continuous functions},
journal = {Journal of Automata, Languages and Combinatorics},
volume = {6},
number = {2},
year = {2001},
pages = {139--143},
}
@article{BM01a,
author = {Bridges, Douglas S. and Mahalanobis, Ayan},
title = {Bounded variation implies regulated: a constructive proof},
journal = {The Journal of Symbolic Logic},
volume = {66},
number = {4},
year = {2001},
pages = {1695--1700},
}
@inproceedings{BM07,
author = {Bienvenu, Laurent and Merkle, Wolfgang},
title = {Effective randomness for computable probability measures},
editor = {Cenzer, Douglas and Dillhage, Ruth and Grubba, Tanja and Weihrauch, Klaus},
booktitle = {Proceedings of the Third International Conference on Computability and Complexity in Analysis},
series = {Electronic Notes in Theoretical Computer Science},
volume = {167},
publisher = {Elsevier},
address = {Amsterdam},
year = {2007},
pages = {117--130},
note = {{CCA} 2006, Gainesville, Florida, USA, November 1--5, 2006},
}
@inproceedings{BM07a,
author = {Barmpalias, George and Montalb{\'a}n, Antonio},
title = {A cappable almost everywhere dominating computably enumerable degree},
editor = {Cenzer, Douglas and Dillhage, Ruth and Grubba, Tanja and Weihrauch, Klaus},
booktitle = {Proceedings of the Third International Conference on Computability and Complexity in Analysis},
series = {Electronic Notes in Theoretical Computer Science},
volume = {167},
publisher = {Elsevier},
address = {Amsterdam},
year = {2007},
pages = {17--31},
note = {{CCA} 2006, Gainesville, Florida, USA, November 1--5, 2006},
}
@article{BM13,
author = {Bridges, D. S. and McKubre-Jordens, M.},
title = {Solving the {D}irichlet problem constructively},
journal = {J. Log. Anal.},
volume = {5},
year = {2013},
pages = {Paper 3, 22},
}
@inproceedings{BM19,
author = {Boche, H. and M{\"o}nich, U. J.},
title = {Turing Computability of the {F}ourier Transform of Bandlimited Functions},
booktitle = {2019 IEEE International Symposium on Information Theory (ISIT)},
year = {2019},
pages = {380--384},
doi = {10.1109/ISIT.2019.8849462},
}
@article{BM19a,
author = {Boche, H. and M{\"o}nich, U. J.},
title = {Downsampling of Bounded Bandlimited Signals and the Bandlimited Interpolation: Analytic Properties and Computability},
journal = {IEEE Transactions on Signal Processing},
volume = {67},
number = {24},
year = {2019},
pages = {6424--6439},
doi = {10.1109/TSP.2019.2954972},
}
@inproceedings{BM19b,
author = {Boche, H. and M{\"o}nich, U. J.},
title = {On the {F}ourier Representation of Computable Continuous Signals},
booktitle = {ICASSP 2019 - 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)},
year = {2019},
pages = {5013--5017},
doi = {10.1109/ICASSP.2019.8683074},
}
@article{BM20,
author = {Boche, Holger and M\"{o}nich, Ullrich J.},
title = {Turing computability of {F}ourier transforms of bandlimited and discrete signals},
journal = {IEEE Transactions on Signal Processing},
volume = {68},
year = {2020},
pages = {532--547},
doi = {10.1109/TSP.2020.2964204},
}
@inproceedings{BM20a,
author = {Boche, H. and M{\"o}nich, U. J.},
title = {Optimal Sampling Rate and Bandwidth of Bandlimited Signals -- an Algorithmic Perspective},
booktitle = {ICASSP 2020 - 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)},
year = {2020},
pages = {5905--5909},
doi = {10.1109/ICASSP40776.2020.9053158},
}
@inproceedings{BM20b,
author = {Boche, H. and M{\"o}nich, U. J.},
title = {Computability of the Peak Value of Bandlimited Signals},
booktitle = {ICASSP 2020 - 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)},
year = {2020},
pages = {5280--5284},
doi = {10.1109/ICASSP40776.2020.9053211},
}
@inproceedings{BM20c,
author = {Boche, H. and M{\"o}nich, U. J.},
title = {Effective Approximation of Bandlimited Signals and Their Samples},
booktitle = {ICASSP 2020 - 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)},
year = {2020},
pages = {5590--5594},
doi = {10.1109/ICASSP40776.2020.9053196},
}
@article{BM20d,
author = {Brown, Tyler and McNicholl, Timothy H.},
title = {Analytic computable structure theory and $L^p$-spaces part 2},
journal = {Archive for Mathematical Logic},
volume = {59},
year = {2020},
pages = {427--443},
doi = {10.1007/s00153-019-00697-4},
}
@article{BM20e,
author = {Boche, Holger and M\"{o}nich, Ullrich J.},
title = {Turing meets {S}hannon: computable sampling type reconstruction with error control},
journal = {IEEE Transactions on Signal Processing},
volume = {68},
year = {2020},
pages = {6350--6365},
doi = {10.1109/TSP.2020.3035913},
}
@article{BM21,
author = {Boche, Holger and M\"{o}nich, Ullrich J.},
title = {On the solvability of the peak value problem for bandlimited signals with applications},
journal = {IEEE Transactions on Signal Processing},
volume = {69},
year = {2021},
pages = {103--118},
doi = {10.1109/TSP.2020.3042005},
}
@article{BM21a,
author = {Boche, Holger and M\"{o}nich, Ullrich J.},
title = {Algorithmic computability of the signal bandwidth},
journal = {Institute of Electrical and Electronics Engineers. Transactions on Information Theory},
volume = {67},
number = {4},
year = {2021},
pages = {2450--2471},
doi = {10.1109/TIT.2021.3057672},
}
@article{BM21b,
author = {Boche, Holger and M\"{o}nich, Ullrich J.},
title = {Computable time concentration of bandlimited signals and systems},
journal = {IEEE Transactions on Signal Processing},
volume = {69},
year = {2021},
pages = {5523--5538},
doi = {10.1109/TSP.2021.3112292},
}
@article{BM37,
author = {Banach, Stefan and Mazur, Stanis{\l}aw},
title = {Sur les fonctions calculables},
journal = {Annales de la Soci{\'e}t{\'e} Polonaise de Math{\'e}matique},
volume = {16},
year = {1937},
pages = {219},
}
@article{BM84,
author = {Bridges, D.S. and Mines, R.},
title = {What is constructive mathematics?},
journal = {The Mathematical Intelligencer},
volume = {6},
number = {4},
year = {1984},
pages = {32--38},
}
@article{BM98,
author = {Bridges, Douglas S. and Mines, Ray},
title = {Sequentially continuous linear mappings in constructive analysis},
journal = {The Journal of Symbolic Logic},
volume = {63},
number = {2},
year = {1998},
pages = {579--583},
}
@article{BMM20,
author = {Brown, Tyler A. and McNicholl, Timothy H. and Melnikov, Alexander G.},
title = {On the complexity of classifying {L}ebesgue spaces},
journal = {The Journal of Symbolic Logic},
volume = {85},
number = {3},
year = {2020},
pages = {1254--1288},
doi = {10.1017/jsl.2020.63},
}
@article{BMN16,
author = {Brattka, Vasco and Miller, Joseph S. and Nies, Andr{\'e}},
title = {Randomness and Differentiability},
journal = {Transactions of the American Mathematical Society},
volume = {368},
number = {1},
year = {2016},
pages = {581--605},
doi = {10.1090/tran/6484},
}
@article{BMRS04,
author = {Bridges, Douglas S. and Mines, Ray and Richman, Fred and Schuster, Peter},
title = {The polydisk {N}ullstellensatz},
journal = {Proceedings of the American Mathematical Society},
volume = {132},
number = {7},
year = {2004},
pages = {2133--2140},
}
@incollection{BMST16,
author = {Berger, Ulrich and Miyamoto, Kenji and Schwichtenberg, Helmut and Tsuiki, Hideki},
title = {Logic for {G}ray-code computation},
booktitle = {Concepts of proof in mathematics, philosophy, and computer science},
series = {Ontos Math. Log.},
volume = {6},
publisher = {De Gruyter},
address = {Berlin},
year = {2016},
pages = {69--110},
}
@article{Boe05,
author = {Boehm, Hans-J.},
title = {The constructive reals as a {J}ava library},
journal = {The Journal of Logic and Algebraic Programming},
volume = {64},
year = {2005},
pages = {3--11},
}
@article{Bor12,
author = {Borel, {\'E}mil},
title = {Le calcul des int\'egral d\'efinies},
journal = {Journal de Mathematiques pures et appliqu\'ees},
volume = {8},
number = {2},
year = {1912},
pages = {159--210},
}
@incollection{Bor50,
author = {Borel, {\'{E}}mile},
title = {{La th\'{e}orie de la mesure et al th\'{e}orie de l'integration}},
booktitle = {{Le\c{c}ons sur la th\'{e}orie des fonctions}},
edition = {4},
publisher = {Gauthier-Villars},
address = {Paris},
year = {1950},
pages = {214--256},
}
@book{Bor72,
author = {Borel, {\'E}mil},
title = {Euvres de {\'E}mil {B}orel Vol. 1--4},
publisher = {\'Editions du CNRS},
address = {Paris},
year = {1972},
}
@inproceedings{Bos07,
author = {Bosserhoff, Volker},
title = {Computability of solutions of operator equations},
editor = {Cenzer, Douglas and Dillhage, Ruth and Grubba, Tanja and Weihrauch, Klaus},
booktitle = {Proceedings of the Third International Conference on Computability and Complexity in Analysis},
series = {Electronic Notes in Theoretical Computer Science},
volume = {167},
publisher = {Elsevier},
address = {Amsterdam},
year = {2007},
pages = {179--202},
note = {{CCA} 2006, Gainesville, Florida, USA, November 1--5, 2006},
}
@article{Bos07a,
author = {Bosserhoff, Volker},
title = {Computability of solutions of operator equations},
journal = {Mathematical Logic Quarterly},
volume = {53},
number = {4--5},
year = {2007},
pages = {326--344},
}
@inproceedings{Bos08,
author = {Bosserhoff, Volker},
title = {Notions of Probabilistic Computability on Represented Spaces},
editor = {Dillhage, Ruth and Grubba, Tanja and Sorbi, Andrea and Weihrauch, Klaus and Zhong, Ning},
booktitle = {Proceedings of the Fourth International Conference on Computability and Complexity in Analysis ({CCA} 2007)},
series = {Electronic Notes in Theoretical Computer Science},
volume = {202},
publisher = {Elsevier},
year = {2008},
pages = {137--170},
note = {{CCA} 2007, Siena, Italy, June 16--18, 2007},
}
@article{Bos08a,
author = {Bosserhoff, Volker},
title = {The Bit-Complexity of Finding Nearly Optimal Quadrature Rules for Weighted Integration},
journal = {Journal of Universal Computer Science},
volume = {14},
number = {6},
year = {2008},
pages = {938--955},
}
@article{Bos08b,
author = {Bosserhoff, Volker},
title = {Notions of Probabilistic Computability on Represented Spaces},
journal = {Journal of Universal Computer Science},
volume = {14},
number = {6},
year = {2008},
pages = {956--995},
}
@article{Bos08c,
author = {Bosserhoff, Volker},
title = {Are unbounded linear operators computable on the average for {G}aussian measures?},
journal = {Journal of Complexity},
volume = {24},
number = {4},
year = {2008},
pages = {477--491},
}
@inproceedings{Bos08e,
author = {Bosserhoff, Volker},
title = {On the Effective Existence of {S}chauder Bases (Extended Abstract)},
editor = {Brattka, Vasco and Dillhage, Ruth and Grubba, Tanja and Klutsch, Angela},
booktitle = {{CCA} 2008, Fifth International Conference on Computability and Complexity in Analysis},
series = {Electronic Notes in Theoretical Computer Science},
volume = {221},
publisher = {Elsevier},
year = {2008},
pages = {17--21},
note = {{CCA} 2008, Fifth International Conference, Hagen, Germany, August 21--24, 2008},
}
@phdthesis{Bos08f,
author = {Bosserhoff, Volker},
title = {Computable Functional Analysis and Probabilistic Computability},
school = {University of the Armed Forces},
address = {Munich},
year = {2008},
}
@article{Bos09,
author = {Bosserhoff, Volker},
title = {On the effective existence of {S}chauder bases},
journal = {Journal of Universal Computer Science},
volume = {15},
number = {6},
year = {2009},
pages = {1145--1161},
}
@article{Bou06,
author = {Bournez, Olivier},
title = {How much can analog and hybrid systems be proved (super-){T}uring},
journal = {Applied Mathematics and Computation},
volume = {178},
number = {1},
year = {2006},
pages = {58--71},
doi = {10.1016/j.amc.2005.09.070},
}
@inproceedings{Bou20,
author = {Bournez, Olivier},
title = {Computability, Complexity and Programming with Ordinary Differential Equations (Invited Talk)},
editor = {Paul, Christophe and Bl{\"a}ser, Markus},
booktitle = {37th International Symposium on Theoretical Aspects of Computer Science ({STACS} 2020)},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
volume = {154},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
year = {2020},
pages = {3:1--3:13},
doi = {10.4230/LIPIcs.STACS.2020.3},
}
@article{BP03,
author = {Brattka, Vasco and Presser, Gero},
title = {Computability on subsets of metric spaces},
journal = {Theoretical Computer Science},
volume = {305},
year = {2003},
pages = {43--76},
}
@article{BP03a,
author = {Bridges, Douglas S. and Popa, Gabriela},
title = {Exact, continuous boundary crossings out of convex sets in $R^N$},
journal = {The Quarterly Journal of Mathematics},
volume = {54},
number = {4},
year = {2003},
pages = {391--398},
}
@inproceedings{BP10,
author = {Brattka, Vasco and Pauly, Arno},
title = {Computation with Advice},
editor = {Zheng, Xizhong and Zhong, Ning},
booktitle = {{CCA} 2010, Proceedings of the Seventh International Conference on Computability and Complexity in Analysis},
series = {Electronic Proceedings in Theoretical Computer Science},
volume = {24},
year = {2010},
pages = {41--55},
}
@inproceedings{BP17a,
author = {Bournez, Olivier and Pouly, Amaury},
title = {A universal ordinary differential equation},
editor = {Chatzigiannakis, Ioannis and Indyk, Piotr and Kuhn, Fabian and Muscholl, Anca},
booktitle = {44th {I}nternational {C}olloquium on {A}utomata, {L}anguages, and {P}rogramming},
series = {LIPIcs. Leibniz Int. Proc. Inform.},
volume = {80},
publisher = {Schloss Dagstuhl. Leibniz-Zent. Inform.},
address = {Dagstuhl, Germany},
year = {2017},
pages = {Art. No. 116, 14},
doi = {10.4230/LIPIcs.ICALP.2017.116},
}
@article{BP18,
author = {Brattka, Vasco and Pauly, Arno},
title = {On the Algebraic Structure of {W}eihrauch Degrees},
journal = {Logical Methods in Computer Science},
volume = {14},
number = {4:4},
year = {2018},
pages = {1--36},
doi = {10.23638/LMCS-14(4:4)2018},
}
@inproceedings{BP18a,
author = {Boche, H. and Pohl, V.},
title = {On the Computability of System Approximations Under Causality Constraints},
booktitle = {2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)},
year = {2018},
pages = {4559--4563},
doi = {10.1109/ICASSP.2018.8461586},
}
@inproceedings{BP19,
author = {Boche, H. and Pohl, V.},
title = {The Divergence of all Sampling-based Methods for Calculating the Spectral Factorization},
booktitle = {2019 IEEE 58th Conference on Decision and Control (CDC)},
year = {2019},
pages = {7714--7720},
doi = {10.1109/CDC40024.2019.9030276},
}
@inproceedings{BP19a,
author = {Boche, H. and Pohl, V.},
title = {The Solvability Complexity Index of Sampling-based {H}ilbert Transform Approximations},
booktitle = {2019 13th International conference on Sampling Theory and Applications (SampTA)},
year = {2019},
pages = {1--4},
doi = {10.1109/SampTA45681.2019.9030934},
}
@inproceedings{BP19b,
author = {Boche, H. and Pohl, V.},
title = {Energy Blowup of Sampling-based Approximation Methods},
booktitle = {ICASSP 2019 - 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)},
year = {2019},
pages = {5082--5086},
doi = {10.1109/ICASSP.2019.8682984},
}
@article{BP20,
author = {Bournez, Olivier and Pouly, Amaury},
title = {A Universal Ordinary Differential Equation},
journal = {Logical Methods in Computer Science},
volume = {16},
number = {1},
year = {2020},
month = Feb,
pages = {28:1-28:37},
doi = {10.23638/LMCS-16(1:28)2020},
}
@article{BP20a,
author = {Boche, Holger and Pohl, Volker},
title = {Investigations on the approximability and computability of the {H}ilbert transform with applications},
journal = {Applied and Computational Harmonic Analysis. Time-Frequency and Time-Scale Analysis, Wavelets, Numerical Algorithms, and Applications},
volume = {48},
number = {2},
year = {2020},
pages = {706--730},
doi = {10.1016/j.acha.2018.09.001},
}
@article{BP20b,
author = {Boche, Holger and Pohl, Volker},
title = {Calculating the spectral factorization and outer functions by sampling-based approximations---fundamental limitations},
journal = {Journal of Approximation Theory},
volume = {257},
year = {2020},
pages = {105450, 18},
doi = {10.1016/j.jat.2020.105450},
}
@article{BP20c,
author = {Boche, Holger and Pohl, Volker},
title = {On the algorithmic solvability of spectral factorization and applications},
journal = {Institute of Electrical and Electronics Engineers. Transactions on Information Theory},
volume = {66},
number = {7},
year = {2020},
pages = {4574--4592},
doi = {10.1109/TIT.2020.2968028},
}
@article{BP20d,
author = {Boche, Holger and Pohl, Volker},
title = {On approximations for functions in the space of uniformly convergent {F}ourier series},
journal = {Journal of Approximation Theory},
volume = {249},
year = {2020},
pages = {105307, 28},
doi = {10.1016/j.jat.2019.105307},
}
@inproceedings{BP20e,
author = {Boche, H. and Pohl, V.},
title = {Can every analog system be simulated on a digital computer?},
booktitle = {ICASSP 2020 - 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)},
year = {2020},
pages = {1783--1787},
doi = {10.1109/ICASSP40776.2020.9054494},
}
@article{BP20f,
author = {Boche, H. and Pohl, V.},
title = {Turing Meets Circuit Theory: Not Every Continuous-Time {LTI} System Can Be Simulated on a Digital Computer},
journal = {IEEE Transactions on Circuits and Systems I: Regular Papers},
year = {2020},
pages = {1--14},
doi = {10.1109/TCSI.2020.3018619},
}
@inproceedings{BP20g,
author = {Boche, H. and Pohl, V.},
title = {Computing {H}ilbert Transform and Spectral Factorization for Signal Spaces of Smooth Functions},
booktitle = {ICASSP 2020 - 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)},
year = {2020},
pages = {5300--5304},
doi = {10.1109/ICASSP40776.2020.9053807},
}
@incollection{BP21,
author = {Bournez, Olivier and Pouly, Amaury},
title = {A Survey on Analog Models of Computation},
editor = {Brattka, Vasco and Hertling, Peter},
booktitle = {Handbook of Computability and Complexity in Analysis},
series = {Theory and Applications of Computability},
publisher = {Springer},
address = {Cham},
year = {2021},
pages = {173--226},
doi = {10.1007/978-3-030-59234-9_6},
}
@article{BP22,
author = {Boche, Holger and Pohl, Volker},
title = {On Non-Detectability of Non-Computability and the Degree of Non-Computability of Solutions of Circuit and Wave Equations on Digital Computers},
journal = {IEEE Transactions on Information Theory},
volume = {68},
number = {8},
year = {2022},
pages = {5561--5578},
doi = {10.1109/TIT.2022.3172837},
}
@article{BPS20,
author = {Brecht, Matthew de and Pauly, Arno and Schr\"{o}der, Matthias},
title = {Overt choice},
journal = {Computability},
volume = {9},
number = {3-4},
year = {2020},
pages = {169--191},
doi = {10.3233/com-190253},
}
@article{BR17,
author = {Brattka, Vasco and Rakotoniaina, Tahina},
title = {On the Uniform Computational Content of {R}amsey's Theorem},
journal = {Journal of Symbolic Logic},
volume = {82},
number = {4},
year = {2017},
pages = {1278--1316},
doi = {10.1017/jsl.2017.43},
}
@article{BR87,
author = {Brady, S.S. and Remmel, J.B.},
title = {The undecidability of the lattice of r.e. closed subsets of an effective topological space},
journal = {Annals of Pure and Applied Logic},
volume = {35},
year = {1987},
pages = {193--203},
}
@book{BR87a,
author = {Bridges, Douglas S. and Richman, Fred},
title = {Varieties of Constructive Mathematics},
series = {London Mathematical Society Lecture Note Series},
volume = {97},
publisher = {Cambridge University Press},
address = {Cambridge},
year = {1987},
}
@article{BR91,
author = {Bridges, Douglas S. and Richman, Fred},
title = {A recursive counterexample to {D}ebreu's theorem on the existence of a utility function},
journal = {Mathematical Social Sciences},
volume = {21},
number = {2},
year = {1991},
pages = {179--182},
}
@article{BR99,
author = {Bridges, Douglas S. and Reeves, Steve},
title = {Constructive mathematics in theory and programming practice},
journal = {Philosophia Mathematica. Philosophy of Mathematics, its Learning, and its Application. Series III},
volume = {7},
number = {1},
year = {1999},
pages = {65--104},
}
@inproceedings{Bra00a,
author = {Brattka, Vasco},
title = {Realistic models of computability on the real numbers},
editor = {Yoshikawa, Atsushi},
booktitle = {Relevance and Feasibility of Mathematical Analysis on the Computer},
series = {S\={u}rikaisekikenky\={u}sho K\={o}ky\={u}roku},
volume = {1169},
publisher = {Research Institute for Mathematical Sciences},
address = {Kyoto},
year = {2000},
pages = {62--75},
}
@inproceedings{Bra01a,
author = {Brattka, Vasco},
title = {Computable versions of {B}aire's category theorem},
editor = {Sgall, Ji{\v{r}}{\'{\i}} and Pultr, Ale{\v{s}} and Kolman, Petr},
booktitle = {Mathematical Foundations of Computer Science 2001},
series = {Lecture Notes in Computer Science},
volume = {2136},
publisher = {Springer},
address = {Berlin},
year = {2001},
pages = {224--235},
note = {26th International Symposium, MFCS 2001, Mari{\'{a}}nsk{\'{e}} L{\'{a}}zn{\v{e}}, Czech Republic, August 27-31, 2001},
}
@inproceedings{Bra02b,
author = {Brattka, Vasco},
title = {Random Numbers and an Incomplete Immune Recursive Set},
editor = {Widmayer, Peter and Triguero, Francisco and Morales, Rafael and Hennessy, Matthew and Eidenbenz, Stephan and Conejo, Ricardo},
booktitle = {Automata, Languages and Programming},
series = {Lecture Notes in Computer Science},
volume = {2380},
publisher = {Springer},
address = {Berlin},
year = {2002},
pages = {950--961},
note = {29th International Colloquium, ICALP, M{\'{a}}laga, Spain, July 8--13, 2002},
}
@article{Bra02c,
author = {Brattka, Vasco},
title = {Some notes on {F}ine computability},
journal = {Journal of Universal Computer Science},
volume = {8},
number = {3},
year = {2002},
pages = {382--395},
doi = {10.3217/jucs-008-03-0382},
}
@inproceedings{Bra02d,
author = {Brattka, Vasco},
title = {Computing Uniform Bounds},
editor = {Brattka, Vasco and Schr{\"{o}}der, Matthias and Weihrauch, Klaus},
booktitle = {{CCA} 2002 Computability and Complexity in Analysis},
series = {Electronic Notes in Theoretical Computer Science},
volume = {66},
publisher = {Elsevier},
address = {Amsterdam},
year = {2002},
note = {5th International Workshop, {CCA} 2002, M{\'{a}}laga, Spain, July 12--13, 2002},
}
@phdthesis{Bra02e,
author = {Brattka, Vasco},
title = {Computability on Asymmetric Spaces},
school = {Department of Computer Science, University of Hagen},
address = {Hagen, Germany},
year = {2002},
note = {Habilitation Thesis},
}
@incollection{Bra03,
author = {Brattka, Vasco},
title = {Computability over Topological Structures},
editor = {Cooper, S. Barry and Goncharov, Sergey S.},
booktitle = {Computability and Models},
publisher = {Kluwer Academic Publishers},
address = {New York},
year = {2003},
pages = {93--136},
}
@inproceedings{Bra03b,
author = {Brattka, Vasco},
title = {The Inversion Problem for Computable Linear Operators},
editor = {Alt, Helmut and Habib, Michel},
booktitle = {STACS 2003},
series = {Lecture Notes in Computer Science},
volume = {2607},
publisher = {Springer},
address = {Berlin},
year = {2003},
pages = {391--402},
note = {20th Annual Symposium on Theoretical Aspects of Computer Science, Berlin, Germany, February 27--March 1, 2003},
}
@article{Bra03c,
author = {Brattka, Vasco},
title = {Effective Representations of the Space of Linear Bounded Operators},
journal = {Applied General Topology},
volume = {4},
number = {1},
year = {2003},
pages = {115--131},
doi = {10.4995/agt.2003.2014},
}
@article{Bra03e,
author = {Brattka, Vasco},
title = {Recursive Quasi-Metric Spaces},
journal = {Theoretical Computer Science},
volume = {305},
year = {2003},
pages = {17--42},
}
@inproceedings{Bra03f,
author = {Brattka, Vasco},
title = {The Emperor's New Recursiveness: The Epigraph of the Exponential Function in Two Models of Computability},
editor = {Ito, Masami and Imaoka, Teruo},
booktitle = {Words, Languages \& Combinatorics III},
publisher = {World Scientific Publishing},
address = {Singapore},
year = {2003},
pages = {63--72},
note = {ICWLC 2000, Kyoto, Japan, March 14--18, 2000},
}
@incollection{Bra04,
author = {Brattka, Vasco},
title = {Du 13-i{\`e}me probl{\`e}me de {H}ilbert {\`a} la th{\'e}orie des r{\'e}seaux de neurones : aspects constructifs du th{\'e}or{\`e}me de superposition de {K}olmogorov},
editor = {Charpentier, {\'E}ric and Lesne, Annick and Nikolski, Nikola{\"\i}},
booktitle = {L'h{\'e}ritage de {K}olmogorov en math{\'e}matiques},
publisher = {{\'E}ditions Belin},
address = {Paris},
year = {2004},
pages = {241--268},
}
@article{Bra05,
author = {Brattka, Vasco},
title = {Effective {B}orel measurability and reducibility of functions},
journal = {Mathematical Logic Quarterly},
volume = {51},
number = {1},
year = {2005},
pages = {19--44},
}
@inproceedings{Bra05a,
author = {Brattka, Vasco},
title = {On the {B}orel Complexity of {H}ahn-{B}anach Extensions},
editor = {Brattka, Vasco and Staiger, Ludwig and Weihrauch, Klaus},
booktitle = {Proceedings of the 6th Workshop on Computability and Complexity in Analysis},
series = {Electronic Notes in Theoretical Computer Science},
volume = {120},
publisher = {Elsevier},
address = {Amsterdam},
year = {2005},
pages = {3--16},
note = {6th International Workshop, {CCA} 2004, Wittenberg, Germany, August 16--20, 2004},
}
@inproceedings{Bra05b,
author = {Braverman, Mark},
title = {Hyperbolic {J}ulia Sets are Poly-Time Computable},
editor = {Brattka, Vasco and Staiger, Ludwig and Weihrauch, Klaus},
booktitle = {Proceedings of the 6th Workshop on Computability and Complexity in Analysis},
series = {Electronic Notes in Theoretical Computer Science},
volume = {120},
publisher = {Elsevier},
address = {Amsterdam},
year = {2005},
pages = {17--30},
note = {6th International Workshop, {CCA} 2004, Wittenberg, Germany, August 16--20, 2004},
}
@incollection{Bra05d,
author = {Brattka, Vasco},
title = {Computability on Non-Separable {B}anach Spaces and {L}andau's Theorem},
editor = {Crosilla, Laura and Schuster, Peter},
booktitle = {From Sets and Types to Topology and Analysis: Towards Practicable Foundations for Constructive Mathematics},
publisher = {Oxford University Press},
year = {2005},
pages = {316--333},
}
@inproceedings{Bra05e,
author = {Braverman, Mark},
title = {On the Complexity of Real Functions},
booktitle = {Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science},
series = {FOCS '05},
publisher = {IEEE Computer Society},
address = {Washington, DC, USA},
year = {2005},
pages = {155--164},
doi = {10.1109/SFCS.2005.58},
}
@inproceedings{Bra06,
author = {Brattka, Vasco},
title = {Computable Versions of the Uniform Boundedness Theorem},
editor = {Chatzidakis, Z. and Koepke, P. and Pohlers, W.},
booktitle = {Logic Colloquium 2002},
series = {Lecture Notes in Logic},
volume = {27},
publisher = {Association for Symbolic Logic},
address = {Urbana},
year = {2006},
pages = {130--151},
}
@article{Bra06a,
author = {Braverman, Mark},
title = {Parabolic {J}ulia sets are polynomial time computable},
journal = {Nonlinearity},
volume = {19},
number = {6},
year = {2006},
pages = {1383--1401},
}
@incollection{Bra07,
author = {Brattka, Vasco},
title = {From {H}ilbert's 13th {P}roblem to the theory of neural networks: constructive aspects of {K}olmogorov's {S}uperposition {T}heorem},
editor = {Charpentier, {\'E}ric and Lesne, Annick and Nikolski, Nikola{\"\i}},
booktitle = {Kolmogorov's Heritage in Mathematics},
publisher = {Springer},
address = {Berlin},
year = {2007},
pages = {253--280},
}
@article{Bra08,
author = {Brattka, Vasco},
title = {Plottable real number functions and the computable graph theorem},
journal = {SIAM Journal on Computing},
volume = {38},
number = {1},
year = {2008},
pages = {303--328},
}
@phdthesis{Bra08a,
author = {Braverman, Mark},
title = {Computability and Complexity of {J}ulia Sets},
school = {University of Toronto},
address = {Toronto, Canada},
year = {2008},
}
@article{Bra08b,
author = {Brattka, Vasco},
title = {Borel Complexity and Computability of the {H}ahn-{B}anach {T}heorem},
journal = {Archive for Mathematical Logic},
volume = {46},
number = {7--8},
year = {2008},
pages = {547--564},
}
@article{Bra09,
author = {Brattka, Vasco},
title = {A computable version of {B}anach's Inverse Mapping Theorem},
journal = {Annals of Pure and Applied Logic},
volume = {157},
year = {2009},
pages = {85--96},
}
@article{Bra13,
author = {Braverman, Mark},
title = {Computing with Real Numbers, from {A}rchimedes to {T}uring and Beyond},
journal = {Communications of the ACM},
volume = {56},
number = {9},
publisher = {ACM},
address = {New York, NY, USA},
year = {2013},
month = sep,
pages = {74--83},
doi = {10.1145/2500890},
}
@inproceedings{Bra16,
author = {Brattka, Vasco},
title = {Computability and Analysis, a Historical Approach},
editor = {Beckmann, Arnold and Bienvenu, Laurent and Jonoska, Nata\v{s}a},
booktitle = {Pursuit of the Universal},
series = {Lecture Notes in Computer Science},
volume = {9709},
publisher = {Springer},
address = {Switzerland},
year = {2016},
pages = {45--57},
note = {12th Conference on Computability in Europe, CiE 2016, Paris, France, June 27 - July 1, 2016},
doi = {10.1007/978-3-319-40189-8_5},
}
@article{Bra18,
author = {Brattka, Vasco},
title = {A {G}alois connection between {T}uring jumps and limits},
journal = {Logical Methods in Computer Science},
volume = {14},
number = {3:13},
year = {2018},
month = Aug,
pages = {1--37},
doi = {10.23638/LMCS-14(3:13)2018},
}
@article{Bra21,
author = {Brattka, Vasco},
title = {Stashing-Parallelization Pentagons},
journal = {Logical Methods in Computer Science},
volume = {17},
number = {4},
year = {2021},
pages = {20:1-20:29},
doi = {10.46298/LMCS-17(4:20)2021},
}
@article{Bra22,
author = {Brattka, Vasco},
title = {The Discontinuity Problem},
journal = {Journal of Symbolic Logic},
year = {2022},
note = {electronically published},
doi = {10.1017/jsl.2021.106},
}
@incollection{Bra22a,
author = {Brattka, Vasco},
title = {Weihrauch complexity and the {H}agen school of computable analysis},
editor = {L{\"o}we, Benedikt and Sarikaya, Deniz},
booktitle = {60 {J}ahre {DVMLG}},
series = {Tributes},
volume = {48},
publisher = {College Publications},
address = {London},
year = {2022},
pages = {13--44},
}
@inproceedings{Bra95,
author = {Brattka, Vasco},
title = {Computable selection in analysis},
editor = {Ko, Ker-I and Weihrauch, Klaus},
booktitle = {Computability and Complexity in Analysis},
series = {Informatik Berichte},
volume = {190},
publisher = {FernUniversit\"at Hagen},
year = {1995},
month = sep,
pages = {125--138},
note = {{CCA} Workshop, Hagen, August 19--20, 1995},
}
@article{Bra96,
author = {Brattka, Vasco},
title = {Recursive characterization of computable real-valued functions and relations},
journal = {Theoretical Computer Science},
volume = {162},
year = {1996},
pages = {45--77},
}
@article{Bra97,
author = {Brattka, Vasco},
title = {Order-free Recursion on the Real Numbers},
journal = {Mathematical Logic Quarterly},
volume = {43},
year = {1997},
pages = {216--234},
doi = {10.1002/malq.19970430206},
}
@inproceedings{Bra97a,
author = {Brattka, Vasco},
title = {Computable Invariance},
editor = {Jiang, Tao and Lee, D.T.},
booktitle = {Computing and Combinatorics},
series = {Lecture Notes in Computer Science},
volume = {1276},
publisher = {Springer},
address = {Berlin},
year = {1997},
pages = {146--155},
note = {Third Annual Conference, COCOON'97, Shanghai, China, August 1997},
}
@phdthesis{Bra98b,
author = {Brattka, Vasco},
title = {Recursive and Computable Operations over Topological Structures},
school = {Department of Computer Science, University of Hagen},
address = {Hagen, Germany},
year = {1998},
note = {{Ph.D.} thesis},
}
@article{Bra99,
author = {Brattka, Vasco},
title = {Computable invariance},
journal = {Theoretical Computer Science},
volume = {210},
year = {1999},
pages = {3--20},
}
@inproceedings{Bra99a,
author = {Brattka, Vasco},
title = {A Stability Theorem for Recursive Analysis},
editor = {Cristian S. Calude and Michael J. Dinneen},
booktitle = {Combinatorics, Computation \& Logic},
series = {Discrete Mathematics and Theoretical Computer Science},
publisher = {Springer},
address = {Singapore},
year = {1999},
pages = {144--158},
note = {Proceedings of DMTCS'99 and CATS'99, Auckland, New Zealand, January 1999},
}
@article{Bri00,
author = {Bridges, Douglas S.},
title = {Converses of {B}ishop's lemma on located sets},
journal = {Indagationes Mathematicae},
volume = {11},
number = {1},
year = {2000},
pages = {31--38},
}
@article{Bri00a,
author = {Bridges, Douglas S.},
title = {A constructive look at functions of bounded variation},
journal = {Bull. London Math. Soc.},
volume = {32},
number = {3},
year = {2000},
pages = {316--324},
}
@article{Bri00b,
author = {Bridges, Douglas S.},
title = {Constructive methods in {B}anach algebra theory},
journal = {Mathematica Japonica},
volume = {52},
number = {1},
year = {2000},
pages = {145--161},
}
@article{Bri01,
author = {Bridges, Douglas S.},
title = {Prime and maximal ideals in constructive ring theory},
journal = {Communications in Algebra},
volume = {29},
number = {7},
year = {2001},
pages = {2787--2803},
}
@inproceedings{Bri01a,
author = {Bridges, Douglas S.},
title = {Dini's Theorem: A Constructive Case Study},
editor = {Calude, C.S. and Dinneen, M.J. and Sburlan, S.},
booktitle = {Combinatorics, Computability and Logic},
series = {Discrete Mathematics and Theoretical Computer Science},
publisher = {Springer},
address = {London},
year = {2001},
pages = {69--80},
note = {Proceedings of DMTCS 2001},
}
@article{Bri02,
author = {Bridges, Douglas S.},
title = {Reality and virtual reality in mathematics},
journal = {Bulletin of the European Association for Theoretical Computer Science},
volume = {78},
year = {2002},
pages = {221--230},
}
@inproceedings{Bri03,
author = {Bridges, Douglas S.},
title = {First steps in constructive game theory},
editor = {Brattka, Vasco and Schr{\"{o}}der, Matthias and Weihrauch, Klaus and Zhong, Ning},
booktitle = {Computability and Complexity in Analysis},
series = {Informatik Berichte},
volume = {302},
publisher = {FernUniversit\"at in Hagen},
year = {2003},
month = aug,
pages = {3--9},
note = {International Conference, CCA 2003, Cincinnati, USA, August 28--30, 2003},
}
@article{Bri04,
author = {Bridges, Douglas S.},
title = {First steps in constructive game theory},
journal = {Mathematical Logic Quarterly},
volume = {50},
number = {4,5},
year = {2004},
pages = {501--506},
}
@article{Bri04a,
author = {Bridges, Douglas S.},
title = {Constructivity in Mathematics},
journal = {Cubo},
volume = {6},
number = {1},
year = {2004},
pages = {209--258},
}
@article{Bri04b,
author = {Bridges, Douglas S.},
title = {Constructive complements of unions of two closed sets},
journal = {Mathematical Logic Quarterly},
volume = {50},
number = {3},
year = {2004},
pages = {293--294},
}
@incollection{Bri06,
author = {Bridges, Douglas S.},
title = {{C}hurch's thesis and {B}ishop's constructivism},
editor = {Olszewski, Adam},
booktitle = {{C}hurch's Thesis After 70 Years},
publisher = {Ontos},
address = {Berlin},
year = {2006},
pages = {58--65},
}
@inproceedings{Bri07,
author = {Bridges, Douglas S.},
title = {Colocatedness and {L}ebesgue Integrability},
editor = {Cooper, S. Barry and L{\"o}we, Benedikt and Sorbi, Andrea},
booktitle = {Computation and Logic in the Real World},
series = {Lecture Notes in Computer Science},
volume = {4497},
publisher = {Springer},
address = {Berlin},
year = {2007},
pages = {98--104},
note = {Third Conference on Computability in Europe, CiE 2007, Siena, Italy, June 18-23, 2007},
}
@article{Bri07a,
author = {Bridges, Douglas S.},
title = {Constructing local optima on a compact interval},
journal = {Archive for Mathematical Logic},
volume = {46},
year = {2007},
pages = {149--154},
}
@incollection{Bri07b,
author = {Bridges, Douglas S.},
title = {Philosophy of mathematics: 5 questions},
editor = {Hendricks, Vincent F. and Leitgeb, Hannes},
booktitle = {Philosophy of mathematics: 5 questions},
publisher = {Automatic Press/VIP},
address = {New York, London},
year = {2007},
pages = {45--49},
}
@article{Bri07c,
author = {Briseid, Eyvind},
title = {A rate of convergence for asymptotic contractions},
journal = {J. Math. Anal. Appl.},
volume = {330},
year = {2007},
pages = {364--376},
}
@article{Bri07d,
author = {Briseid, Eyvind},
title = {Some results on {K}irk's asymptotic contractions},
journal = {Fixed Point Theory},
volume = {8},
year = {2007},
pages = {17--27},
}
@article{Bri07g,
author = {Briseid, E. M.},
title = {Addendum to the paper: ``{S}ome results on {K}irk's asymptotic contractions'' [{F}ixed {P}oint {T}heory {\bf 8} (2007), no. 1, 17--27},
journal = {Fixed Point Theory},
volume = {8},
number = {2},
year = {2007},
pages = {321--322},
}
@article{Bri08,
author = {Bridges, Douglas S.},
title = {Uniform continuity properties of preference relations},
journal = {Notre Dame Journal of Formal Logic},
volume = {49},
number = {1},
year = {2008},
pages = {97--106},
}
@article{Bri08a,
author = {Bridges, Douglas S.},
title = {Product a-frames and proximity},
journal = {Mathematical Logic Quarterly},
volume = {54},
number = {1},
year = {2008},
pages = {12--25},
}
@article{Bri08b,
author = {Briseid, E. M.},
title = {Fixed points of generalized contractive mappings},
journal = {Journal of Nonlinear and Convex Analysis},
volume = {9},
number = {2},
year = {2008},
pages = {181--204},
}
@article{Bri09,
author = {Bridges, Douglas S.},
title = {Constructive notions of equicontinuity},
journal = {Archive for Mathematical Logic},
volume = {48},
number = {5},
year = {2009},
pages = {437--448},
doi = {10.1007/s00153-009-0131-9},
}
@article{Bri09a,
author = {Briseid, Eyvind Martol},
title = {Logical aspects of rates of convergence in metric spaces},
journal = {Journal of Symbolic Logic},
volume = {74},
number = {4},
year = {2009},
pages = {1401--1428},
doi = {10.2178/jsl/1254748697},
}
@article{Bri10,
author = {Bridges, Douglas S.},
title = {Continuity and {L}ipschitz constants for projections},
journal = {J. Log. Algebr. Program.},
volume = {79},
number = {1},
year = {2010},
pages = {2--9},
doi = {10.1016/j.jlap.2009.02.002},
}
@article{Bri10a,
author = {Bridges, Douglas S.},
title = {Inheriting the anti-{S}pecker property},
journal = {Doc. Math.},
volume = {15},
year = {2010},
pages = {973--980},
}
@article{Bri10b,
author = {Briseid, Eyvind Martol},
title = {A new uniformity for asymptotic contractions in the sense of {K}irk},
journal = {Int. J. Math. Stat.},
volume = {6},
number = {S10},
year = {2010},
pages = {2--13},
}
@article{Bri11,
author = {Bridges, Douglas S.},
title = {Omniscience, sequential compactness, and the anti-{S}pecker property},
journal = {Log. J. IGPL},
volume = {19},
number = {1},
year = {2011},
pages = {53--61},
doi = {10.1093/jigpal/jzq001},
}
@article{Bri11a,
author = {Bridges, Douglas S.},
title = {The anti-{S}pecker property, uniform sequential continuity, and a countable compactness property},
journal = {Log. J. IGPL},
volume = {19},
number = {1},
year = {2011},
pages = {174--182},
doi = {10.1093/jigpal/jzq039},
}
@article{Bri11b,
author = {Bridges, Douglas S.},
title = {Locating subsets of {$B(H)$} relative to seminorms inducing the strong-operator topology},
journal = {J. Log. Anal.},
volume = {3},
year = {2011},
pages = {Paper 3, 11},
doi = {10.4115/jla.2011.3.3},
}
@article{Bri11c,
author = {Bridges, Douglas S.},
title = {Characterising weak-operator continuous linear functionals on {$B(H)$} constructively},
journal = {Doc. Math.},
volume = {16},
year = {2011},
pages = {597--617},
}
@article{Bri12,
author = {Bridges, Douglas S.},
title = {Reflections on function spaces},
journal = {Ann. Pure Appl. Logic},
volume = {163},
number = {2},
year = {2012},
pages = {101--110},
doi = {10.1016/j.apal.2011.06.018},
}
@article{Bri12a,
author = {Bridges, Douglas S.},
title = {Almost new pre-apartness from old},
journal = {Ann. Pure Appl. Logic},
volume = {163},
number = {8},
year = {2012},
pages = {1009--1015},
doi = {10.1016/j.apal.2011.12.023},
}
@article{Bri12b,
author = {Bridges, Douglas S.},
title = {Compactness notions for an apartness space},
journal = {Arch. Math. Logic},
volume = {51},
number = {5-6},
year = {2012},
pages = {517--534},
doi = {10.1007/s00153-012-0279-6},
}
@article{Bri12c,
author = {Bridges, Douglas S.},
title = {Precompact apartness spaces},
journal = {Log. Methods Comput. Sci.},
volume = {8},
number = {2},
year = {2012},
pages = {2:15, 10},
doi = {10.2168/LMCS-8(2:15)2012},
}
@article{Bri12d,
author = {Bridges, Douglas S.},
title = {How to construct a product of a-frames},
journal = {Math. Log. Q.},
volume = {58},
number = {4-5},
year = {2012},
pages = {281--293},
doi = {10.1002/malq.201110059},
}
@incollection{Bri12e,
author = {Bridges, Douglas S.},
title = {Constructive Solutions of Ordinary Differential Equations},
editor = {Ulrich Berger and Hannes Diener and Peter Schuster and Monika Seisenberger},
booktitle = {Logic, Construction, Computation},
series = {Ontos Mathematical Logic},
volume = {3},
publisher = {de Gruyter},
year = {2012},
pages = {67--77},
}
@article{Bri13,
author = {Bridges, Douglas S.},
title = {Characterising dominated weak-operator continuous functionals on subspaces of {${B}(H)$}},
journal = {Ann. Pure Appl. Logic},
volume = {164},
number = {4},
year = {2013},
pages = {416--420},
doi = {10.1016/j.apal.2012.10.005},
}
@article{Bri14,
author = {Bridges, Douglas S.},
title = {Locating {$Ax$}, where {$A$} is a subspace of {$B(H)$}},
journal = {Log. Methods Comput. Sci.},
number = {The Ninth International Conference on Computability and Complexity in Analysis (CCA) 2012},
year = {2014},
pages = {2:9, 10},
doi = {10.2168/LMCS-10(2:9)2014},
}
@article{Bri14a,
author = {Bridges, Douglas S.},
title = {Tightly bordered convex and co-convex sets},
journal = {Sci. Math. Jpn.},
volume = {77},
number = {1},
year = {2014},
pages = {45--57},
}
@article{Bri14b,
author = {Bridges, Douglas S.},
title = {Tightly bordered convex and co-convex sets},
journal = {Scientiae Mathematicae Japonicae},
volume = {77},
number = {1},
year = {2014},
pages = {45--57},
}
@article{Bri16,
author = {Bridges, Douglas S.},
title = {Apartness spaces and uniform neighbourhood structures},
journal = {Annals of Pure and Applied Logic},
volume = {167},
number = {9},
year = {2016},
pages = {850--864},
doi = {10.1016/j.apal.2016.04.007},
}
@incollection{Bri16a,
author = {Bridges, Douglas S.},
title = {The continuum hypothesis implies excluded middle},
booktitle = {Concepts of proof in mathematics, philosophy, and computer science},
series = {Ontos Math. Log.},
volume = {6},
publisher = {De Gruyter, Berlin},
year = {2016},
pages = {111--114},
}
@article{Bri18,
author = {Bridges, Douglas S.},
title = {Intuitionistic sequential compactness?},
journal = {Indagationes Mathematicae},
volume = {29},
number = {6},
year = {2018},
pages = {1477--1496},
doi = {10.1016/j.indag.2017.10.011},
}
@article{Bri76,
author = {Bridges, Douglas S.},
title = {Some notes on continuity in constructive analysis},
journal = {Bull. London Math. Soc.},
volume = {8},
number = {2},
year = {1976},
pages = {179--182},
}
@article{Bri77,
author = {Bridges, Douglas S.},
title = {A constructive look at orthonormal bases in {H}ilbert space},
journal = {Amer. Math. Monthly},
volume = {84},
number = {3},
year = {1977},
pages = {189--191},
}
@article{Bri77a,
author = {Bridges, Douglas S.},
title = {The constructive {R}adon-{N}ikod\'ym theorem},
journal = {Pacific J. Math.},
volume = {70},
number = {1},
year = {1977},
pages = {51--65},
}
@article{Bri78,
author = {Bridges, Douglas S.},
title = {A note on {M}orse's lambda-notation in set theory},
journal = {Zeitschrift f\"ur Mathematische Logik und Grundlagen der Mathematik},
volume = {24},
number = {2},
year = {1978},
pages = {113--114},
}
@article{Bri78a,
author = {Bridges, Douglas S.},
title = {On weak operator compactness of the unit ball of ${L}({H})$},
journal = {Zeitschrift f\"ur Mathematische Logik und Grundlagen der Mathematik},
volume = {24},
number = {6},
year = {1978},
pages = {493--494},
}
@article{Bri78b,
author = {Bridges, Douglas S.},
title = {On the connectivity of convex sets},
journal = {The Bulletin of the London Mathematical Society},
volume = {10},
number = {1},
year = {1978},
pages = {86--90},
}
@article{Bri78c,
author = {Bridges, Douglas S.},
title = {On continuous mappings between locally compact metric spaces},
journal = {The Bulletin of the London Mathematical Society},
volume = {10},
number = {2},
year = {1978},
pages = {201--208},
}
@article{Bri78d,
author = {Bridges, D. S.},
title = {More on the connectivity of convex sets},
journal = {Proceedings of the American Mathematical Society},
volume = {68},
number = {2},
year = {1978},
pages = {214--216},
}
@book{Bri79,
author = {Bridges, Douglas S.},
title = {Constructive Functional Analysis},
publisher = {Pitman},
address = {London},
year = {1979},
}
@article{Bri79a,
author = {Bridges, Douglas S.},
title = {Connectivity properties of metric spaces},
journal = {Pacific Journal of Mathematics},
volume = {80},
number = {2},
year = {1979},
pages = {325--331},
}
@article{Bri79b,
author = {Bridges, Douglas S.},
title = {On the constructive convergence of series of independent functions},
journal = {Zeitschrift f\"ur Mathematische Logik und Grundlagen der Mathematik},
volume = {25},
number = {1},
year = {1979},
pages = {93--96},
}
@article{Bri79c,
author = {Bridges, Douglas S.},
title = {A criterion for compactness in metric spaces?},
journal = {Zeitschrift f\"ur Mathematische Logik und Grundlagen der Mathematik},
volume = {25},
number = {2},
year = {1979},
pages = {97--98},
}
@article{Bri79d,
author = {Bridges, Douglas S.},
title = {Geometric intuition and elementary constructive analysis},
journal = {Zeitschrift f\"ur Mathematische Logik und Grundlagen der Mathematik},
volume = {25},
number = {6},
year = {1979},
pages = {521--523},
}
@article{Bri80,
author = {Bridges, Douglas S.},
title = {On the foundations of best-approximation theory},
journal = {Journal of Approximation Theory},
volume = {28},
number = {3},
year = {1980},
pages = {273--292},
}
@article{Bri80a,
author = {Bridges, Douglas S.},
title = {A constructive development of {C}hebyshev approximation theory},
journal = {Journal of Approximation Theory},
volume = {30},
number = {2},
year = {1980},
pages = {99--120},
}
@inproceedings{Bri81,
author = {Bridges, Douglas S.},
title = {Towards a constructive foundation for quantum mechanics},
editor = {Richman, F.},
booktitle = {Constructive Mathematics},
series = {Lecture Notes in Mathematics},
volume = {873},
year = {1981},
pages = {260--273},
note = {Proc. New Mexico State Univ. Conf., Aug. 11--15, 1980, Las Cruces, NM},
}
@article{Bri81a,
author = {Bridges, Douglas S.},
title = {A constructive look at positive linear functionals on ${L}({H})$},
journal = {Pacific Journal of Mathematics},
volume = {95},
number = {1},
year = {1981},
pages = {11--25},
}
@article{Bri81b,
author = {Bridges, Douglas S.},
title = {On the isolation of zeroes of an analytic function},
journal = {Pacific Journal of Mathematics},
volume = {96},
number = {1},
year = {1981},
pages = {13--22},
}
@article{Bri81c,
author = {Bridges, Douglas S.},
title = {Correction to: ``{O}n the isolation of zeroes of an analytic function''\ [{P}acific {J}. {M}ath. {\bf 96} (1981), no. 1, 13--22; {M}{R} 82k:03095]},
journal = {Pacific Journal of Mathematics},
volume = {97},
number = {2},
year = {1981},
pages = {487--488},
}
@article{Bri81d,
author = {Bridges, Douglas S.},
title = {A constructive analysis of the {R}emes algorithm},
journal = {Journal of Approximation Theory},
volume = {32},
number = {4},
year = {1981},
pages = {257--270},
}
@article{Bri81e,
author = {Bridges, Douglas S.},
title = {A constructive proximinality property of finite-dimensional linear subspaces},
journal = {The Rocky Mountain Journal of Mathematics},
volume = {11},
number = {4},
year = {1981},
pages = {491--497},
}
@article{Bri81f,
author = {Bridges, Douglas S.},
title = {On {M}ontel's proof of the great {P}icard theorem},
journal = {The American Mathematical Monthly},
volume = {88},
number = {1},
year = {1981},
pages = {45--47},
}
@article{Bri82,
author = {Bridges, Douglas S.},
title = {Preference and utility: a constructive development},
journal = {Journal of Mathematical Economics},
volume = {9},
number = {1-2},
year = {1982},
pages = {165--185},
}
@article{Bri82a,
author = {Bridges, Douglas S.},
title = {Lipschitz constants and moduli of continuity for the {C}hebyshev projection},
journal = {Proceedings of the American Mathematical Society},
volume = {85},
number = {4},
year = {1982},
pages = {557--561},
}
@incollection{Bri82b,
author = {Bridges, Douglas S.},
title = {Recent progress in constructive approximation theory},
booktitle = {The L. E. J. Brouwer Centenary Symposium (Noordwijkerhout, 1981)},
publisher = {North-Holland},
address = {Amsterdam},
year = {1982},
pages = {41--50},
}
@article{Bri83,
author = {Bridges, Douglas S.},
title = {Numerical representation of intransitive preferences on a countable set},
journal = {Journal of Economic Theory},
volume = {30},
number = {1},
year = {1983},
pages = {213--217},
}
@article{Bri83a,
author = {Bridges, Douglas S.},
title = {A numerical representation of preferences with intransitive indifference},
journal = {Journal of Mathematical Economics},
volume = {11},
number = {1},
year = {1983},
pages = {25--42},
}
@article{Bri85,
author = {Bridges, Douglas S.},
title = {Representing interval orders by a single real-valued function},
journal = {Journal of Economic Theory},
volume = {36},
number = {1},
year = {1985},
pages = {149--155},
}
@article{Bri85a,
author = {Bridges, Douglas S.},
title = {Operator ranges, integrable sets, and the functional calculus},
journal = {Houston Journal of Mathematics},
volume = {11},
number = {1},
year = {1985},
pages = {31--44},
}
@article{Bri86,
author = {Bridges, Douglas S.},
title = {Numerical representation of interval orders on a topological space},
journal = {Journal of Economic Theory},
volume = {38},
number = {1},
year = {1986},
pages = {160--166},
}
@incollection{Bri87,
author = {Bridges, Douglas S.},
title = {A constructive {M}orse theory of sets},
booktitle = {Mathematical logic and its applications (Druzhba, 1986)},
publisher = {Plenum},
address = {New York},
year = {1987},
pages = {61--79},
}
@article{Bri88,
author = {Bridges, Douglas S.},
title = {Locatedness, convexity, and Lebesque measurability},
journal = {Quart. J. Math. Oxford Ser. 2},
volume = {39},
year = {1988},
pages = {411--421},
}
@article{Bri88a,
author = {Bridges, Douglas S.},
title = {The {E}uclidean distance construction of order homomorphisms},
journal = {Mathematical Social Sciences},
volume = {15},
number = {2},
year = {1988},
pages = {179--188},
}
@article{Bri89,
author = {Bridges, Douglas S.},
title = {A general constructive intermediate value theorem},
journal = {Zeitschrift f\"ur Mathematische Logik und Grundlagen der Mathematik},
volume = {35},
year = {1989},
pages = {433--435},
}
@article{Bri89a,
author = {Bridges, Douglas S.},
title = {The constructive theory of preference relations on a locally compact space},
journal = {Indagationes Mathematicae},
volume = {51},
number = {2},
year = {1989},
pages = {141--165},
}
@article{Bri89b,
author = {Bridges, Douglas S.},
title = {Approximate interpolation by functions in a {H}aar space},
journal = {Journal of Approximation Theory},
volume = {57},
number = {1},
year = {1989},
pages = {35--39},
}
@article{Bri90,
author = {Bridges, Douglas S.},
title = {Preference, indifference, and {M}arkov's principle},
journal = {Mathematical Social Sciences},
volume = {20},
number = {2},
year = {1990},
pages = {131--145},
}
@incollection{Bri90a,
author = {Bridges, Douglas S.},
title = {Order isomorphisms---a constructive measure-theoretic view},
booktitle = {Mathematical logic},
publisher = {Plenum},
address = {New York},
year = {1990},
pages = {243--255},
}
@article{Bri91,
author = {Bridges, Douglas S.},
title = {The constructive inequivalence of various notions of preference ordering},
journal = {Mathematical Social Sciences},
volume = {21},
number = {2},
year = {1991},
pages = {169--176},
}
@article{Bri93,
author = {Bridges, Douglas S.},
title = {Sequential, pointwise, and uniform continuity: a constructive note},
journal = {Mathematical Logic Quarterly},
volume = {39},
number = {1},
year = {1993},
pages = {55--61},
}
@article{Bri93a,
author = {Bridges, Douglas S.},
title = {Constructive notions of strict convexity},
journal = {Mathematical Logic Quarterly},
volume = {39},
number = {3},
year = {1993},
pages = {295--300},
}
@incollection{Bri94a,
author = {Bridges, Douglas S.},
title = {A constructive look at the real number line},
booktitle = {Real numbers, generalizations of the reals, and theories of continua},
publisher = {Kluwer Acad. Publ.},
address = {Dordrecht},
year = {1994},
pages = {29--92},
}
@article{Bri94b,
author = {Bridges, Douglas S.},
title = {The constructive theory of preference relations on a locally compact space. {I}{I}},
journal = {Mathematical Social Sciences},
volume = {27},
number = {1},
year = {1994},
pages = {1--9},
}
@article{Bri95,
author = {Bridges, Douglas S.},
title = {Constructive mathematics and unbounded operations},
journal = {J. Philos. Logic},
volume = {24},
number = {5},
year = {1995},
pages = {549--561},
}
@inproceedings{Bri98,
author = {Bridges, Douglas S.},
title = {Bishop's Principle},
editor = {Ko, Ker-I and Nerode, Anil and Pour-El, Marian B. and Weihrauch, Klaus and Wiedermann, Ji{\v{r}}{\'{\i}}},
booktitle = {Computability and Complexity in Analysis},
series = {Informatik Berichte},
volume = {235},
publisher = {FernUniversit\"at Hagen},
year = {1998},
month = aug,
pages = {17--20},
note = {CCA Workshop, Brno, Czech Republic, August, 1998},
}
@incollection{Bri98a,
author = {Bridges, Douglas S.},
title = {Constructive truth in practice},
booktitle = {Truth in mathematics (Mussomeli, 1995)},
publisher = {Oxford Univ. Press},
address = {New York},
year = {1998},
pages = {53--69},
}
@article{Bri99,
author = {Bridges, Douglas S.},
title = {Constructive mathematics: a foundation for computable analysis},
journal = {Theoretical Computer Science},
volume = {219},
year = {1999},
pages = {95--109},
}
@article{Bri99a,
author = {Bridges, Douglas S.},
title = {Can constructive mathematics be applied in physics?},
journal = {Journal of Philosophical Logic},
volume = {28},
number = {5},
year = {1999},
pages = {439--453},
}
@incollection{Bri99b,
author = {Bridges, Douglas S.},
title = {Constructive methods in mathematical economics},
editor = {Herden, Gerhard and Knoche, Norbert and Seidl, Christian and Trockel, Walter},
booktitle = {Mathematical utility theory (Essen, 1997)},
series = {Journal of Economy},
volume = {Supp. 8},
publisher = {Springer},
address = {Vienna},
year = {1999},
pages = {1--21},
}
@article{BRJM92,
author = {Bridges, D. S. and Richman, F. and Julian, W. H. and Mines, R.},
title = {Extensions and fixed points of contractive maps in $R^n$},
journal = {Journal of Mathematical Analysis and Applications},
volume = {165},
number = {2},
year = {1992},
pages = {438--456},
}
@inproceedings{Bro07,
author = {Brodhead, Paul},
title = {Enumerations of {$\Pi^0_1$} classes: acceptability and decidable classes},
editor = {Cenzer, Douglas and Dillhage, Ruth and Grubba, Tanja and Weihrauch, Klaus},
booktitle = {Proceedings of the Third International Conference on Computability and Complexity in Analysis},
series = {Electronic Notes in Theoretical Computer Science},
volume = {167},
publisher = {Elsevier},
address = {Amsterdam},
year = {2007},
pages = {289--301},
note = {{CCA} 2006, Gainesville, Florida, USA, November 1--5, 2006},
}
@article{Bro21,
author = {Brown, Tyler A.},
title = {Computing on the {B}anach space {$C[0,1]$}},
journal = {Computability},
volume = {10},
number = {3},
year = {2021},
pages = {257--270},
doi = {10.3233/COM-200306},
}
@article{Bro25,
author = {Brouwer, L.E.J.},
title = {Intuitionistischer {B}eweis des {J}ordanschen {K}urvensatzes},
journal = {Koninklijke Nederl. Akad. Wentensch, Proc.},
volume = {28},
year = {1925},
pages = {503--508},
note = {translated in: A. Heyting (ed.), Collected Works, Vol. 1, Philosophy and Foundations of Mathematics, North-Holland, Amsterdam, 1975, 315--320},
}
@article{Bro52,
author = {Brouwer, L.E.J.},
title = {An intuitionist correction of the fixed-point theorem on the sphere},
journal = {Proceedings of the Royal Society. London. Series A.},
volume = {213},
year = {1952},
pages = {1--2},
}
@article{Bro54,
author = {Brouwer, L.E.J.},
title = {Points and spaces},
journal = {Canad. Journ. Math.},
volume = {6},
year = {1954},
pages = {1--17},
}
@inproceedings{Bro75,
author = {Brouwer, L.E.J.},
title = {The unreliability of logical principles},
editor = {Heyting, A.},
booktitle = {Collected Works, Vol. 1, Philosophy and Foundations of Mathematics},
publisher = {North-Holland},
address = {Amsterdam},
year = {1975},
pages = {107--111},
}
@inproceedings{Bro75a,
author = {Brouwer, L.E.J.},
title = {Fixed cores which cannot be found, though they are claimed to exist by classical theorems},
editor = {Heyting, A.},
booktitle = {Collected Works, Vol. 1, Philosophy and Foundations of Mathematics},
publisher = {North-Holland},
address = {Amsterdam},
year = {1975},
pages = {516--518},
}
@book{Bro75b,
author = {Brouwer, L.E.J.},
title = {Collected Works, Vol. 1, Philosophy and Foundations of Mathematics},
publisher = {North-Holland},
address = {Amsterdam},
year = {1975},
note = {Heyting, A. (ed)},
}
@book{Bro75c,
author = {Brouwer, L.E.J.},
title = {Collected Works, Vol. 2, Geometry, Analysis, Topology and Mechanics},
editor = {Freudenthal, H.},
publisher = {North-Holland},
address = {Amsterdam},
year = {1976},
}
@book{Bro81,
author = {Brouwer, L.E.J.},
title = {Brouwer's Cambridge Lectures on Intuitionism},
editor = {van Dalen, D.},
publisher = {Cambridge University Press},
year = {1981},
}
@article{BRS00,
author = {Bridges, Douglas S. and Richman, Fred and Schuster, Peter},
title = {Linear independence without choice},
journal = {Annals of Pure and Applied Logic},
volume = {101},
number = {1},
year = {2000},
pages = {95--102},
}
@article{BRS00a,
author = {Bridges, Douglas S. and Richman, Fred and Schuster, Peter},
title = {A weak countable choice principle},
journal = {Proceedings of the American Mathematical Society},
volume = {128},
number = {9},
year = {2000},
pages = {2749--2752},
}
@article{BRS00b,
author = {Bridges, Douglas S. and Richman, Fred and Schuster, Peter},
title = {Adjoints, absolute values, and polar decompositions},
journal = {J. Operator Theory},
volume = {44},
number = {2},
year = {2000},
pages = {243--254},
}
@article{BRS17,
author = {Braverman, M. and Rojas, C. and Schneider, J.},
title = {Tight space-noise tradeoffs in computing the ergodic measure},
journal = {Sbornik: Mathematics},
volume = {208},
number = {12},
publisher = {{IOP} Publishing},
year = {2017},
month = {dec},
pages = {1758--1783},
doi = {10.1070/sm8884},
}
@article{BRY14,
author = {Binder, Ilia and Rojas, Cristobal and Yampolsky, Michael},
title = {Computable {C}arath{\'e}odory theory},
journal = {Adv. Math.},
volume = {265},
year = {2014},
pages = {280--312},
doi = {10.1016/j.aim.2014.07.039},
}
@article{BRY15,
author = {Binder, Ilia and Rojas, Cristobal and Yampolsky, Michael},
title = {Non-computable impressions of computable external rays of quadratic polynomials},
journal = {Communications in Mathematical Physics},
volume = {335},
number = {2},
year = {2015},
pages = {739--757},
doi = {10.1007/s00220-014-2218-3},
}
@article{BRY19,
author = {Binder, Ilia and Rojas, Cristobal and Yampolsky, Michael},
title = {Carath\'{e}odory convergence and harmonic measure},
journal = {Potential Analysis},
volume = {51},
number = {4},
year = {2019},
pages = {499--509},
doi = {10.1007/s11118-018-9721-7},
}
@article{BRY96,
author = {Bridges, Douglas S. and Richman, Fred and Yuchuan, Wang},
title = {Sets, complements and boundaries},
journal = {Indagationes Mathematicae},
volume = {7},
number = {4},
year = {1996},
pages = {425--445},
}
@article{BS00,
author = {Bridges, Douglas S. and Svozil, Karl},
title = {Constructive mathematics and quantum physics},
journal = {J. Theor. Physics},
volume = {39},
year = {2000},
pages = {501--513},
}
@inproceedings{BS03,
author = {Bauer, Andrej and Simpson, Alex},
title = {Locally non-compact spaces and continuity principles},
editor = {Brattka, Vasco and Schr{\"{o}}der, Matthias and Weihrauch, Klaus and Zhong, Ning},
booktitle = {Computability and Complexity in Analysis},
series = {Informatik Berichte},
volume = {302},
publisher = {FernUniversit\"at in Hagen},
year = {2003},
month = aug,
pages = {103--116},
note = {International Conference, CCA 2003, Cincinnati, USA, August 28--30, 2003},
}
@article{BS04,
author = {Bauer, Andrej and Simpson, Alex},
title = {Two constructive embedding-extension theorems with applications to continuity principles and to {B}anach-{M}azur computability},
journal = {Mathematical Logic Quarterly},
volume = {50},
number = {4,5},
year = {2004},
pages = {351--369},
}
@article{BS04a,
author = {Binns, Stephen and Simpson, Stephen G.},
title = {Embeddings into the {M}edvedev and {M}uchnik lattices of {$\Pi^0_1$} classes},
journal = {Archive for Mathematical Logic},
volume = {43},
number = {3},
year = {2004},
pages = {399--414},
doi = {10.1007/s00153-003-0195-x},
}
@inproceedings{BS05,
author = {Brattka, Vasco and Schr{\"{o}}der, Matthias},
title = {Computing with Sequences, Weak Topologies and the Axiom of Choice},
editor = {Ong, Luke},
booktitle = {Computer science logic},
series = {Lecture Notes in Computer Science},
volume = {3634},
publisher = {Springer},
year = {2005},
pages = {462--476},
}
@article{BS05a,
author = {Badaev, Serikzhan and Spreen, Dieter},
title = {A note on partial numberings},
journal = {Mathematical Logic Quarterly},
volume = {51},
number = {2},
year = {2005},
pages = {129--136},
}
@article{BS06,
author = {Bridges, Douglas S. and Schuster, Peter},
title = {A simple constructive proof of {K}ronecker's density theorem},
journal = {Elemente der Mathematik},
volume = {61},
year = {2006},
pages = {152--154},
}
@article{BS06a,
author = {Berger, Josef and Schuster, Peter},
title = {Classifying {D}ini's Theorem},
journal = {Notre Dame Journal of Formal Logic},
volume = {47},
number = {2},
year = {2006},
pages = {253--262},
}
@inproceedings{BS07,
author = {Bauer, Andrej and Stone, Christopher A.},
title = {{RZ}: {A} Tool for Bringing Constructive and Computable Mathematics Closer to Programming Practice},
editor = {Cooper, S. Barry and L{\"o}we, Benedikt and Sorbi, Andrea},
booktitle = {Computation and Logic in the Real World},
series = {Lecture Notes in Computer Science},
volume = {4497},
publisher = {Springer},
address = {Berlin},
year = {2007},
pages = {28--42},
note = {Third Conference on Computability in Europe, CiE 2007, Siena, Italy, June 18-23, 2007},
}
@article{BS07a,
author = {Becher, Ver{\'{o}}nica and Grigorieff, Serge},
title = {Random reals {\'a} la {C}haitin with or without prefix-freeness},
journal = {Theoretical Computer Science},
volume = {385},
year = {2007},
pages = {193--201},
}
@article{BS07b,
author = {Buser, Peter and Scarpellini, Bruno},
title = {Undecidable propositions by {ODE}'s},
journal = {Annales Academi\ae \ Scientiarum Fennic\ae . Mathematica},
volume = {32},
number = {2},
year = {2007},
pages = {317--340},
}
@article{BS09,
author = {Bauer, Andrej and Stone, Christopher A.},
title = {{RZ}: a Tool for Bringing Constructive and Computable Mathematics Closer to Programming Practice},
journal = {Journal of Logic and Computation},
volume = {19},
number = {1},
year = {2009},
pages = {17--43},
}
@incollection{BS09a,
author = {Berger, Josef and Schuster, Peter},
title = {Dini's theorem in the light of reverse mathematics},
booktitle = {Logicism, intuitionism, and formalism},
series = {Synth. Libr.},
volume = {341},
publisher = {Springer},
address = {Dordrecht},
year = {2009},
pages = {153--166},
doi = {10.1007/978-1-4020-8926-8_7},
}
@article{BS10,
author = {Buser, Peter and Scarpellini, Bruno},
title = {Recursive analysis of singular ordinary differential equations},
journal = {Annals of Pure and Applied Logic},
volume = {162},
year = {2010},
pages = {20--35},
}
@article{BS16,
author = {Buser, Peter and Scarpellini, Bruno},
title = {Undecidability through {F}ourier series},
journal = {Annals of Pure and Applied Logic},
volume = {167},
number = {7},
year = {2016},
pages = {507--524},
doi = {10.1016/j.apal.2016.03.001},
}
@article{BS16a,
author = {Berger, Josef and Svindland, Gregor},
title = {A separating hyperplane theorem, the fundamental theorem of asset pricing, and {M}arkov's principle},
journal = {Annals of Pure and Applied Logic},
volume = {167},
number = {11},
year = {2016},
pages = {1161--1170},
doi = {10.1016/j.apal.2016.05.003},
}
@article{BS16b,
author = {Berger, Josef and Svindland, Gregor},
title = {Convexity and constructive infima},
journal = {Archive for Mathematical Logic},
volume = {55},
number = {7-8},
year = {2016},
pages = {873--881},
doi = {10.1007/s00153-016-0502-y},
}
@article{BS16c,
author = {Berger, Ulrich and Spreen, Dieter},
title = {A coinductive approach to computing with compact sets},
journal = {Journal of Logic and Analysis},
volume = {8},
year = {2016},
pages = {Paper No. 3, 35},
}
@article{BS17,
author = {Berger, Josef and Schwichtenberg, Helmut},
title = {A bound for {D}ickson's lemma},
journal = {Logical Methods in Computer Science},
volume = {13},
number = {3},
year = {2017},
pages = {30:8},
}
@article{BS18,
author = {Berger, Josef and Svindland, Gregor},
title = {{B}rouwer's fan theorem and convexity},
journal = {The Journal of Symbolic Logic},
volume = {83},
number = {4},
year = {2018},
pages = {1363--1375},
doi = {10.1017/jsl.2018.49},
}
@article{BS19,
author = {Berger, Josef and Svindland, Gregor},
title = {Convexity and unique minimum points},
journal = {Archive for Mathematical Logic},
volume = {58},
number = {1-2},
year = {2019},
pages = {27--34},
doi = {10.1007/s00153-018-0619-2},
}
@article{BS19a,
author = {Bauer, Andrej and Swan, Andrew},
title = {Every metric space is separable in function realizability},
journal = {Logical Methods in Computer Science},
volume = {15},
number = {2},
year = {2019},
pages = {Paper No. 14, 7},
}
@article{BSBP19,
author = {Boche, Holger and Schaefer, Rafael F. and Baur, Sebastian and Poor, H. Vincent},
title = {On the algorithmic computability of the secret key and authentication capacity under channel, storage, and privacy leakage constraints},
journal = {IEEE Transactions on Signal Processing},
volume = {67},
number = {17},
year = {2019},
pages = {4636--4648},
doi = {10.1109/TSP.2019.2929467},
}
@inproceedings{BSP18,
author = {Boche, H. and Schaefer, R. F. and Poor, H. V.},
title = {Performance Evaluation of Secure Communication Systems on {T}uring Machines},
booktitle = {2018 IEEE International Workshop on Information Forensics and Security (WIFS)},
year = {2018},
pages = {1--7},
doi = {10.1109/WIFS.2018.8630789},
}
@inproceedings{BSP19,
author = {Boche, H. and Schaefer, R. F. and Poor, H. Vincent},
title = {Identification Capacity of Correlation-Assisted Discrete Memoryless Channels: Analytical Properties and Representations},
booktitle = {2019 IEEE International Symposium on Information Theory (ISIT)},
year = {2019},
pages = {470--474},
doi = {10.1109/ISIT.2019.8849851},
}
@inproceedings{BSP19a,
author = {Boche, H. and Schaefer, R.F. and Poor, H. Vincent},
title = {Detectability of Denial-of-service Attacks on Communication Systems},
booktitle = {ICASSP 2019 - 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)},
year = {2019},
pages = {2532--2536},
doi = {10.1109/ICASSP.2019.8683553},
}
@inproceedings{BSP19b,
author = {Boche, H. and Schaefer, R.F. and Poor, H. V.},
title = {On the Structure of the Capacity Formula for General Finite State Channels with Applications},
booktitle = {2019 IEEE Information Theory Workshop (ITW)},
year = {2019},
pages = {1--5},
doi = {10.1109/ITW44776.2019.8989035},
}
@article{BSP20,
author = {Boche, Holger and Schaefer, Rafael F. and Poor, H. Vincent},
title = {Denial-of-service attacks on communication systems: detectability and jammer knowledge},
journal = {IEEE Transactions on Signal Processing},
volume = {68},
year = {2020},
pages = {3754--3768},
doi = {10.1109/tsp.2020.2993165},
}
@article{BSP20a,
author = {Boche, H. and Schaefer, R.F. and Poor, H. V.},
title = {Secure Communication and Identification Systems -- Effective Performance Evaluation on {T}uring Machines},
journal = {IEEE Transactions on Information Forensics and Security},
volume = {15},
year = {2020},
pages = {1013--1025},
doi = {10.1109/TIFS.2019.2932226},
}
@inproceedings{BSP20b,
author = {Boche, H. and Schaefer, R.F. and Poor, H. V.},
title = {Robust Transmission Over Channels with Channel Uncertainty: an Algorithmic Perspective},
booktitle = {ICASSP 2020 - 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)},
year = {2020},
pages = {5230--5234},
doi = {10.1109/ICASSP40776.2020.9054467},
}
@article{BSP20c,
author = {Boche, Holger and Schaefer, Rafael F. and Poor, H. Vincent},
title = {Identification capacity of channels with feedback: discontinuity behavior, super-activation, and {T}uring computability},
journal = {Institute of Electrical and Electronics Engineers. Transactions on Information Theory},
volume = {66},
number = {10},
year = {2020},
pages = {6184--6199},
doi = {10.1109/TIT.2020.3005458},
}
@article{BSP20d,
author = {Boche, Holger and Schaefer, Rafael F. and Poor, H. Vincent},
title = {Communication under channel uncertainty: an algorithmic perspective and effective construction},
journal = {IEEE Transactions on Signal Processing},
volume = {68},
year = {2020},
pages = {6224--6239},
doi = {10.1109/TSP.2020.3027902},
}
@article{BSP20e,
author = {Boche, Holger and Schaefer, Rafael F. and Poor, H. Vincent},
title = {Shannon meets {T}uring: non-computability and non-approximability of the finite state channel capacity},
journal = {Communications in Information and Systems},
volume = {20},
number = {2},
year = {2020},
pages = {81--116},
doi = {10.4310/CIS.2020.v20.n2.a1},
}
@article{BSR15,
author = {Braverman, Mark and Schneider, Jonathan and Rojas, Crist{\'o}bal},
title = {Space-bounded {C}hurch-{T}uring thesis and computational tractability of closed systems},
journal = {Physical review letters},
volume = {115},
number = {9},
publisher = {APS},
year = {2015},
pages = {098701},
}
@article{BSS06,
author = {Battenfeld, Ingo and Schr{\"o}der, Matthias and Simpson, Alex},
title = {Compactly generated domain theory},
journal = {Mathematical Structures in Computer Science},
volume = {16},
number = {2},
publisher = {Cambridge University Press},
year = {2006},
pages = {141--161},
doi = {10.1017/S0960129506005202},
}
@article{BSS07,
author = {Battenfeld, Ingo and Schr{\"o}der, Matthias and Simpson, Alex},
title = {A Convenient Category of Domains},
journal = {Electronic Notes in Theoretical Computer Science},
volume = {172},
publisher = {Elsevier Science Publishers B. V.},
address = {Amsterdam, The Netherlands},
year = {2007},
pages = {69--99},
}
@article{BST02,
author = {Blanck, Jens and Stoltenberg-Hansen, Viggo and Tucker, John V.},
title = {Domain representations of partial functions, with applications to spatial objects and constructive volume geometry},
journal = {Theoretical Computer Science},
volume = {284},
number = {2},
year = {2002},
pages = {207--240},
}
@inproceedings{BST08,
author = {Blanck, Jens and Stoltenberg-Hansen, Viggo and Tucker, John V.},
title = {Stability for Effective Algebras},
editor = {Brattka, Vasco and Dillhage, Ruth and Grubba, Tanja and Klutsch, Angela},
booktitle = {{CCA} 2008, Fifth International Conference on Computability and Complexity in Analysis},
series = {Electronic Notes in Theoretical Computer Science},
volume = {221},
publisher = {Elsevier},
year = {2008},
pages = {3--15},
note = {{CCA} 2008, Fifth International Conference, Hagen, Germany, August 21--24, 2008},
}
@article{BST17,
author = {Bauwens, Bruno and Shen, Alexander and Takahashi, Hayato},
title = {Conditional Probabilities and van {L}ambalgen's Theorem Revisited},
journal = {Theory of Computing Systems},
volume = {61},
number = {4},
year = {2017},
pages = {1315-1336},
doi = {10.1007/s00224-017-9789-2},
}
@article{BSV02,
author = {Bridges, Douglas S. and Schuster, Peter and V{\^{\i}}{\c{t}}{\u{a}}, Lumini{\c{t}}a},
title = {Apartness, Topology, and Uniformity: a Constructive View},
journal = {Mathematical Logic Quarterly},
volume = {48},
number = {Suppl. 1},
year = {2002},
pages = {16--28},
}
@inproceedings{BSVP19,
author = {Boche, H. and Schaefer, R. F. and Vincent Poor, H.},
title = {On the Computability of the Secret Key Capacity under Rate Constraints},
booktitle = {ICASSP 2019 - 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)},
year = {2019},
pages = {2427--2431},
doi = {10.1109/ICASSP.2019.8683122},
}
@proceedings{BSW02,
title = {Computability and Complexity in Analysis},
editor = {Brattka, Vasco and Schr{\"{o}}der, Matthias and Weihrauch, Klaus},
series = {Electronic Notes in Theoretical Computer Science},
volume = {66(1)},
publisher = {Elsevier},
address = {Amsterdam},
year = {2002},
note = {5th International Workshop, {CCA} 2002, M{\'{a}}laga, Spain, July 12--13, 2002},
doi = {10.1016/S1571-0661(05)80392-5},
}
@proceedings{BSW05,
title = {Proceedings of the 6th Workshop on Computability and Complexity in Analysis},
editor = {Brattka, Vasco and Staiger, Ludwig and Weihrauch, Klaus},
series = {Electronic Notes in Theoretical Computer Science},
volume = {120},
publisher = {Elsevier},
address = {Amsterdam},
year = {2005},
note = {6th International Workshop, {CCA} 2004, Wittenberg, Germany, August 16--20, 2004},
}
@inproceedings{BT05,
author = {Bauer, Andrej and Taylor, Paul},
title = {The {D}edekind reals in abstract {S}tone duality},
editor = {Grubba, Tanja and Hertling, Peter and Tsuiki, Hideki and Weihrauch, Klaus},
booktitle = {Computability and Complexity in Analysis},
series = {Informatik Berichte},
volume = {326},
publisher = {FernUniversit\"at in Hagen},
year = {2005},
month = jul,
pages = {25--64},
note = {Proccedings, Second International Conference, CCA 2005, Kyoto, Japan, August 25--29, 2005},
}
@article{BT07,
author = {Beggs, Edwin J. and Tucker, John V.},
title = {Can {N}ewtonian systems, bounded in space, time, mass and energy compute all functions?},
journal = {Theoretical Computer Science},
volume = {371},
year = {2007},
pages = {4--19},
}
@article{BT09,
author = {Bauer, Andrej and Taylor, Paul},
title = {The {D}edekind reals in abstract {S}tone duality},
journal = {Mathematical Structures in Computer Science},
volume = {19},
number = {4},
year = {2009},
pages = {757--838},
doi = {10.1017/S0960129509007695},
}
@inproceedings{Buy00,
author = {Buy, Dmitry},
title = {Some Remarks about Fixpoint Theorems},
editor = {Blanck, Jens and Brattka, Vasco and Hertling, Peter and Weihrauch, Klaus},
booktitle = {Computability and Complexity in Analysis},
series = {Informatik Berichte},
volume = {272},
publisher = {FernUniversit\"at Hagen},
year = {2000},
month = sep,
pages = {43--52},
note = {CCA 2000 Workshop, Swansea, Wales, September 17--19, 2000},
}
@article{BV00,
author = {Bridges, Douglas S. and V{\^{\i}}{\c{t}}{\u{a}}, Lumini{\c{t}}a},
title = {Constructing extensions of ultraweakly continuous linear functionals},
journal = {J. Functional Analysis},
volume = {178},
number = {2},
year = {2000},
pages = {421--434},
}
@article{BV01,
author = {Bridges, Douglas S. and V{\^{\i}}{\c{t}}{\u{a}}, Lumini{\c{t}}a},
title = {Characterising Near Continuity Constructively},
journal = {Mathematical Logic Quarterly},
volume = {47},
number = {4},
year = {2001},
pages = {535--538},
}
@article{BV02,
author = {Bridges, Douglas S. and V{\^{\i}}{\c{t}}{\u{a}}, Lumini{\c{t}}a},
title = {Cauchy nets in the constructive theory of apartness spaces},
journal = {Scientiae Mathematicae Japonicae},
volume = {56},
number = {1},
year = {2002},
pages = {123--132},
}
@article{BV03,
author = {Bridges, Douglas S. and V{\^{\i}}{\c{t}}{\u{a}}, Lumini{\c{t}}a},
title = {Apartness spaces as a framework for constructive topology},
journal = {Annals of Pure and Applied Logic},
volume = {119},
number = {1-3},
year = {2003},
pages = {61--83},
}
@article{BV03a,
author = {Bridges, Douglas S. and V{\^{\i}}{\c{t}}{\u{a}}, Lumini{\c{t}}a},
title = {A proof-technique in uniform space theory},
journal = {The Journal of Symbolic Logic},
volume = {68},
number = {3},
year = {2003},
pages = {795--802},
}
@article{BV03b,
author = {Bridges, Douglas S. and V{\^{\i}}{\c{t}}{\u{a}}, Lumini{\c{t}}a},
title = {Separatedness in constructive topology},
journal = {Documenta Mathematica},
volume = {8},
year = {2003},
pages = {567--576},
}
@article{BV03c,
author = {Bridges, Douglas S. and V{\^{\i}}{\c{t}}{\u{a}}, Lumini{\c{t}}a},
title = {Cauchy nets in uniform apartness spaces},
journal = {Revue Roumaine de Math\'ematiques Pures et Appliqu\'ees},
volume = {48},
number = {5-6},
year = {2003},
pages = {467--474},
}
@article{BV03d,
author = {Bridges, Douglas S. and V{\^{\i}}{\c{t}}{\u{a}}, Lumini{\c{t}}a},
title = {Strong and uniform continuity---the uniform space case},
journal = {LMS Journal of Computation and Mathematics},
volume = {6},
year = {2003},
pages = {326--334},
}
@article{BV04a,
author = {Bridges, Douglas S. and V{\^{\i}}{\c{t}}{\u{a}}, Lumini{\c{t}}a},
title = {Corrigendum to: ``{A} proof-technique in uniform space theory''},
journal = {The Journal of Symbolic Logic},
volume = {69},
number = {1},
year = {2004},
pages = {328},
}
@inproceedings{BV05,
author = {Bridges, Douglas S. and V{\^{\i}}{\c{t}}{\u{a}}, Lumini{\c{t}}a},
title = {A general constructive proof technique},
editor = {Brattka, Vasco and Staiger, Ludwig and Weihrauch, Klaus},
booktitle = {Proceedings of the 6th Workshop on Computability and Complexity in Analysis},
series = {Electronic Notes in Theoretical Computer Science},
volume = {120},
publisher = {Elsevier},
address = {Amsterdam},
year = {2005},
pages = {31--43},
note = {6th International Workshop, {CCA} 2004, Wittenberg, Germany, August 16--20, 2004},
}
@inproceedings{BV05a,
author = {Bridges, Douglas S. and V{\^{\i}}{\c{t}}{\u{a}}, Lumini{\c{t}}a},
title = {An extension theorem for ultraweakly continuous linear functionals on $B(X,Y)$},
editor = {Grubba, Tanja and Hertling, Peter and Tsuiki, Hideki and Weihrauch, Klaus},
booktitle = {Computability and Complexity in Analysis},
series = {Informatik Berichte},
volume = {326},
publisher = {FernUniversit\"at in Hagen},
year = {2005},
month = jul,
pages = {77--89},
note = {Proccedings, Second International Conference, CCA 2005, Kyoto, Japan, August 25--29, 2005},
}
@inproceedings{BV05b,
author = {Bridges, Douglas S. and V{\^{\i}}{\c{t}}{\u{a}}, Lumini{\c{t}}a},
title = {Proximal connectedness},
editor = {Grubba, Tanja and Hertling, Peter and Tsuiki, Hideki and Weihrauch, Klaus},
booktitle = {Computability and Complexity in Analysis},
series = {Informatik Berichte},
volume = {326},
publisher = {FernUniversit\"at in Hagen},
year = {2005},
month = jul,
pages = {91--101},
note = {Proccedings, Second International Conference, CCA 2005, Kyoto, Japan, August 25--29, 2005},
}
@book{BV06,
author = {Bridges, Douglas S. and V{\^{\i}}{\c{t}}{\u{a}}, Lumini{\c{t}}a Simona},
title = {Techniques of Constructive Analysis},
publisher = {Springer},
address = {New York},
year = {2006},
}
@article{BV06a,
author = {Bridges, Douglas S. and V{\^{\i}}{\c{t}}{\u{a}}, Lumini{\c{t}}a},
title = {Pre-apartness structures on spaces of functions},
journal = {Journal of Complexity},
volume = {22},
number = {6},
year = {2006},
pages = {881--893},
}
@article{BV08,
author = {Bridges, Douglas S. and V{\^{\i}}{\c{t}}{\u{a}}, Lumini{\c{t}}a},
title = {Proximal Connectedness},
journal = {Fundamenta Informaticae},
volume = {83},
number = {1--2},
year = {2008},
pages = {25--34},
}
@article{BV09,
author = {Bridges, D. S. and V{\^{\i}}{\c{t}}{\u{a}}, L. S.},
title = {A constructive theory of apartness on lattices},
journal = {Scientiae Mathematicae Japonicae},
volume = {69},
number = {2},
year = {2009},
pages = {187--206},
}
@incollection{BV09a,
author = {Bridges, Douglas S. and V{\^{\i}}{\c{t}}{\u{a}}, Lumini{\c{t}}a Simona},
title = {Journey into apartness space},
booktitle = {Logicism, intuitionism, and formalism},
series = {Synth. Libr.},
volume = {341},
publisher = {Springer},
address = {Dordrecht},
year = {2009},
pages = {167--187},
doi = {10.1007/978-1-4020-8926-8_8},
}
@book{BV11,
author = {Bridges, Douglas S. and V{\^{\i}}{\c{t}}{\u{a}}, Lumini{\c{t}}a Simona},
title = {Apartness and Uniformity},
series = {Theory and Applications of Computability},
publisher = {Springer},
address = {Heidelberg},
year = {2011},
pages = {xiv+198},
doi = {10.1007/978-3-642-22415-7},
}
@inproceedings{BV12,
author = {Bridges, Douglas S. and V{\^{\i}}{\c{t}}{\u{a}}, Luminita},
title = {Constructing the infimum of two projections},
booktitle = {Computation, physics and beyond},
series = {Lecture Notes in Comput. Sci.},
volume = {7160},
publisher = {Springer},
address = {Heidelberg},
year = {2012},
pages = {46--58},
}
@article{BV13,
author = {Bridges, Douglas S. and V{\^{\i}}{\c{t}}a, Lumini{\c{t}}a S.},
title = {A first constructive look at the comparison of projections},
journal = {Log. J. IGPL},
volume = {21},
number = {1},
year = {2013},
pages = {14--27},
doi = {10.1093/jigpal/jzs019},
}
@article{BV98,
author = {Boldi, Paolo and Vigna, Sebastiano},
title = {$\delta$-uniform {BSS} Machines},
journal = {Journal of Complexity},
volume = {14},
number = {2},
year = {1998},
pages = {234--256},
}
@article{BV99,
author = {Boldi, Paolo and Vigna, Sebastiano},
title = {Equality is a Jump},
journal = {Theoretical Computer Science},
volume = {219},
year = {1999},
pages = {49--64},
}
@article{BW02,
author = {Bridges, Douglas S. and Ward, Nicholas Dudley},
title = {Kernels of seminorms in constructive analysis},
journal = {Theoretical Computer Science},
volume = {284},
number = {2},
year = {2002},
pages = {259--267},
}
@article{BW20,
author = {Burr, Michael and Wolf, Christian},
title = {Computability at zero temperature},
journal = {Nonlinearity},
volume = {33},
number = {11},
publisher = {IOP Publishing},
year = {2020},
month = {oct},
pages = {6157--6175},
doi = {10.1088/1361-6544/ab9c71},
}
@article{BW97,
author = {Bridges, Douglas S. and Wang, Yuchuan},
title = {Constructive aspects of the {D}irichlet problem},
journal = {Journal of Universal Computer Science},
volume = {3},
number = {11},
year = {1997},
pages = {1148--1161 (electronic)},
note = {Proceedings of the First Japan-New Zealand Workshop on Logic in Computer Science (Auckland, 1997)},
}
@article{BW97a,
author = {Bridges, Douglas S. and Wang, Yuchuan},
title = {Constructing cutoff functions},
journal = {New Zealand Journal of Mathematics},
volume = {26},
number = {1},
year = {1997},
pages = {25--30},
}
@article{BW98a,
author = {Bridges, Douglas S. and Wang, Yuchuan},
title = {Constructive weak solutions of the {D}irichlet problem},
journal = {The Journal of the London Mathematical Society. Second Series},
volume = {57},
number = {3},
year = {1998},
pages = {655--667},
}
@article{BW98b,
author = {Bridges, Douglas S. and Wang, Yuchuan},
title = {Constructing best approximations on a {J}ordan curve},
journal = {Journal of Approximation Theory},
volume = {94},
number = {2},
year = {1998},
pages = {222--234},
}
@article{BW98c,
author = {Bridges, Douglas S. and Wang, Yuchuan},
title = {Weak solutions of the {D}irichlet problem and the locatedness of ${H}^1_0(\Omega)$},
journal = {New Zealand Journal of Mathematics},
volume = {27},
number = {1},
year = {1998},
pages = {1--5},
}
@article{BW99,
author = {Brattka, Vasco and Weihrauch, Klaus},
title = {Computability on Subsets of {E}uclidean Space {I}: Closed and Compact Subsets},
journal = {Theoretical Computer Science},
volume = {219},
year = {1999},
pages = {65--93},
}
@article{BY06,
author = {Brattka, Vasco and Yoshikawa, Atsushi},
title = {Towards computability of elliptic boundary value problems in variational formulation},
journal = {Journal of Complexity},
volume = {22},
number = {6},
year = {2006},
pages = {858--880},
}
@article{BY06a,
author = {Braverman, M. and Yampolsky, M.},
title = {Non-computable {J}ulia sets},
journal = {Journal of the American Mathematical Society},
volume = {19},
number = {3},
year = {2006},
pages = {551--578},
doi = {10.1090/S0894-0347-05-00516-3},
}
@inproceedings{BY07,
author = {Braverman, Mark and Yampolsky, Michael},
title = {Constructing non-computable {J}ulia sets},
booktitle = {S{TOC}'07---{P}roceedings of the 39th {A}nnual {ACM} {S}ymposium on {T}heory of {C}omputing},
publisher = {ACM},
address = {New York},
year = {2007},
pages = {709--716},
doi = {10.1145/1250790.1250893},
}
@book{BY08,
author = {Braverman, Mark and Yampolsky, Michael},
title = {Computability of {J}ulia Sets},
series = {Algorithms and Computation in Mathematics},
volume = {23},
publisher = {Springer},
address = {Berlin},
year = {2008},
}
@article{BY08a,
author = {Braverman, Mark and Yampolsky, Michael},
title = {Computability of {J}ulia sets},
journal = {Moscow Mathematical Journal},
volume = {8},
number = {2},
year = {2008},
pages = {185--231, 399},
}
@article{BY09a,
author = {Braverman, Mark and Yampolsky, Michael},
title = {Constructing locally connected non-computable {J}ulia sets},
journal = {Communications in Mathematical Physics},
volume = {291},
number = {2},
year = {2009},
pages = {513--532},
doi = {10.1007/s00220-009-0858-5},
}
@inproceedings{BZ02,
author = {Brattka, Vasco and Ziegler, Martin},
title = {Computability of linear equations},
editor = {Baeza-Yates, Ricardo and Montanari, Ugo and Santoro, Nicola},
booktitle = {Foundations of Information Technology in the Era of Network and Mobile Computing},
series = {IFIP International Federation for Information Processing},
volume = {223},
publisher = {Kluwer Academic Publishers},
address = {Dordrecht},
year = {2002},
pages = {95--106},
note = {2nd IFIP International Conference on Theoretical Computer Science, Montr{\'e}al, Canada, August 25--30, 2002},
}
@article{Cal02,
author = {Calude, Cristian S.},
title = {A characterization of c.e. random reals},
journal = {Theoretical Computer Science},
volume = {271},
year = {2002},
pages = {3--14},
}
@article{Cal02a,
author = {Calude, Cristian S.},
title = {Chaitin $\Omega$ numbers, {S}olovay machines, and {G}{\"{o}}del incompleteness},
journal = {Theoretical Computer Science},
volume = {284},
number = {2},
year = {2002},
pages = {269--277},
}
@phdthesis{Cam01,
author = {Campagnolo, Manuel Lameiras},
title = {Computational Complexity of Real Valued Recursive Functions and Analog Circuits},
school = {Instituto Superior T{\'e}cnico, Universidade T{\'e}cnica de Lisboa},
address = {Lisbon},
year = {2001},
}
@inproceedings{Cam02,
author = {Campagnolo, Manuel Lameiras},
title = {The Complexity of Real Recursive Functions},
editor = {Calude, C.S. and Dinneen, M.J. and Peper, F.},
booktitle = {Unconventional Models of Computation},
series = {Lecture Notes in Computer Science},
volume = {2509},
publisher = {Springer},
address = {Berlin},
year = {2002},
pages = {1--14},
note = {Third International Conference, UMC 2002, Kobe, Japan, October 15-19, 2002},
}
@phdthesis{Car13,
author = {Carroy, Rapha{\"e}l},
title = {Functions of the first {B}aire class},
school = {University of Lausanne and University Paris 7},
year = {2013},
}
@article{Car13a,
author = {Carroy, Rapha{\"e}l},
title = {A quasi-order on continuous functions},
journal = {Journal of Symbolic Logic},
volume = {78},
number = {2},
year = {2013},
pages = {663--648},
doi = {10.2178/jsl.7802150},
}
@book{Car19,
author = {Carl, Merlin},
title = {Ordinal Computability, An Introduction to Infinitary Machines},
volume = {9},
publisher = {de Gruyter},
address = {Berlin},
year = {2019},
}
@article{Car21,
author = {Carl, Merlin},
title = {Effectivity and reducibility with ordinal {T}uring machines},
journal = {Computability},
volume = {10},
number = {4},
year = {2021},
pages = {289--304},
doi = {10.3233/COM-210307},
}
@article{Car22,
author = {Carl, Merlin},
title = {Space-bounded {OTM}s and {$\rm REG^\infty$}},
journal = {Computability},
volume = {11},
number = {1},
year = {2022},
pages = {41--56},
doi = {10.3233/com-200327},
}
@inproceedings{CCHK99,
author = {Calude, C. S. and Coles, R. and Hertling, P. H. and Khoussainov, B.},
title = {Degree Theoretic Aspects of Computably Enumerable Reals},
editor = {S. B. Cooper and J. K. Truss},
booktitle = {Models and Computability},
series = {London Math.\ Society Lecture Note Series},
volume = {259},
publisher = {Cambridge University Press},
address = {Cambridge},
year = {1999},
pages = {23--39},
note = {Invited Papers from {L}ogic {C}olloquium 1997, {L}eeds.},
}
@proceedings{CDGW07,
title = {Proceedings of the Third International Conference on Computability and Complexity in Analysis},
editor = {Cenzer, Douglas and Dillhage, Ruth and Grubba, Tanja and Weihrauch, Klaus},
series = {Electronic Notes in Theoretical Computer Science},
volume = {167},
publisher = {Elsevier},
address = {Amsterdam},
year = {2007},
note = {{CCA} 2006, Gainesville, Florida, USA, November 1--5, 2006},
}
@article{CDHP20,
author = {Cholak, Peter A. and Dzhafarov, Damir D. and Hirschfeldt, Denis R. and Patey, Ludovic},
title = {Some results concerning the {$\rm SRT^2_2$} vs. {COH} problem},
journal = {Computability},
volume = {9},
number = {3-4},
year = {2020},
pages = {193--217},
doi = {10.3233/COM-190251},
}
@inproceedings{CDK08,
author = {Cenzer, Douglas and Dashti, S. Ali and King, Jonathan L.F.},
title = {Effective Symbolic Dynamics},
editor = {Dillhage, Ruth and Grubba, Tanja and Sorbi, Andrea and Weihrauch, Klaus and Zhong, Ning},
booktitle = {Proceedings of the Fourth International Conference on Computability and Complexity in Analysis ({CCA} 2007)},
series = {Electronic Notes in Theoretical Computer Science},
volume = {202},
publisher = {Elsevier},
year = {2008},
pages = {89--99},
note = {{CCA} 2007, Siena, Italy, June 16--18, 2007},
}
@article{CDK08a,
author = {Cenzer, Douglas and Dashti, S. Ali and King, Jonathan L.F.},
title = {Computable symbolic dynamics},
journal = {Mathematical Logic Quarterly},
volume = {54},
number = {5},
year = {2008},
pages = {460--469},
}
@article{CDM12,
author = {Couch, P. J. and Daniel, B. D. and McNicholl, Timothy H.},
title = {Computing space-filling curves},
journal = {Theory of Computing Systems},
volume = {50},
number = {2},
year = {2012},
pages = {370--386},
doi = {10.1007/s00224-010-9306-3},
}
@inproceedings{CDTW10,
author = {Cenzer, Douglas and Dashti, Ali and Toska, Ferit and Wyman, Sebastian},
title = {Computability of countable subshifts},
booktitle = {Programs, proofs, processes},
series = {Lecture Notes in Comput. Sci.},
volume = {6158},
publisher = {Springer},
address = {Berlin},
year = {2010},
pages = {88--97},
doi = {10.1007/978-3-642-13962-8_10},
}
@article{CDTW12,
author = {Cenzer, Douglas and Dashti, Ali and Toska, Ferit and Wyman, Sebastian},
title = {Computability of countable subshifts in one dimension},
journal = {Theory Comput. Syst.},
volume = {51},
number = {3},
year = {2012},
pages = {352--371},
doi = {10.1007/s00224-011-9358-z},
}
@article{Cei55,
author = {Ce{\u{\i}}tin, G.S.},
title = {On a theorem of {C}auchy in constructive analysis ({R}ussian)},
journal = {Uspehi Mat.\ Nauk},
volume = {10},
year = {1955},
pages = {207--209},
}
@inproceedings{Cei56,
author = {Ce{\u{\i}}tin, G.S.},
title = {Uniform recursiveness of algorithmic operators on general recursive functions and a canonical representation for constructive functions of a real argument ({R}ussian)},
booktitle = {Proc.\ Third All--Union Math.\ Congr., Moscow 1956},
volume = {1},
publisher = {Izdat.\ Akad.\ Nauk SSSR},
address = {Moscow},
year = {1956},
pages = {188--189},
}
@article{Cei59,
author = {Ce{\u{\i}}tin, G.S.},
title = {Algorithmic Operators in Constructive Complete Separable Metric Spaces ({R}ussian)},
journal = {Doklady Akademii Nauk},
volume = {128},
year = {1959},
pages = {49--52},
}
@article{Cei62,
author = {Ce{\u{\i}}tin, G.S.},
title = {Algorithmic Operators in Constructive Metric Spaces ({R}ussian)},
journal = {Tr.\ Mat.\ Inst.\ Steklov},
volume = {67},
year = {1962},
pages = {295--361},
note = {(English trans. in AMS Trans. 64, 1967)},
}
@article{Cei62a,
author = {Ce{\u{\i}}tin, G.S.},
title = {Mean value theorems in constructive analysis ({R}ussian)},
journal = {Tr.\ Mat.\ Inst.\ Steklov},
volume = {67},
year = {1962},
pages = {362--384},
note = {(English trans. in AMS Trans. 98, 1971)},
}
@article{Cei64,
author = {Ce{\u{\i}}tin, G.S.},
title = {Three theorems on constructive functions ({R}ussian)},
journal = {Tr.\ Mat.\ Inst.\ Steklov},
volume = {72},
year = {1964},
pages = {537--543},
note = {(English trans. in AMS Trans. 100, 1972)},
}
@article{Cei70,
author = {Ce{\u{\i}}tin, G.S.},
title = {On upper bounds of recursively enumerable sets of constructive real numbers ({R}ussian)},
journal = {Tr.\ Mat.\ Inst.\ Steklov},
volume = {113},
year = {1970},
pages = {102--172},
}
@inproceedings{Cen93,
author = {Cenzer, Douglas},
title = {Effective real dynamics},
editor = {Crossley, John N. and Remmel, Jefferey B. and Shore, Richard A. and Sweedler, Moss E.},
booktitle = {Logical Methods in Honor of Anil Nerode's Sixtieth Birthday},
series = {Progress in Computer Science and Applied Logic},
volume = {12},
publisher = {Birkh\"auser},
address = {Boston},
year = {1993},
pages = {162--177},
}
@incollection{Cen99,
author = {Cenzer, Douglas},
title = {{$\Pi^0_1$}--classes in computability theory},
editor = {Griffor, Edward R.},
booktitle = {Handbook of Computability Theory},
series = {Studies in Logic and the Foundations of Mathematics},
volume = {140},
publisher = {Elsevier},
address = {Amsterdam},
year = {1999},
pages = {37--85},
}
@article{CFHR22,
author = {Coronel, Daniel and Frank, Alexander and Hoyrup, Mathieu and Rojas, Crist{\'o}bal},
title = {Realizing semicomputable simplices by computable dynamical systems},
journal = {Theoretical Computer Science},
volume = {933},
year = {2022},
pages = {43--54},
doi = {10.1016/j.tcs.2022.09.001},
}
@inproceedings{CG00,
author = {Ciaffaglione, Alberto and Di Gianantonio, Pietro},
title = {A Co-inductive Approach to Real Numbers},
editor = {Coquand, Thierry and Dybjer, Peter and Nordstr{\"{o}}m, Bengt and Smith, Jan},
booktitle = {Types for Proofs and Programs},
series = {Lecture Notes in Computer Science},
volume = {1956},
publisher = {Springer},
address = {Berlin},
year = {2000},
pages = {114--130},
note = {International Workshop, TYPES'99, L{\"{o}}keberg, Sweden, June 12--16, 1999},
}
@inproceedings{CG02,
author = {Ciaffaglione, Alberto and Di Gianantonio, Pietro},
title = {A Tour with Constructive Real Numbers},
editor = {Callaghan, P. and Luo, Z. and McKinna, J. and Pollack, R.},
booktitle = {Types for Proofs and Programs},
series = {LNCS},
volume = {2277},
publisher = {Springer},
address = {Berlin},
year = {2002},
pages = {41--52},
note = {International Workshop, TYPES 2000, Durham, UK, December 8--12, 2000},
}
@article{CG06,
author = {Ciaffaglione, Alberto and Di Gianantonio, Pietro},
title = {A certified, corecursive implementation of exact real numbers},
journal = {Theoretical Computer Science},
volume = {351},
number = {1},
year = {2006},
pages = {39--51},
}
@inproceedings{CG08,
author = {Collins, Peter and Gra{\c{c}}a, Daniel},
title = {Effective Computability of Solutions of Ordinary Differential Equations The Thousand Monkeys Approach},
editor = {Brattka, Vasco and Dillhage, Ruth and Grubba, Tanja and Klutsch, Angela},
booktitle = {{CCA} 2008, Fifth International Conference on Computability and Complexity in Analysis},
series = {Electronic Notes in Theoretical Computer Science},
volume = {221},
publisher = {Elsevier},
year = {2008},
pages = {103--114},
note = {{CCA} 2008, Fifth International Conference, Hagen, Germany, August 21--24, 2008},
}
@article{CG09,
author = {Collins, Pieter and Gra{\c{c}}a, Daniel S.},
title = {Effective computability of solutions of differential inclusions: the ten thousand monkeys approach},
journal = {Journal of Universal Computer Science},
volume = {15},
number = {6},
year = {2009},
pages = {1162--1185},
doi = {10.3217/jucs-015-06-1206},
}
@incollection{CGK93,
author = {Cosnard, Michel and Garzon, Max and Koiran, Pascal},
title = {Computability properties of low-dimensional dynamical systems},
booktitle = {S{TACS} 93 ({W}\"urzburg, 1993)},
series = {Lecture Notes in Comput. Sci.},
volume = {665},
publisher = {Springer, Berlin},
year = {1993},
pages = {365--373},
doi = {10.1007/3-540-56503-5_37},
}
@inproceedings{CH07,
author = {Cenzer, Douglas and Hinman, Peter G.},
title = {{M}edvedev degrees of generalized r.e. separating classes},
editor = {Cenzer, Douglas and Dillhage, Ruth and Grubba, Tanja and Weihrauch, Klaus},
booktitle = {Proceedings of the Third International Conference on Computability and Complexity in Analysis},
series = {Electronic Notes in Theoretical Computer Science},
volume = {167},
publisher = {Elsevier},
address = {Amsterdam},
year = {2007},
pages = {203--223},
note = {{CCA} 2006, Gainesville, Florida, USA, November 1--5, 2006},
}
@article{Ch12,
author = {Ch{\'e}ritat, Arnaud},
title = {Braverman and {Y}ampolsky: {\it {C}omputability of {J}ulia sets} [book review of MR2466298]},
journal = {Found. Comput. Math.},
volume = {12},
number = {1},
year = {2012},
pages = {123--137},
doi = {10.1007/s10208-011-9111-7},
}
@inproceedings{CH20,
author = {Callard, Antonin and Hoyrup, Mathieu},
title = {Descriptive Complexity on Non-{P}olish Spaces},
editor = {Paul, Christophe and Bl{\"a}ser, Markus},
booktitle = {37th International Symposium on Theoretical Aspects of Computer Science ({STACS} 2020)},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
volume = {154},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
year = {2020},
pages = {8:1--8:16},
doi = {10.4230/LIPIcs.STACS.2020.8},
}
@article{CH98,
author = {Calude, Cristian S. and Hertling, Peter},
title = {Computable approximations of reals: An information-theoretic analysis},
journal = {Fundamenta Informaticae},
volume = {33},
number = {2},
year = {1998},
pages = {105--120},
}
@article{CH99,
author = {Chadzelek, Thomas and Hotz, G{\"u}nter},
title = {Analytic machines},
journal = {Theoretical Computer Science},
volume = {219},
year = {1999},
pages = {151--167},
}
@article{Cha87a,
author = {Chaitin, G.J.},
title = {Incompleteness theorems for random reals},
journal = {Adv. in Appl. Math.},
volume = {8},
year = {1987},
pages = {119--146},
}
@phdthesis{Cha98,
author = {Chadzelek, Thomas},
title = {Analytische Maschinen},
school = {Technische Fakult\"at der Universit\"at des Saarlandes},
address = {Saarbr\"ucken},
year = {1998},
}
@article{CHJW01,
author = {Calude, C.S. and Hertling, P. and J{\"u}rgensen, H. and Weihrauch, K.},
title = {Randomness on Full Shift Spaces},
journal = {Chaos, Solitons \& Fractals},
volume = {12},
number = {3},
year = {2001},
pages = {491--503},
}
@article{CHK97,
author = {Calude, Cristian S. and Hertling, Peter and Khoussainov, Bakhadyr},
title = {Do the Zeros of {R}iemann's {Z}eta-Function Form a Random Sequence?},
journal = {Bulletin of the European Association for Theoretical Computer Science},
volume = {62},
year = {1997},
pages = {199--207},
}
@article{CHKW01,
author = {Calude, Cristian S. and Hertling, Peter H. and Khoussainov, Bakhadyr and Wang, Yongge},
title = {Recursively enumerable reals and {C}haitin $\Omega$ numbers},
journal = {Theoretical Computer Science},
volume = {255},
year = {2001},
pages = {125--149},
}
@inproceedings{CHKW98,
author = {Calude, Cristian S. and Hertling, Peter and Khoussainov, Bakhadyr and Yongge Wang},
title = {Recursively enumerable reals and {C}haitin $\Omega$ numbers},
editor = {Morvan, Michel et al.},
booktitle = {STACS'98},
series = {Lecture Notes in Computer Science},
volume = {1373},
publisher = {Springer},
address = {Berlin},
year = {1998},
pages = {596--606},
note = {15th Annual Symposium on Theoretical Aspects of Computer Science. Paris, France, February 25--27, 1998},
}
@article{CHM09,
author = {Chubb, Jennifer and Hirst, Jeffry L. and McNicholl, Timothy H.},
title = {Reverse mathematics, computability, and partitions of trees},
journal = {Journal of Symbolic Logic},
volume = {74},
number = {1},
year = {2009},
pages = {201--215},
doi = {10.2178/jsl/1231082309},
}
@inproceedings{Cho95,
author = {Chou, Arthur W.},
title = {Some complexity issues in complex analysis},
editor = {Ko, Ker-I and Weihrauch, Klaus},
booktitle = {Computability and Complexity in Analysis},
series = {Informatik Berichte},
volume = {190},
publisher = {FernUniversit\"at Hagen},
year = {1995},
month = sep,
pages = {91--98},
note = {CCA Workshop, Hagen, August 19--20, 1995},
}
@phdthesis{Cia03,
author = {Ciaffaglione, Alberto},
title = {Certified Reasoning on Real Numbers and Objects in Co-inductive Type Theory},
school = {Universit{\'a} degli Studi di Udine},
year = {2003},
}
@article{CIV21,
author = {{\v{C}}i{\v{c}}kovi{\'c}, Eugen and Iljazovi{\'c}, Zvonko and Valid{\v{z}}i{\'c}, Lucija},
title = {Chainable and circularly chainable semicomputable sets in computable topological spaces},
journal = {Archive for Mathematical Logic},
volume = {58},
year = {2021},
pages = {885--897},
doi = {10.1007/s00153-019-00667-w},
}
@incollection{CJ00,
author = {Cenzer, Douglas and Jockusch, Jr., Carl G.},
title = {{$\Pi\sb 1\sp 0$} classes--Structure and Applications},
booktitle = {Computability theory and its applications},
series = {Contemporary Mathematics},
volume = {257},
publisher = {American Mathematical Society},
address = {Providence},
year = {2000},
pages = {39--59},
}
@inproceedings{CJ94,
author = {Calude, Cristian and J\"{u}rgensen, Helmut},
title = {Randomness as an invariant for number representations},
editor = {Maurer, H. and Karhum{\"a}ki, J. and Rozenberg, G.},
booktitle = {Results and Trends in Theoretical Computer Science},
publisher = {Springer},
address = {Berlin},
year = {1994},
pages = {44--66},
}
@article{CK04,
author = {Chou, Arthur W. and Ko, Ker-I},
title = {On the complexity of finding paths in a two-dimensional domain {I}: Shortest paths},
journal = {Mathematical Logic Quarterly},
volume = {50},
number = {6},
year = {2004},
pages = {551--572},
}
@inproceedings{CK05,
author = {Chou, Arthur W. and Ko, Ker-I},
title = {On the complexity of finding paths in a two-dimensional domain {II}: Picewise straight-line paths},
editor = {Brattka, Vasco and Staiger, Ludwig and Weihrauch, Klaus},
booktitle = {Proceedings of the 6th Workshop on Computability and Complexity in Analysis},
series = {Electronic Notes in Theoretical Computer Science},
volume = {120},
publisher = {Elsevier},
address = {Amsterdam},
year = {2005},
pages = {45--57},
note = {6th International Workshop, {CCA} 2004, Wittenberg, Germany, August 16--20, 2004},
}
@article{CK05a,
author = {Chou, Arthur W. and Ko, Ker-I},
title = {The computational complexity of distance functions of two-dimensional domains},
journal = {Theoretical Computer Science},
volume = {337},
year = {2005},
pages = {360--369},
}
@article{CK95,
author = {Chou, Arthur and Ko, Ker-I},
title = {Computational complexity of two-dimensional regions},
journal = {SIAM Journal on Computing},
volume = {24},
year = {1995},
pages = {923--947},
}
@article{CKWW09,
author = {Cenzer, Douglas and Kihara, Takayuki and Weber, Rebecca and Wu, Guohua},
title = {Immunity and non-cupping for closed sets},
journal = {Tbilisi Mathematical Journal},
volume = {2},
year = {2009},
pages = {77--94},
}
@article{CL06,
author = {Chernavskya, A.V. and Leksineb, V.P.},
title = {Unrecognizability of manifolds},
journal = {Annals of Pure and Applied Logic},
volume = {141},
number = {3},
year = {2006},
pages = {447--455},
}
@article{Cle69,
author = {Cleave, J.P.},
title = {The primitive recursive analysis of ordinary differential equations and the complexity of their solutions},
journal = {Journal of Computer and Systems Sciences},
volume = {3},
year = {1969},
pages = {447--455},
doi = {10.1016/S0022-0000(69)80031-0},
}
@inproceedings{CLM07,
author = {Costa, Jos\'{e} F\'{e}lix and Loff, Bruno and Mycka, Jerzy},
title = {The New Promise of Analog Computation},
editor = {Cooper, S. Barry and L{\"o}we, Benedikt and Sorbi, Andrea},
booktitle = {Computation and Logic in the Real World},
series = {Lecture Notes in Computer Science},
volume = {4497},
publisher = {Springer},
address = {Berlin},
year = {2007},
pages = {189--195},
note = {{T}hird Conference on Computability in Europe, CiE 2007, Siena, Italy, June 18-23, 2007},
}
@article{CLW09,
author = {Cenzer, Douglas and Laforte, Geoffrey and Wu, Guohua},
title = {Pseudojumps and {$\Pi^0_1$} Classes},
journal = {Journal of Logic and Computation},
volume = {19},
number = {1},
year = {2009},
pages = {77--87},
}
@inproceedings{CM01,
author = {Campagnolo, Manuel Lameiras and Moore, Cristopher},
title = {Upper and lower bounds on continuous-time computation},
editor = {Antoniou, I. and Calude, C.S. and Dinneen, M.J.},
booktitle = {Unconventional Models of Computation, UMC2'K},
series = {Discrete Mathematics and Theoretical Computer Science},
publisher = {Springer},
address = {London},
year = {2001},
pages = {135--153},
note = {Second International Conference, UMC 2000, Brussels, Belgium},
}
@article{CMC01,
author = {Campagnolo, Manuel Lameiras and Moore, Cristopher and Costa, Jos\'{e} F\'{e}lix},
title = {Iteration, Inequalities, and Differentiability in Analog Computers},
journal = {Journal of Complexity},
volume = {16},
number = {4},
year = {2001},
pages = {642--660},
}
@article{CMC02,
author = {Campagnolo, Manuel Lameiras and Moore, Cristopher and Costa, Jos\'{e} F\'{e}lix},
title = {An Analog Characterization of the {G}rzegorczyk Hierarchy},
journal = {Journal of Complexity},
volume = {18},
number = {4},
year = {2002},
pages = {977--1000},
}
@article{CMS19,
author = {Clanin, Joe and McNicholl, Timothy H. and Stull, Don M.},
title = {Analytic computable structure theory and {$L^p$} spaces},
journal = {Fundamenta Mathematicae},
volume = {244},
number = {3},
year = {2019},
pages = {255--285},
doi = {10.4064/fm448-5-2018},
}
@inproceedings{CN16,
author = {Carotenuto, Gemma and Nies, Andr\'{e}},
title = {Lightface {$\Pi^0_3$}--Completeness of Density Sets Under Effective {W}adge Reducibility},
editor = {Beckmann, Arnold and Bienvenu, Laurent and Jonoska, Nata\v{s}a},
booktitle = {Pursuit of the Universal},
series = {Lecture Notes in Computer Science},
volume = {9709},
publisher = {Springer},
address = {Switzerland},
year = {2016},
pages = {234--239},
note = {12th Conference on Computability in Europe, CiE 2016, Paris, France, June 27 - July 1, 2016},
doi = {10.1007/978-3-319-40189-8_24},
}
@article{CNR11,
author = {Collins, Pieter and Niqui, Milad and Revol, Nathalie},
title = {A validated real function calculus},
journal = {Math. Comput. Sci.},
volume = {5},
number = {4},
year = {2011},
pages = {437--467},
doi = {10.1007/s11786-011-0102-5},
}
@inproceedings{CO07,
author = {Campagnolo, Manuel L. and Ojakian, Kerry},
title = {The methods of approximation and lifting in real computation},
editor = {Cenzer, Douglas and Dillhage, Ruth and Grubba, Tanja and Weihrauch, Klaus},
booktitle = {Proceedings of the Third International Conference on Computability and Complexity in Analysis},
series = {Electronic Notes in Theoretical Computer Science},
volume = {167},
publisher = {Elsevier},
address = {Amsterdam},
year = {2007},
pages = {387--423},
note = {{CCA} 2006, Gainesville, Florida, USA, November 1--5, 2006},
}
@article{CO08,
author = {Campagnolo, Manuel L. and Ojakian, Kerry},
title = {The elementary computable functions over the real numbers: applying two new techniques},
journal = {Archive for Mathematical Logic},
volume = {46},
number = {7--8},
year = {2008},
pages = {593--627},
}
@inproceedings{CO08a,
author = {Campagnolo, Manuel L. and Ojakian, Kerry},
title = {Characterizing Computable Analysis with Differential Equations},
editor = {Brattka, Vasco and Dillhage, Ruth and Grubba, Tanja and Klutsch, Angela},
booktitle = {{CCA} 2008, Fifth International Conference on Computability and Complexity in Analysis},
series = {Electronic Notes in Theoretical Computer Science},
volume = {221},
publisher = {Elsevier},
year = {2008},
pages = {23--35},
note = {{CCA} 2008, Fifth International Conference, Hagen, Germany, August 21--24, 2008},
}
@article{CO11,
author = {Campagnolo, Manuel L. and Ojakian, Kerry},
title = {A characterization of computable analysis on unbounded domains using differential equations},
journal = {Inform. and Comput.},
volume = {209},
number = {8},
year = {2011},
pages = {1135--1159},
doi = {10.1016/j.ic.2011.04.002},
}
@article{Col05,
author = {Collins, Pieter},
title = {Continuity and computability on reachable sets},
journal = {Theoretical Computer Science},
volume = {341},
year = {2005},
pages = {162--195},
}
@inproceedings{Col07,
author = {Collins, Pieter},
title = {Effective Computation for Nonlinear Systems},
editor = {Cooper, S. Barry and L{\"o}we, Benedikt and Sorbi, Andrea},
booktitle = {Computation and Logic in the Real World},
series = {Lecture Notes in Computer Science},
volume = {4497},
publisher = {Springer},
address = {Berlin},
year = {2007},
pages = {169--178},
note = {Third Conference on Computability in Europe, CiE 2007, Siena, Italy, June 18-23, 2007},
}
@article{Col07a,
author = {Collins, Pieter},
title = {Optimal Semicomputable Approximations to Reachable and Invariant Sets},
journal = {Theory of Computing Systems},
volume = {41},
number = {1},
year = {2007},
pages = {33--48},
}
@inproceedings{Col08,
author = {Collins, Pieter},
title = {Computability and Representations of the Zero Set},
editor = {Brattka, Vasco and Dillhage, Ruth and Grubba, Tanja and Klutsch, Angela},
booktitle = {{CCA} 2008, Fifth International Conference on Computability and Complexity in Analysis},
series = {Electronic Notes in Theoretical Computer Science},
volume = {221},
publisher = {Elsevier},
year = {2008},
pages = {37--43},
note = {{CCA} 2008, Fifth International Conference, Hagen, Germany, August 21--24, 2008},
}
@inproceedings{Col09,
author = {Collins, Pieter},
title = {Computability of Homology for Compact Absolute Neighbourhood Retracts},
editor = {Bauer, Andrej and Hertling, Peter and Ko, Ker-I},
booktitle = {{CCA} 2009, Proceedings of the Sixth International Conference on Computability and Complexity in Analysis},
publisher = {Leibniz-Zentrum f\"ur Informatik},
address = {Schloss Dagstuhl, Germany},
year = {2009},
pages = {107--118},
}
@article{Col10,
author = {Collins, Pieter J.},
title = {Computable Analysis with Applications to Dynamic Systems},
journal = {CWI Report, Modelling, Analysis and Computing},
volume = {MAC-1002},
year = {2010},
}
@article{Col11,
author = {Collins, Pieter},
title = {Semantics and computability of the evolution of hybrid systems},
journal = {SIAM J. Control Optim.},
volume = {49},
number = {2},
year = {2011},
pages = {890--925},
doi = {10.1137/080716955},
}
@article{Col20,
author = {Collins, Pieter},
title = {Computable analysis with applications to dynamic systems},
journal = {Mathematical Structures in Computer Science},
volume = {30},
number = {2},
year = {2020},
pages = {173--233},
doi = {10.1017/s096012952000002x},
}
@article{Col78,
author = {Collins, W.},
title = {Provably recursive real numbers},
journal = {Notre Dame J. Formal Logic},
volume = {19},
year = {1978},
pages = {513--522},
}
@phdthesis{COlg16,
author = {Callejas Olgu{\'{i}}n, Claudio Andr{\'{e}}s},
title = {A topological and domain theoretical study of total computable functions},
school = {Federal University of Rio Grande do Norte},
year = {2016},
}
@inproceedings{Coo92,
author = {Cook, Stephen A.},
title = {Computability and complexity of higher type functions},
editor = {Moschovakis, Y.N.},
booktitle = {Logic from computer science},
series = {Mathematical Sciences Research Institute Publications},
volume = {21},
publisher = {Springer},
address = {New York},
year = {1992},
pages = {51--72},
note = {Proceedings of the workshop held in Berkeley, California, November 13--17, 1989},
}
@article{Coq05,
author = {Coquand, Thierry},
title = {Formal Topology and Constructive Mathematics: the {G}elfand and {S}tone-{Y}osida Representation Theorems},
journal = {Journal of Universal Computer Science},
volume = {11},
number = {12},
year = {2005},
pages = {1932--1944},
}
@article{CP23,
author = {Cenzer, Douglas and Porter, Christopher P.},
title = {Randomness extraction in computability theory},
journal = {Computability},
volume = {12},
number = {1},
year = {2023},
pages = {1--21},
doi = {10.3233/COM-210343},
}
@article{CPW15,
author = {Cubitt, Toby S. and Perez-Garcia, David and Wolf, Michael M.},
title = {Undecidability of the spectral gap},
journal = {Nature},
volume = {528},
year = {2015},
pages = {207--211},
doi = {10.1038/nature16059},
}
@article{CR02,
author = {Cenzer, Douglas and Remmel, Jeffrey B.},
title = {Effectively closed sets and graphs of computable real functions},
journal = {Theoretical Computer Science},
volume = {284},
number = {2},
year = {2002},
pages = {279--318},
}
@article{CR03,
author = {Cenzer, Douglas and Remmel, Jeffrey B.},
title = {Index sets for $\omega$--languages},
journal = {Mathematical Logic Quarterly},
volume = {49},
number = {1},
year = {2003},
pages = {22--33},
doi = {10.1002/malq.200310002},
}
@inproceedings{CR03a,
author = {Cenzer, Douglas and Remmel, Jeffrey B.},
title = {Index sets for computable real functions},
editor = {Brattka, Vasco and Schr{\"{o}}der, Matthias and Weihrauch, Klaus and Zhong, Ning},
booktitle = {Computability and Complexity in Analysis},
series = {Informatik Berichte},
volume = {302},
publisher = {FernUniversit\"at in Hagen},
year = {2003},
month = aug,
pages = {164--182},
note = {International Conference, CCA 2003, Cincinnati, USA, August 28--30, 2003},
}
@article{CR04,
author = {Cenzer, Douglas and Remmel, Jeffrey B.},
title = {Index sets for computable differential equations},
journal = {Mathematical Logic Quarterly},
volume = {50},
number = {4,5},
year = {2004},
pages = {329--344},
doi = {10.1002/malq.200310102},
}
@inproceedings{CR08,
author = {Ciobanu, Gabriel and Rusu, D\u{a}nu\c{t}},
title = {Supermetrics over Apartness Lattice-Ordered Semigroup},
editor = {Dillhage, Ruth and Grubba, Tanja and Sorbi, Andrea and Weihrauch, Klaus and Zhong, Ning},
booktitle = {Proceedings of the Fourth International Conference on Computability and Complexity in Analysis ({CCA} 2007)},
series = {Electronic Notes in Theoretical Computer Science},
volume = {202},
publisher = {Elsevier},
year = {2008},
pages = {191--200},
note = {{CCA} 2007, Siena, Italy, June 16--18, 2007},
}
@inproceedings{CR18,
author = {Cenzer, Douglas and Rojas, Diego A.},
title = {Online Computability and Differentiation in the {C}antor Space},
editor = {Manea, Florin and Miller, Russell G. and Nowotka, Dirk},
booktitle = {Sailing Routes in the World of Computation},
publisher = {Springer},
address = {Cham},
year = {2018},
pages = {136--145},
doi = {10.1007/978-3-319-94418-0_14},
}
@incollection{CR98,
author = {Cenzer, Douglas and Remmel, J.B.},
title = {{$\Pi^0_1$}--classes in mathematics},
editor = {Ershov, Yu. L. and Goncharov, S.S. and Nerode, A. and Remmel, J.B. and Marek, V.W.},
booktitle = {Handbook of Recursive Mathematics},
series = {Studies in Logic and the Foundations of Mathematics},
volume = {139},
publisher = {Elsevier},
address = {Amsterdam},
year = {1998},
pages = {623--821},
note = {Volume 2, Recursive Algebra, Analysis and Combinatorics},
}
@article{CR99,
author = {Cenzer, Douglas and Remmel, Jeffrey B.},
title = {Index sets in computable analysis},
journal = {Theoretical Computer Science},
volume = {219},
year = {1999},
pages = {111--150},
}
@article{CRY18,
author = {Coronel, Daniel and Rojas, Cristobal and Yampolsky, Michael},
title = {Non computable {M}andelbrot-like sets for a one-parameter complex family},
journal = {Information and Computation},
volume = {262},
number = {part 1},
year = {2018},
pages = {110--122},
doi = {10.1016/j.ic.2018.07.003},
}
@article{CS05,
author = {Calude, Cristian S. and Staiger, Ludwig},
title = {Generalisations of disjunctive sequences},
journal = {Mathematical Logic Quarterly},
volume = {51},
number = {2},
year = {2005},
pages = {120--128},
}
@article{CS07,
author = {Cagnard, Benoit and Simonnet, Pierre},
title = {Automata, {B}orel Functions and Real Numbers in {P}isot Base},
journal = {Theoretical Informatics and Applications},
volume = {41},
number = {1},
year = {2007},
pages = {27--44},
}
@inproceedings{CSZ07,
author = {Chen, Qingliang and Su, Kaile and Zheng, Xizhong},
title = {Primitive recursiveness of real numbers under different representation},
editor = {Cenzer, Douglas and Dillhage, Ruth and Grubba, Tanja and Weihrauch, Klaus},
booktitle = {Proceedings of the Third International Conference on Computability and Complexity in Analysis},
series = {Electronic Notes in Theoretical Computer Science},
volume = {167},
publisher = {Elsevier},
address = {Amsterdam},
year = {2007},
pages = {303--324},
note = {{CCA} 2006, Gainesville, Florida, USA, November 1--5, 2006},
}
@article{CSZ07a,
author = {Chen, Qingliang and Su, Kaile and Zheng, Xizhong},
title = {Primitive recursive real numbers},
journal = {Mathematical Logic Quarterly},
volume = {53},
number = {4--5},
year = {2007},
pages = {365--380},
}
@article{Cur03,
author = {Curi, Giovanni},
title = {Constructive metrisability in point-free topology},
journal = {Theoretical Computer Science},
volume = {305},
year = {2003},
pages = {85--109},
}
@article{CW13,
author = {Cenzer, Douglas and Weber, Rebecca},
title = {Effective randomness of unions and intersections},
journal = {Theory Comput. Syst.},
volume = {52},
number = {1},
year = {2013},
pages = {48--64},
doi = {10.1007/s00224-012-9416-1},
}
@inproceedings{CWW09,
author = {Cenzer, Douglas and Weber, Rebecca and Wu, Guohua},
title = {Immunity for closed sets},
booktitle = {Mathematical theory and computational practice},
series = {Lecture Notes in Comput. Sci.},
volume = {5635},
publisher = {Springer},
address = {Berlin},
year = {2009},
pages = {109--117},
doi = {10.1007/978-3-642-03073-4_12},
}
@article{CY83,
author = {Collins, W. and Young, P.},
title = {Discountinuities of provably correct operators on the provably recursive real numbers},
journal = {The Journal of Symbolic Logic},
volume = {48},
year = {1983},
pages = {913--920},
}
@article{CZ11,
author = {Collins, Pieter and Zapreev, Ivan S.},
title = {Computable semantics for {${\rm CTL}^\ast$} on discrete-time and continuous-space dynamic systems},
journal = {Internat. J. Found. Comput. Sci.},
volume = {22},
number = {4},
year = {2011},
pages = {801--821},
doi = {10.1142/S012905411100843X},
}
@article{CZ62,
author = {Ce{\u{\i}}tin, Gregory S. and Zaslavski{\u{i}}, Igor D.},
title = {Singular coverings and properties of constructive functions connected with them ({R}ussian)},
journal = {Tr.\ Mat.\ Inst.\ Steklov},
volume = {67},
year = {1962},
pages = {458--502},
}
@article{CZ70,
author = {Ce{\u{\i}}tin, Gregory S. and Zaslavski{\u{i}}, Igor D.},
title = {A criterion of the rectifiability of constructive plane curves ({R}ussian)},
journal = {Izv. {A}kad {N}auk {A}rmjan. SSR Ser. Mat.},
volume = {5},
year = {1970},
pages = {434--440},
}
@article{CZ71,
author = {Ce{\u{\i}}tin, Gregory S. and Zaslavski{\u{i}}, Igor D.},
title = {Yet another constructive variant of the {C}auchy theorem ({R}ussian)},
journal = {{Z}ap. {N}au\v{c}n. {S}em. {L}eningrad. {O}tdel. {M}at. {I}nst. {S}teklov ({L}{O}{M}{I})},
volume = {20},
year = {1971},
pages = {36--39,282--283},
}
@inproceedings{CZS68,
author = {Ce{\u{\i}}tin, Gregory S. and Zaslavski{\u{i}}, Igor D. and \v{S}anin N.A.},
title = {Peculiarities of constructive mathematical analysis ({R}ussian)},
booktitle = {Proc. Internat. Congr. Math.},
publisher = {Mir},
address = {Moscow},
year = {1968},
pages = {253--261},
}
@article{Dah04,
author = {Dahlgren, Fredrik},
title = {Computability and continuity in metric partial algebras equipped with computability structures},
journal = {Mathematical Logic Quarterly},
volume = {50},
number = {4,5},
year = {2004},
pages = {486--500},
}
@inproceedings{Dah06,
author = {Dahlgren, Fredrik},
title = {Partial Continuous Functions and Admissible Domain Representations},
editor = {Beckmann, A. and Berger, U. and L{\"o}we, B. and Tucker, J.V.},
booktitle = {Logical Approaches to Computational Barriers},
series = {Lecture Notes in Computer Science},
volume = {3988},
publisher = {Springer},
address = {Berlin},
year = {2006},
pages = {94--104},
note = {Second Conference on Computability in Europe, CiE 2006, Swansea, UK, June 30-July 5, 2006},
}
@article{Dal05,
author = {van Dalen, Dirk},
title = {How the Mathematical Objects Determine the Mathematical Principles},
journal = {Journal of Universal Computer Science},
volume = {11},
number = {12},
year = {2005},
pages = {2132--2141},
}
@inproceedings{Dal73,
author = {van Dalen, Dirk},
title = {Lectures on Intuitionism},
editor = {Mathais, A. R. D. and Rogers, H.},
booktitle = {Cambridge Summer School in Mathematical Logic},
series = {Lecture Notes in Mathematics},
year = {1973},
pages = {1--94},
note = {Aug. 1--21, 1971},
}
@article{Dal78,
author = {van Dalen, D.},
title = {An interpretation of intuitionistic analysis},
journal = {Ann. Math. Logic},
volume = {13},
year = {1978},
pages = {1--43},
note = {with an appendix by {T}roelstra, A.S.},
}
@incollection{Dav04,
author = {Davis, Martin},
title = {The myth of hypercomputation},
editor = {Teuscher, Christof},
booktitle = {Alan Turing: Life and Legacy of a Great Thinker},
publisher = {Springer},
address = {Berlin, Heidelberg},
year = {2004},
pages = {195--211},
doi = {10.1007/978-3-662-05642-4_8},
}
@inproceedings{DB08,
author = {Dillhage, Ruth and Brattka, Vasco},
title = {Computability of the Metric Projection Onto Finite-dimensional Linear Subspaces},
editor = {Brattka, Vasco and Dillhage, Ruth and Grubba, Tanja and Klutsch, Angela},
booktitle = {{CCA} 2008, Fifth International Conference on Computability and Complexity in Analysis},
series = {Electronic Notes in Theoretical Computer Science},
volume = {221},
publisher = {Elsevier},
year = {2008},
pages = {45--60},
note = {{CCA} 2008, Fifth International Conference, Hagen, Germany, August 21--24, 2008},
}
@inproceedings{DB99,
author = {Dediu, Lumini{\c{t}}a and Bridges, Douglas S.},
title = {Constructive notes on uniform and locally convex spaces},
editor = {Ciobanu, G. and Pun, G.},
booktitle = {Fundamentals of computation theory},
series = {Lecture Notes in Computer Science},
volume = {1684},
publisher = {Springer},
address = {Berlin},
year = {1999},
pages = {195--203},
note = {12th International Symposium, FCT'99, Iasi, Romania, August/September 1999},
}
@phdthesis{dBre10,
author = {de Brecht, Matthew},
title = {Topological and Algebraic Aspects of Algorithmic Learning Theory},
school = {Graduate School of Informatics, Kyoto University},
year = {2010},
}
@article{dBre13,
author = {de Brecht, Matthew},
title = {Quasi-{P}olish spaces},
journal = {Ann. Pure Appl. Logic},
volume = {164},
number = {3},
year = {2013},
pages = {356--381},
doi = {10.1016/j.apal.2012.11.001},
}
@incollection{dBre14,
author = {de Brecht, Matthew},
title = {Levels of Discontinuity, Limit-Computability, and Jump Operators},
editor = {Brattka, Vasco and Diener, Hannes and Spreen, Dieter},
booktitle = {Logic, Computation, Hierarchies},
series = {Ontos Mathematical Logic},
publisher = {Walter de Gruyter},
address = {Boston},
year = {2014},
pages = {93--122},
}
@article{dBre18,
author = {de Brecht, Matthew},
title = {A generalization of a theorem of {H}urewicz for quasi-{P}olish spaces},
journal = {Logical Methods in Computer Science},
volume = {14},
number = {1},
year = {2018},
month = Feb,
pages = {1:13, 18},
doi = {10.23638/LMCS-14(1:13)2018},
}
@inproceedings{dBre20,
author = {de Brecht, Matthew},
title = {Some Notes on Spaces of Ideals and Computable Topology},
editor = {Anselmo, Marcella and Della Vedova, Gianluca and Manea, Florin and Pauly, Arno},
booktitle = {Beyond the Horizon of Computability},
publisher = {Springer International Publishing},
address = {Cham},
year = {2020},
pages = {26--37},
doi = {10.1007/978-3-030-51466-2_3},
}
@incollection{dBre22,
author = {de Brecht, Matthew},
title = {Constructing the space of valuations of a quasi-{P}olish space as a space of ideals},
editor = {Manea, Florin and Simpson, Alex},
booktitle = {30th {EACSL} {A}nnual {C}onference on {C}omputer {S}cience {L}ogic},
series = {LIPIcs. Leibniz Int. Proc. Inform.},
volume = {216},
publisher = {Schloss Dagstuhl. Leibniz-Zent. Inform., Wadern},
year = {2022},
pages = {Art. No. 9, 10},
doi = {10.4230/LIPIcs.CSL.2022.9},
}
@inproceedings{dBSS15,
author = {de Brecht, Matthew and Schr{\"o}der, Matthias and Selivanov, Victor},
title = {Base-Complexity Classification of {QCB$_0$}--Spaces (Extended Abstract)},
editor = {Beckmann, Arnold and Mitrana, Victor and Soskova, Mariya},
booktitle = {Evolving Computability},
series = {Lecture Notes in Computer Science},
volume = {9136},
publisher = {Springer},
address = {Cham},
year = {2015},
pages = {156--166},
note = {11th Conference on Computability in Europe, CiE 2015, Bucharest, Romania, June 29--July 3, 2015},
doi = {10.1007/978-3-319-20028-6_16},
}
@article{dBSS16,
author = {de Brecht, Matthew and Schr{\"o}der, Matthias and Selivanov, Victor},
title = {Base-Complexity Classification of {QCB$_0$}--Spaces},
journal = {Computability},
volume = {5},
number = {1},
year = {2016},
pages = {75--102},
doi = {10.3233/COM-150044},
}
@inproceedings{dBY09,
author = {de Brecht, Matthew and Yamamoto, Akihiro},
title = {{$\Sigma^0_\alpha$}-Admissible Representations (Extended Abstract)},
editor = {Bauer, Andrej and Hertling, Peter and Ko, Ker-I},
booktitle = {6th International Conference on Computability and Complexity in Analysis (CCA 2009)},
series = {OpenAccess Series in Informatics (OASIcs)},
volume = {11},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
year = {2009},
doi = {10.4230/OASIcs.CCA.2009.2264},
}
@article{DDH+16,
author = {Dorais, Fran\c{c}ois G. and Dzhafarov, Damir D. and Hirst, Jeffry L. and Mileti, Joseph R. and Shafer, Paul},
title = {On uniform relationships between combinatorial problems},
journal = {Transactions of the American Mathematical Society},
volume = {368},
number = {2},
year = {2016},
pages = {1321--1359},
doi = {10.1090/tran/6465},
}
@inproceedings{DE13,
author = {Di Gianantonio, Pietro and Edalat, Abbas},
title = {A Language for Differentiable Functions},
editor = {Pfenning, Frank},
booktitle = {Foundations of Software Science and Computation Structures ({FoSSaCS}'13)},
series = {Lecture Notes in Computer Science},
volume = {7794},
publisher = {Springer},
address = {Berlin},
year = {2013},
pages = {337--352},
doi = {10.1007/978-3-642-37075-5},
}
@phdthesis{Dei84a,
author = {Deil, Thomas},
title = {Darstellungen und {B}erechenbarkeit reeller {Z}ahlen},
school = {Fachbereich Mathematik und Informatik},
address = {FernUniversit\"{a}t Hagen},
year = {1984},
}
@article{Dem65,
author = {Demuth, Osvald},
title = {On {L}ebesgue integration in constructive analysis ({R}ussian)},
journal = {Dokl. Akad. Nauk SSSR},
volume = {160},
year = {1965},
pages = {1239--1241},
}
@article{Dem67,
author = {Demuth, Osvald},
title = {The {L}ebesgue integral in constructive analysis ({R}ussian)},
journal = {Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov.},
volume = {4},
year = {1967},
pages = {30--43},
note = {[translation in: A.O. Slisenko (ed.), Studies in constructive mathematics and mathematical logic, Part II, Consultants Bureau, New York, 1970]},
}
@article{Dem67a,
author = {Demuth, Osvald},
title = {A necessary and sufficient condition for the {R}iemann integrability of constructive functions},
journal = {Dokl. Akad. Nauk SSSR},
volume = {176},
year = {1967},
pages = {757--758},
}
@article{Dem68,
author = {Demuth, Osvald},
title = {Fubini's theorem for the {R}iemann integral in constructive mathematics. ({R}ussian)},
journal = {Comment. Math. Univ. Carolinae},
volume = {9},
year = {1968},
pages = {677--686},
}
@article{Dem68a,
author = {Demuth, Osvald},
title = {The {L}ebesgue integral and the concept of measurability of functions in constructive analysis ({R}ussian)},
journal = {Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov.},
volume = {8},
year = {1968},
pages = {21--28},
note = {[translation in: A.O. Slisenko (ed.), Studies in constructive mathematics and mathematical logic, Part II, Consultants Bureau, New York, 1970]},
}
@article{Dem68b,
author = {Demuth, Osvald},
title = {The connection between {R}iemann and {L}ebesgue integrability of constructive functions ({R}ussian)},
journal = {Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov.},
volume = {8},
year = {1968},
pages = {29--31},
note = {[translation in: A.O. Slisenko (ed.), Studies in constructive mathematics and mathematical logic, Part II, Consultants Bureau, New York, 1970]},
}
@article{Dem69,
author = {Demuth, Osvald},
title = {Note on the paper: ``{F}ubini's theorem for the {R}iemann integral in constructive mathematics'' ({R}ussian)},
journal = {Comment. Math. Univ. Carolinae},
volume = {10},
year = {1969},
pages = {115--120},
}
@article{Dem69a,
author = {Demuth, Osvald},
title = {The differentiability of constructive functions ({R}ussian)},
journal = {Comment. Math. Univ. Carolinae},
volume = {10},
year = {1969},
pages = {167--175},
}
@article{Dem69b,
author = {Demuth, Osvald},
title = {The spaces ${L}\sb{n}$ and ${S}$ in constructive mathematics ({R}ussian)},
journal = {Comment. Math. Univ. Carolinae},
volume = {10},
year = {1969},
pages = {261--284},
}
@article{Dem69c,
author = {Demuth, Osvald},
title = {Linear functionals in the constructive spaces ${L}\sb{r}$ ({R}ussian)},
journal = {Comment. Math. Univ. Carolinae},
volume = {10},
year = {1969},
pages = {357--390},
}
@article{Dem69d,
author = {Demuth, Osvald},
title = {The representability of constructive functions of weakly bounded variation ({R}ussian)},
journal = {Comment. Math. Univ. Carolinae},
volume = {11},
year = {1970},
pages = {421--434},
}
@article{Dem69e,
author = {Demuth, Osvald},
title = {The {L}ebesgue measurability of sets in constructive mathematic ({R}ussian)},
journal = {Comment. Math. Univ. Carolinae},
volume = {10},
year = {1969},
pages = {463--492},
}
@article{Dem70,
author = {Demuth, Osvald},
title = {Mean value theorems for the constructive {L}ebesgue integral ({R}ussian)},
journal = {Comment. Math. Univ. Carolinae},
volume = {11},
year = {1970},
pages = {249--269},
}
@article{Dem70a,
author = {Demuth, Osvald},
title = {The representability of constructive functions of weakly bounded variation ({R}ussian)},
journal = {Comment. Math. Univ. Carolinae},
volume = {11},
year = {1970},
pages = {421--434},
}
@article{Dem70b,
author = {Demuth, Osvald},
title = {The integrability of derivatives of constructive functions ({R}ussian)},
journal = {Comment. Math. Univ. Carolinae},
volume = {11},
year = {1970},
pages = {667--691},
}
@article{Dem70c,
author = {Demuth, Osvald},
title = {Necessary and sufficient conditions for the absolute continuity of constructive functions ({R}ussian)},
journal = {Comment. Math. Univ. Carolinae},
volume = {11},
year = {1970},
pages = {705--726},
}
@article{Dem71,
author = {Demuth, Osvald},
title = {The superpositions of absolutely continuous constructive functions ({R}ussian)},
journal = {Comment. Math. Univ. Carolinae},
volume = {12},
year = {1971},
pages = {423--451},
}
@article{Dem71a,
author = {Demuth, Osvald},
title = {A necessary and sufficient condition for the representability of constructive functions in the form of the sum of a singular and an absolutely continuous function ({R}ussian)},
journal = {Comment. Math. Univ. Carolinae},
volume = {12},
year = {1971},
pages = {587--610},
}
@article{Dem71b,
author = {Demuth, Osvald},
title = {A certain condition for the differentiability of constructive functions of bounded variation ({R}ussian)},
journal = {Comment. Math. Univ. Carolinae},
volume = {12},
year = {1971},
pages = {687--711},
}
@article{Dem72,
author = {Demuth, Osvald},
title = {A necessary and sufficient condition for the representability of constructive functions in the form of a superposition of absolutely continuous functions ({R}ussian)},
journal = {Comment. Math. Univ. Carolinae},
volume = {13},
year = {1972},
pages = {227--251},
}
@article{Dem72a,
author = {Demuth, Osvald},
title = {A sufficient condition for the representability of constructive functions in the form of the sum of two superpositions of absolutely continuous functions ({R}ussian)},
journal = {Comment. Math. Univ. Carolinae},
volume = {13},
year = {1972},
pages = {265--282},
}
@article{Dem73,
author = {Demuth, Osvald},
title = {The representability of uniformly continuous constructive functions ({R}ussian)},
journal = {Comment. Math. Univ. Carolinae},
volume = {14},
year = {1973},
pages = {7--25},
}
@article{Dem73a,
author = {Demuth, Osvald},
title = {The constructive analogue of the connection between the {L}ebesgue measurability of sets and of functions ({R}ussian)},
journal = {Comment. Math. Univ. Carolinae},
volume = {14},
year = {1973},
pages = {377--396},
}
@article{Dem73b,
author = {Demuth, Osvald and N{\v{e}}me{\v{c}}kov{\'a}, L.},
title = {The constructive analogues of the properties $({N})$ and $({S})$ ({R}ussian)},
journal = {Comment. Math. Univ. Carolinae},
volume = {14},
year = {1973},
pages = {565--582},
}
@article{Dem74,
author = {Demuth, Osvald},
title = {The representability of constructive functions possessing the properties $({\rm {S}})$ and $({\rm {T}}\sb{1})$ in the form of superpositions ({R}ussian)},
journal = {Comment. Math. Univ. Carolinae},
volume = {15},
year = {1974},
pages = {49--64},
}
@article{Dem74a,
author = {Demuth, Osvald},
title = {The connection between the representability of a constructive function in the form of a superposition of two absolutely continuous functions and the differentiability of this function ({R}ussian)},
journal = {Comment. Math. Univ. Carolinae},
volume = {15},
year = {1974},
pages = {195--210},
}
@article{Dem75,
author = {Demuth, Osvald},
title = {Constructive pseudonumbers ({R}ussian)},
journal = {Comment. Math. Univ. Carolinae},
volume = {16},
year = {1975},
pages = {315--331},
}
@article{Dem75a,
author = {Demuth, Osvald},
title = {The differentiability of constructive functions of weakly bounded variation on pseudo numbers ({R}ussian)},
journal = {Comment. Math. Univ. Carolinae},
volume = {16},
number = {3},
year = {1975},
pages = {583--599},
}
@article{Dem76,
author = {Demuth, Osvald},
title = {The constructive analogue of the {D}enjoy-{Y}oung theorem on derived numbers ({R}ussian)},
journal = {Comment. Math. Univ. Carolinae},
volume = {17},
number = {1},
year = {1976},
pages = {111--126},
}
@article{Dem76a,
author = {Demuth, Osvald},
title = {The domains of definition of effective operators over general recursive functions and of constructive functions of a real variable ({R}ussian)},
journal = {Comment. Math. Univ. Carolinae},
volume = {17},
number = {4},
year = {1976},
pages = {633--646},
}
@article{Dem77,
author = {Demuth, Osvald},
title = {A constructive analogue of the functions of the $n$th {B}aire class ({R}ussian)},
journal = {Comment. Math. Univ. Carolinae},
volume = {18},
number = {2},
year = {1977},
pages = {231--245},
}
@article{Dem77a,
author = {Demuth, Osvald},
title = {A generalization of the constructive {L}ebesgue integral ({R}ussian)},
journal = {Comment. Math. Univ. Carolinae},
volume = {18},
number = {3},
year = {1977},
pages = {499--514},
}
@article{Dem78,
author = {Demuth, Osvald},
title = {Some questions of the theory of constructive functions of a real variable ({R}ussian)},
journal = {Acta Universitatis Carolinae. Mathematica et Physica},
volume = {19},
number = {1},
year = {1978},
pages = {61--96},
}
@article{Dem78a,
author = {Demuth, Osvald},
title = {The pseudodifferentiability of uniformly continuous constructive functions on constructive real numbers ({R}ussian)},
journal = {Comment. Math. Univ. Carolin.},
volume = {19},
number = {2},
year = {1978},
pages = {319--333},
}
@article{Dem78b,
author = {Demuth, Osvald},
title = {Constructive analogues of generalized absolutely continuous functions of generalized bounded variation ({R}ussian)},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {19},
number = {3},
year = {1978},
pages = {471--487},
}
@article{Dem79,
author = {Demuth, Osvald},
title = {Constructive {D}enjoy integrals ({R}ussian)},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {20},
number = {2},
year = {1979},
pages = {213--227},
}
@article{Dem79a,
author = {Demuth, Osvald},
title = {The use of the {R}iemann-{S}tieltjes integral in the theory of the constructive {L}ebesgue integral, and its generalizations ({R}ussian)},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {20},
number = {4},
year = {1979},
pages = {781--793},
}
@article{Dem80,
author = {Demuth, Osvald},
title = {On the constructive {P}erron integral ({R}ussian)},
journal = {Acta Universitatis Carolinae. Mathematica et Physica},
volume = {21},
number = {1},
year = {1980},
pages = {3--57},
}
@article{Dem80a,
author = {Demuth, Osvald},
title = {A constructive analogue of {K}. {M}. {G}arg's theorem on derivative numbers ({R}ussian)},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {21},
number = {3},
year = {1980},
pages = {457--472},
}
@article{Dem80b,
author = {Demuth, Osvald},
title = {Pseudodifferentiability of constructive functions on constructive real numbers ({R}ussian)},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {21},
number = {3},
year = {1980},
pages = {489--505},
}
@article{Dem81,
author = {Demuth, Osvald},
title = {On the pseudodifferentiability of uniformly continuous constructive functions from functions of the same type ({R}ussian)},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {22},
number = {3},
year = {1981},
pages = {497--512},
}
@article{Dem81a,
author = {Demuth, Osvald},
title = {A generalization of a constructive analogue of {K}. {M}. {G}arg's theorem ({R}ussian)},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {22},
number = {3},
year = {1981},
pages = {607--620},
}
@article{Dem82,
author = {Demuth, Osvald},
title = {Borel types of some classes of arithmetical real numbers ({R}ussian)},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {23},
number = {3},
year = {1982},
pages = {593--606},
}
@article{Dem82a,
author = {Demuth, Osvald},
title = {Some classes of arithmetical real numbers ({R}ussian)},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {23},
number = {3},
year = {1982},
pages = {453--465},
}
@article{Dem83,
author = {Demuth, Osvald},
title = {Arithmetic complexity of differentiation in constructive mathematics ({R}ussian)},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {24},
number = {2},
year = {1983},
pages = {301--316},
}
@article{Dem83a,
author = {Demuth, Osvald},
title = {On the pseudodifferentiability of pseudo-uniformly continuous constructive functions from functions of the same type ({R}ussian)},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {24},
number = {3},
year = {1983},
pages = {391--406},
}
@article{Dem87,
author = {Demuth, Oswald},
title = {A notion of semigenericity},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {28},
number = {1},
year = {1987},
pages = {71--84},
}
@inproceedings{Dem87a,
author = {Demuth, Osvald},
title = {An example of the construction of pseudonumbers by the methods of recursion theory},
editor = {Tonoyan, R.N.},
booktitle = {Applied mathematics, No. 5 (Russian)},
publisher = {Erevan. Univ.},
address = {Erevan},
year = {1987},
pages = {55--73, 131--132},
}
@article{Dem88,
author = {Demuth, Osvald},
title = {Reducibilities of sets based on constructive functions of a real variable},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {29},
number = {1},
year = {1988},
pages = {143--156},
}
@article{Dem88a,
author = {Demuth, Osvald},
title = {Remarks on the structure of tt-degrees based on constructive measure theory},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {29},
number = {2},
year = {1988},
pages = {233--247},
}
@inproceedings{Dem90,
author = {Demuth, Osvald},
title = {Remarks on {D}enjoy sets},
booktitle = {Mathematical logic},
publisher = {Plenum},
address = {New York},
year = {1990},
pages = {267--280},
}
@inproceedings{DEMY02,
author = {Du, Zilin and Eleftheriou, Maria and Moreira, Jos{\'e} E. and Yap, Chee},
title = {Hypergeometric Functions in Exact Geometric Computation},
editor = {Brattka, Vasco and Schr{\"{o}}der, Matthias and Weihrauch, Klaus},
booktitle = {{CCA} 2002 Computability and Complexity in Analysis},
series = {Electronic Notes in Theoretical Computer Science},
volume = {66},
publisher = {Elsevier},
address = {Amsterdam},
year = {2002},
note = {5th International Workshop, {CCA} 2002, M{\'{a}}laga, Spain, July 12--13, 2002},
}
@phdthesis{Det85,
author = {Dettki, Hans Joachim},
title = {Untersuchungen zur Darstellungsberechenbarkeit von Ordinalzahlfunktionen},
school = {Fachbereich Mathematik und Informatik},
address = {FernUniversit\"{a}t Hagen},
year = {1985},
}
@article{DF13,
author = {Davie, George and Fouch{\'e}, Willem L.},
title = {On the computability of a construction of {B}rownian motion},
journal = {Mathematical Structures in Computer Science},
volume = {23},
year = {2013},
month = {12},
pages = {1257--1265},
doi = {10.1017/S0960129513000157},
}
@inproceedings{DF87,
author = {Demuth, Osvald and Filipec, Pavel},
title = {Differentiation of constructive functions of a real variable and relative computability},
editor = {Skordev, D.G.},
booktitle = {Mathematical Logic and Its Applications},
publisher = {Plenum Press},
address = {New York},
year = {1987},
pages = {81--106},
note = {Proceedings of an advanced international summer school and conference in honor of the 80th anniversary of Kurt G\"odel's birth, held September 24--October 4, 1986 in Druzhba, Bulgaria},
}
@inproceedings{DG02,
author = {Downey, Rod G. and Griffiths, Evan J.},
title = {Schnorr Randomness},
editor = {Brattka, Vasco and Schr{\"{o}}der, Matthias and Weihrauch, Klaus},
booktitle = {{CCA} 2002 Computability and Complexity in Analysis},
series = {Electronic Notes in Theoretical Computer Science},
volume = {66},
publisher = {Elsevier},
address = {Amsterdam},
year = {2002},
note = {5th International Workshop, {CCA} 2002, M{\'{a}}laga, Spain, July 12--13, 2002},
}
@article{DGH+20,
author = {Dzhafarov, Damir D. and Goh, Jun Le and Hirschfeldt, Denis R. and Patey, Ludovic and Pauly, Arno},
title = {Ramsey's theorem and products in the {W}eihrauch degrees},
journal = {Computability},
volume = {9},
number = {2},
year = {2020},
pages = {85--110},
doi = {10.3233/com-180203},
}
@article{DGL04,
author = {Downey, Rod G. and Griffiths, Evan J. and LaForte, Geoffrey L.},
title = {On {S}chnorr and computable randomness, martingales, and machines},
journal = {Mathematical Logic Quarterly},
volume = {50},
number = {6},
year = {2004},
pages = {613--627},
}
@inproceedings{DGS07,
author = {de Miguel Casado, Gregorio and Garc{\'{\i}}a Chamizo, Juan Manuel and Signes Pont, Mar{\'{\i}}a Teresa},
title = {Algebraic Model of an Arithmetic Unit for {TTE}-Computable Normalized Rational Numbers},
editor = {Cooper, S. Barry and L{\"o}we, Benedikt and Sorbi, Andrea},
booktitle = {Computation and Logic in the Real World},
series = {Lecture Notes in Computer Science},
volume = {4497},
publisher = {Springer},
address = {Berlin},
year = {2007},
pages = {218--227},
note = {Third Conference on Computability in Europe, CiE 2007, Siena, Italy, June 18-23, 2007},
}
@proceedings{DGSWZ08,
title = {Proceedings of the Fourth International Conference on Computability and Complexity in Analysis ({CCA} 2007)},
editor = {Dillhage, Ruth and Grubba, Tanja and Sorbi, Andrea and Weihrauch, Klaus and Zhong, Ning},
series = {Electronic Notes in Theoretical Computer Science},
volume = {202},
address = {Amsterdam},
year = {2008},
note = {{CCA} 2007, Siena, Italy, June 16--18, 2007},
}
@article{DH12,
author = {Diener, Hannes and Hedin, Anton},
title = {The {V}itali covering theorem in constructive mathematics},
journal = {Journal of Logic and Analysis},
volume = {4},
year = {2012},
pages = {Paper 7, 22},
doi = {10.4115/jla.2012.4.7},
}
@article{DH18,
author = {Diener, Hannes and Hendtlass, Matthew},
title = {Bishop's lemma},
journal = {Mathematical Logic Quarterly},
volume = {64},
number = {1-2},
year = {2018},
pages = {49--54},
doi = {10.1002/malq.201600041},
}
@article{DH19a,
author = {Diener, Hannes and Hendtlass, Matthew},
title = {Completeness: when enough is enough},
journal = {Documenta Mathematica},
volume = {24},
year = {2019},
pages = {899--914},
}
@article{DH20,
author = {Diener, Hannes and Hendtlass, Matthew},
title = {Differentiating convex functions constructively},
journal = {Journal of Logic and Analysis},
volume = {12},
year = {2020},
pages = {Paper No. 8, 11},
doi = {10.4115/jla.2020.12.8},
}
@article{DH22,
author = {Diener, Hannes and Hendtlass, Matthew},
title = {The Third Trick},
journal = {Logical Methods in Computer Science},
volume = {18},
number = {3},
year = {2022},
month = Aug,
pages = {21:1--21:12},
doi = {10.46298/lmcs-18(3:21)2022},
}
@article{DHH+20,
author = {Davis, Caleb and Hirschfeldt, Denis R. and Hirst, Jeffry and Pardo, Jake and Pauly, Arno and Yokoyama, Keita},
title = {Combinatorial principles equivalent to weak induction},
journal = {Computability},
volume = {9},
number = {3-4},
year = {2020},
pages = {219--229},
doi = {10.3233/com-180244},
}
@inproceedings{DHL01,
author = {Downey, Rod G. and Hirschfeldt, Denis R. and LaForte, Geoffrey L.},
title = {Randomness and Reducibility},
editor = {Sgall, Ji{\v{r}}{\'{\i}} and Pultr, Ale{\v{s}} and Kolman, Petr},
booktitle = {Mathematical Foundations of Computer Science 2001},
series = {Lecture Notes in Computer Science},
volume = {2136},
publisher = {Springer},
address = {Berlin},
year = {2001},
pages = {316--327},
note = {26th International Symposium, MFCS 2001, Mari{\'{a}}nsk{\'{e}} L{\'{a}}zn{\v{e}}, Czech Republic, August 27-31, 2001},
}
@inproceedings{DHNS02,
author = {Downey, Rod G. and Hirschfeldt, Denis R. and Nies, Andr{\'{e}} and Stephan, Frank},
title = {Trivial Reals},
editor = {Brattka, Vasco and Schr{\"{o}}der, Matthias and Weihrauch, Klaus},
booktitle = {{CCA} 2002 Computability and Complexity in Analysis},
series = {Electronic Notes in Theoretical Computer Science},
volume = {66},
publisher = {Elsevier},
address = {Amsterdam},
year = {2002},
note = {5th International Workshop, {CCA} 2002, M{\'{a}}laga, Spain, July 12--13, 2002},
}
@inproceedings{DHNS03,
author = {Downey, Rod G. and Hirschfeldt, Denis R. and Nies, Andr{\'{e}} and Stephan, Frank},
title = {Trivial Reals},
editor = {Downey, Rod and Decheng, Ding and Ping, Tung Shih and Hui, Qiu Yu and Yasugi, Mariko},
booktitle = {Proceedings of the 7th and 8th Asian Logic Conferences},
publisher = {World Scientific},
address = {Singapore},
year = {2003},
pages = {63--102},
note = {7th Conference: Hsi-Tou, Taiwan, June 6--10, 1999; 8th Conference: Chongqing, China, August 29 -- September 2, 2002},
}
@article{DHR22,
author = {Dzhafarov, Damir D. and Hirschfeldt, Denis R. and Reitzes, Sarah C.},
title = {Reduction Games, Provability, and Compactness},
journal = {Journal of Mathematical Logic},
volume = {22},
number = {3},
year = {2022},
pages = {2250009},
doi = {10.1142/S021906132250009X},
}
@incollection{DI21,
author = {Diener, Hannes and Ishihara, Hajime},
title = {Bishop-Style Constructive Reverse Mathematics},
editor = {Brattka, Vasco and Hertling, Peter},
booktitle = {Handbook of Computability and Complexity in Analysis},
series = {Theory and Applications of Computability},
publisher = {Springer},
address = {Cham},
year = {2021},
pages = {347--365},
doi = {10.1007/978-3-030-59234-9_10},
}
@article{Die08,
author = {Diener, Hannes},
title = {Generalising compactness},
journal = {Mathematical Logic Quarterly},
volume = {54},
number = {1},
year = {2008},
pages = {49--57},
doi = {10.1002/malq.200710041},
}
@phdthesis{Die08a,
author = {Diener, Hannes},
title = {Compactness under constructive scrutiny},
school = {University of Canterbury, Christchurch, New Zealand},
year = {2008},
note = {{Ph.D.} thesis},
}
@article{Die12,
author = {Diener, Hannes},
title = {Reclassifying the antithesis of {S}pecker's theorem},
journal = {Arch. Math. Logic},
volume = {51},
number = {7-8},
year = {2012},
pages = {687--693},
doi = {10.1007/s00153-012-0292-9},
}
@article{Die13,
author = {Diener, Hannes},
title = {Weak {K}{\"o}nig's Lemma Implies the Uniform Continuity Theorem},
journal = {Computability},
volume = {2},
number = {1},
year = {2013},
pages = {9--13},
doi = {10.3233/10.3233/COM-13009},
}
@article{Die15,
author = {Diener, Hannes},
title = {Variations on a theme by {I}shihara},
journal = {Mathematical Structures in Computer Science},
volume = {25},
year = {2015},
month = {10},
pages = {1569--1577},
doi = {10.1017/S0960129513000261},
}
@phdthesis{Die18,
author = {Diener, Hannes},
title = {Constructive Reverse Mathematics},
school = {Fachbereich Mathematik, Universit{\"a}t Siegen},
year = {2018},
}
@inproceedings{Dil08,
author = {Dillhage, Ruth},
title = {Computability of the Spectrum of Self-Adjoint Operators and the Computable Operational Calculus},
editor = {Dillhage, Ruth and Grubba, Tanja and Sorbi, Andrea and Weihrauch, Klaus and Zhong, Ning},
booktitle = {Proceedings of the Fourth International Conference on Computability and Complexity in Analysis ({CCA} 2007)},
series = {Electronic Notes in Theoretical Computer Science},
volume = {202},
publisher = {Elsevier},
year = {2008},
pages = {365--384},
note = {{CCA} 2007, Siena, Italy, June 16--18, 2007},
}
@phdthesis{Dil12,
author = {Dillhage, Ruth},
title = {Computable Functional Analysis, Compact Operators on Computable Banach Spaces and Computable Best Approximation},
school = {Faculty for Mathematics and Computer Science, University of Hagen},
address = {Hagen, Germany},
year = {2012},
}
@article{Din65,
author = {Phan D{\`\i}nh-Di{\^{e}}u},
title = {Constructive locally convex linear topological spaces ({R}ussian)},
journal = {Doklady Akademii Nauk},
volume = {162},
year = {1965},
pages = {766--769},
}
@article{Din66,
author = {Phan D{\`\i}nh-Di{\^{e}}u},
title = {The metrizability, normability and multinormability of constructive locally convex spaces ({R}ussian)},
journal = {Doklady Akademii Nauk},
volume = {162},
year = {1965},
pages = {1011--1014},
}
@article{Din66a,
author = {Phan D{\`\i}nh-Di{\^{e}}u},
title = {On conjugates to constructive, locally convex spaces ({R}ussian)},
journal = {Doklady Akademii Nauk},
volume = {166},
year = {1966},
pages = {45--48},
}
@article{Din67,
author = {Phan D{\`\i}nh-Di{\^{e}}u},
title = {Constructive generalized functions ({R}ussian)},
journal = {Doklady Akademii Nauk},
volume = {174},
year = {1967},
pages = {37--40},
}
@article{Din67a,
author = {Phan D{\`\i}nh-Di{\^{e}}u},
title = {Certain properties of constructive generalized functions ({R}ussian)},
journal = {Doklady Akademii Nauk},
volume = {174},
year = {1967},
pages = {298--301},
}
@article{Din67b,
author = {Phan D{\`\i}nh-Di{\^{e}}u},
title = {A language for constructive mathematics, connected with systems of sets ({R}ussian)},
journal = {Trudy Mat. Inst. Steklova},
volume = {93},
year = {1967},
pages = {123--141},
}
@article{Din67c,
author = {Phan D{\`\i}nh-Di{\^{e}}u},
title = {Closed and open sets in constructive topological spaces ({R}ussian)},
journal = {Trudy Mat. Inst. Steklova},
volume = {93},
year = {1967},
pages = {250--256},
}
@article{Din68,
author = {Phan D{\`\i}nh-Di{\^{e}}u},
title = {Spaces of constructive infinitely differentiable functions, and functionals therein ({R}ussian)},
journal = {Doklady Akademii Nauk},
volume = {180},
year = {1968},
pages = {799--802},
}
@book{Din74,
author = {Phan D{\`\i}nh-Di{\^{e}}u},
title = {Some questions in constructive functional analysis},
series = {Proceedings of the Steklov Institute of Mathematics},
volume = {114},
publisher = {American Mathematical Society},
address = {Providence},
year = {1974},
}
@inproceedings{DK09,
author = {Diamondstone, David and Kjos-Hanssen, Bj{\o}rn},
title = {Members of Random Closed Sets},
editor = {Ambos-Spies, Klaus and L{\"o}we, Benedikt and Merkle, Wolfgang},
booktitle = {Mathematical Theory and Computational Practice, 5th Conference on Computability in Europe, CiE 2009, Heidelberg, Germany, July 19-24, 2009. Proceedings},
series = {Lecture Notes in Computer Science},
volume = {5635},
publisher = {Springer},
year = {2009},
pages = {144--153},
doi = {10.1007/978-3-642-03073-4\_16},
}
@inproceedings{DK79,
author = {Demuth, Osvald and Ku{\v{c}}era, A.},
title = {Remarks on constructive mathematical analysis},
booktitle = {Logic Colloquium '78 (Mons, 1978)},
publisher = {North-Holland},
address = {Amsterdam},
year = {1979},
pages = {81--129},
}
@article{DK80,
author = {Demuth, Osvald and Km{\'\i}nek, V.},
title = {Properties of indefinite constructive {L}ebesgue-{S}tieltjes integrals ({R}ussian)},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {21},
number = {4},
year = {1980},
pages = {629--644},
}
@article{DK85,
author = {Downey, Rod and Kalantari, Iraj},
title = {Effective extensions of linear forms on a recursive vector space over a recursive field},
journal = {Zeitschrift f\"ur Mathematische Logik und Grundlagen der Mathematik},
volume = {31},
number = {3},
year = {1985},
pages = {193--200},
}
@article{DK87,
author = {Demuth, Osvald and Ku{\v{c}}era, A.},
title = {Remarks on $1$-genericity, semigenericity and related concepts},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {28},
number = {1},
year = {1987},
pages = {85--94},
}
@article{DK89,
author = {Du, D. and Ko, Ker-I},
title = {Computational complexity of integration and differentiation of convex functions},
journal = {System Sci.\ and Math.\ Sci.},
volume = {2},
year = {1989},
pages = {70--79},
}
@article{DK92,
author = {Du, D. and Ko, Ker-I},
title = {A note on best fractions of a computable real number},
journal = {Journal of Complexity},
volume = {8},
year = {1992},
pages = {216--229},
}
@article{DKK78,
author = {Demuth, Osvald and Kryl, R. and Ku{\v{c}}era, A.},
title = {The use of the theory of functions that are partial recursive relative to numerical sets in constructive mathematics ({R}ussian)},
journal = {Acta Universitatis Carolinae. Mathematica et Physica},
volume = {19},
number = {1},
year = {1978},
pages = {15--60},
}
@article{DKSZ20,
author = {Ding, Longyun and Kihara, Takayuki and Semmes, Brian and Zhao, Jiafei},
title = {Decomposing functions of {B}aire class 2 on {P}olish spaces},
journal = {The Journal of Symbolic Logic},
volume = {85},
number = {3},
year = {2020},
pages = {960--971},
doi = {10.1017/jsl.2020.57},
}
@article{DL02,
author = {Downey, Rodney G. and LaForte, Geoffrey L.},
title = {Presentations of computably enumerable reals},
journal = {Theoretical Computer Science},
volume = {284},
number = {2},
year = {2002},
pages = {539--555},
}
@article{DL09,
author = {Diener, Hannes and Loeb, Iris},
title = {Sequences of real functions on $[0,1]$ in constructive reverse mathematics},
journal = {Annals of Pure and Applied Logic},
volume = {157},
number = {1},
year = {2009},
pages = {1--62},
}
@article{DL11,
author = {Diener, Hannes and Loeb, Iris},
title = {Constructive reverse investigations into differential equations},
journal = {Journal of Logic and Analysis},
volume = {3},
year = {2011},
pages = {Paper 8, 26},
}
@incollection{DL18,
author = {Diener, Hannes and Lubarsky, Robert},
title = {Notions of {C}auchyness and metastability},
booktitle = {Logical foundations of computer science},
series = {Lecture Notes in Comput. Sci.},
volume = {10703},
publisher = {Springer},
address = {Cham},
year = {2018},
pages = {140--153},
}
@article{DM12,
author = {Daniel, Dale and McNicholl, Timothy H.},
title = {Effective versions of local connectivity properties},
journal = {Theory of Computing Systems},
volume = {50},
number = {4},
year = {2012},
pages = {621--640},
doi = {10.1007/s00224-011-9364-1},
}
@article{DM13a,
author = {Day, Adam R. and Miller, Joseph S.},
title = {Randomness for non-computable measures},
journal = {Transactions of the American Mathematical Society},
volume = {365},
number = {7},
year = {2013},
pages = {3575--3591},
doi = {10.1090/S0002-9947-2013-05682-6},
}
@inproceedings{DM20,
author = {Downey, Rodney G. and Melnikov, Alexander G.},
title = {Computable Analysis and Classification Problems},
editor = {Anselmo, Marcella and Della Vedova, Gianluca and Manea, Florin and Pauly, Arno},
booktitle = {Beyond the Horizon of Computability},
publisher = {Springer International Publishing},
address = {Cham},
year = {2020},
pages = {100--111},
doi = {10.1007/978-3-030-51466-2_9},
}
@book{DM22,
author = {Dzhafarov, Damir D. and Mummert, Carl},
title = {Reverse Mathematics},
series = {Theory and Applications of Computability},
publisher = {Springer},
year = {2022},
doi = {10.1007/978-3-031-11367-3},
}
@article{DMR06,
author = {Downey, Rodney and Merkle, Wolfgang and Reimann, Jan},
title = {Schnorr dimension},
journal = {Mathematical Structures in Computer Science},
volume = {16},
number = {5},
year = {2006},
pages = {789--811},
}
@article{DN73,
author = {Demuth, Osvald and Neme{\v{c}}kova, L.},
title = {The constructive analogue of the property $({T}\sb{1})$ ({R}ussian)},
journal = {Comment. Math. Univ. Carolinae},
volume = {14},
year = {1973},
pages = {421--439},
}
@inproceedings{Dow03,
author = {Downey, Rodney G.},
title = {Presentations of reals (Abstract)},
editor = {Brattka, Vasco and Schr{\"{o}}der, Matthias and Weihrauch, Klaus and Zhong, Ning},
booktitle = {Computability and Complexity in Analysis},
series = {Informatik Berichte},
volume = {302},
publisher = {FernUniversit\"at in Hagen},
year = {2003},
month = aug,
pages = {11--12},
note = {International Conference, CCA 2003, Cincinnati, USA, August 28--30, 2003},
}
@inproceedings{DP01,
author = {Dunlop, Anthony J. and Pour-El, Marian B.},
title = {The Degree of Unsolvability of a Real Number},
editor = {Blanck, Jens and Brattka, Vasco and Hertling, Peter},
booktitle = {Computability and Complexity in Analysis},
series = {Lecture Notes in Computer Science},
volume = {2064},
publisher = {Springer},
address = {Berlin},
year = {2001},
pages = {16--29},
note = {4th International Workshop, CCA 2000, Swansea, UK, September 2000},
}
@article{DP21,
author = {Dzhafarov, Damir D. and Patey, Ludovic},
title = {{COH}, {SRT22}, and multiple functionals},
journal = {Computability},
volume = {10},
number = {2},
year = {2021},
pages = {111--121},
doi = {10.3233/COM-190261},
}
@article{DP79,
author = {Demuth, Osvald and Polivka, {\u{I}}.},
title = {The representation of linear functionals in the space of codes of constructive functions that are uniformly continuous on the segment $0\triangle 1$ ({R}ussian)},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {20},
number = {4},
year = {1979},
pages = {765--780},
}
@article{DPSW17,
author = {Dzhafarov, Damir D. and Patey, Ludovic and Solomon, Reed and Westrick, Linda Brown},
title = {Ramsey's theorem for singletons and strong computable reducibility},
journal = {Proceedings of the American Mathematical Society},
volume = {145},
year = {2017},
doi = {10.1090/proc/13315},
}
@article{DS10,
author = {Diener, Hannes and Schuster, Peter},
title = {On choice principles and fan theorems},
journal = {J.UCS},
volume = {16},
number = {18},
year = {2010},
pages = {2556--2562},
}
@article{DS11,
author = {Diener, H. and Schuster, P.},
title = {Uniqueness, continuity and the existence of implicit functions in constructive analysis},
journal = {LMS J. Comput. Math.},
volume = {14},
year = {2011},
pages = {127--136},
doi = {10.1112/S1461157010000057},
}
@inproceedings{DSW86,
author = {Dettki, H.J. and Schuster, H. and Weihrauch, K.},
title = {Type 2 recursion theory},
editor = {Demetrovics, J. and Katona, G. and Salomaa, A.},
booktitle = {Algebra, Combinatorics and Logic in Computer Science, Vol. 1},
series = {Coll. Math. Soc. J\'{a}nos Bolyai},
volume = {42},
year = {1986},
pages = {355--361},
note = {Papers from Colloq., Sept. 12--16, 1983, Gy\"or},
}
@article{DT02,
author = {Downey, Rod and Terwijn, Sebastiaan},
title = {Computably Enumerable Reals and Uniformly Presentable Ideals},
journal = {Mathematical Logic Quarterly},
volume = {48},
number = {Suppl. 1},
year = {2002},
pages = {29--40},
}
@phdthesis{Dud12,
author = {Dudko, Artem},
title = {Dynamics of holomorphic maps: {R}esurgence of {F}atou coordinates, and {P}oly-time computability of {J}ulia sets},
publisher = {ProQuest LLC, Ann Arbor, MI},
school = {University of Toronto},
year = {2012},
pages = {124},
}
@article{Dud14,
author = {Dudko, Artem},
title = {Computability of the {J}ulia set. {N}onrecurrent critical orbits},
journal = {Discrete and Continuous Dynamical Systems. Series A},
volume = {34},
number = {7},
year = {2014},
pages = {2751--2778},
doi = {10.3934/dcds.2014.34.2751},
}
@inproceedings{Dum75,
author = {Dummett, M.},
title = {The {P}hilosophical {B}asis of {I}ntuitionistic {L}ogic},
editor = {Rose, H.E. and Shepherdson, J.C.},
booktitle = {Logic Colloquium '73},
series = {Stud. Logic. Found. Math.},
volume = {80},
year = {1975},
pages = {5--40},
note = {(Bristol 1973)},
}
@book{Dum77,
author = {Dummett, M.},
title = {Elements of {I}ntuitionism},
publisher = {Oxford Univ. Press},
year = {1977},
}
@phdthesis{Dun99,
author = {Dunlop, Anthony James},
title = {Degrees of unsolvability and relative computability of real numbers},
school = {University of Minnesota},
year = {1999},
pages = {78},
note = {{Ph.D.} Thesis},
}
@book{DW20,
title = {Complexity and Approximation, in Memory of Ker-I Ko},
editor = {Du, Ding-Zhu and Wang, Jie},
series = {Lecture Notes in Computer Science},
volume = {12000},
publisher = {Springer},
address = {Cham},
year = {2020},
doi = {10.1007/978-3-030-41672-0},
}
@incollection{DW20a,
author = {Du, Ding-Zhu and Wang, Jie},
title = {In Memoriam: {Ker-I Ko} (1950--2018)},
editor = {Du, Ding-Zhu and Wang, Jie},
booktitle = {Complexity and Approximation: In Memory of {Ker-I Ko}},
publisher = {Springer},
address = {Cham},
year = {2020},
pages = {1--7},
doi = {10.1007/978-3-030-41672-0_1},
}
@inproceedings{DWW07,
author = {Ding, Decheng and Weihrauch, Klaus and Wu, Yongcheng},
title = {Absolutely non-effective predicates and functions in Computable Analysis},
editor = {Cai, Jin-Yi and Cooper, S. Barry and Zhou, Hong},
booktitle = {Theory and Applications of Models of Computation},
series = {Lecture Notes in Computer Science},
volume = {4484},
year = {2007},
pages = {595--604},
}
@article{DWZ04,
author = {Downey, Rod and Wu, Guohua and Zheng, Xizhong},
title = {Degrees of d.c.e. reals},
journal = {Mathematical Logic Quarterly},
volume = {50},
number = {4,5},
year = {2004},
pages = {345--350},
}
@article{DY16,
author = {Dudko, Artem and Yampolsky, Michael},
title = {Poly-time computability of the {F}eigenbaum {J}ulia set},
journal = {Ergodic Theory and Dynamical Systems},
volume = {36},
number = {8},
year = {2016},
pages = {2441--2462},
doi = {10.1017/etds.2015.24},
}
@article{DY21,
author = {Dudko, Artem and Yampolsky, Michael},
title = {On computational complexity of {C}remer {J}ulia sets},
journal = {Fundamenta Mathematicae},
volume = {252},
number = {3},
year = {2021},
pages = {343--353},
doi = {10.4064/fm829-12-2019},
}
@article{Dzh15,
author = {Dzhafarov, Damir D.},
title = {Cohesive avoidance and strong reductions},
journal = {Proceedings of the American Mathematical Society},
volume = {143},
number = {2},
year = {2015},
pages = {869--876},
doi = {10.1090/S0002-9939-2014-12261-1},
}
@article{Dzh16,
author = {Dzhafarov, Damir D.},
title = {Strong reductions between combinatorial principles},
journal = {Journal of Symbolic Logic},
volume = {81},
number = {4},
year = {2016},
pages = {1405-1431},
doi = {10.1017/jsl.2016.1},
}
@article{Dzh19,
author = {Dzhafarov, Damir D.},
title = {Joins in the strong {W}eihrauch degrees},
journal = {Mathematical Research Letters},
volume = {26},
number = {3},
year = {2019},
pages = {749--767},
doi = {10.4310/MRL.2019.v26.n3.a5},
}
@inproceedings{Eda07,
author = {Edalat, Abbas},
title = {A Continuous Derivative for Real-Valued Functions},
editor = {Cooper, S. Barry and L{\"o}we, Benedikt and Sorbi, Andrea},
booktitle = {Computation and Logic in the Real World},
series = {Lecture Notes in Computer Science},
volume = {4497},
publisher = {Springer},
address = {Berlin},
year = {2007},
pages = {248--257},
note = {Third Conference on Computability in Europe, CiE 2007, Siena, Italy, June 18-23, 2007},
}
@inproceedings{Eda07a,
author = {Edalat, Abbas},
title = {A computable approach to measure and integration theory},
booktitle = {LICS '07: Proceedings of the 22nd Annual IEEE Symposium on Logic in Computer Science},
publisher = {IEEE Computer Society},
address = {Washington, DC, USA},
year = {2007},
pages = {463--472},
}
@article{Eda09,
author = {Edalat, Abbas},
title = {A computable approach to measure and integration theory},
journal = {Information and Computation},
volume = {207},
number = {5},
year = {2009},
pages = {642--659},
}
@article{Eda15,
author = {Edalat, Abbas},
title = {A derivative for complex {L}ipschitz maps with generalised {C}auchy-{R}iemann equations},
journal = {Theoretical Computer Science},
volume = {564},
year = {2015},
pages = {89--106},
doi = {10.1016/j.tcs.2014.11.003},
}
@inproceedings{Eda15a,
author = {Edalat, Abbas},
title = {Extensions of domain maps in differential and integral calculus},
booktitle = {2015 30th {A}nnual {ACM}/{IEEE} {S}ymposium on {L}ogic in {C}omputer {S}cience ({LICS} 2015)},
publisher = {IEEE Computer Soc.},
address = {Los Alamitos, CA},
year = {2015},
pages = {426--437},
}
@article{Eda95,
author = {Edalat, Abbas},
title = {Domain theory and integration},
journal = {Theoretical Computer Science},
volume = {151},
year = {1995},
pages = {163--193},
}
@article{Eda95a,
author = {Edalat, Abbas},
title = {Dynamical systems, measures, and fractals via domain theory},
journal = {Information and Computation},
volume = {120},
number = {1},
year = {1995},
pages = {32--48},
}
@article{Eda96,
author = {Edalat, Abbas},
title = {Power domains and iterated function systems},
journal = {Information and Computation},
volume = {124},
number = {2},
year = {1996},
pages = {182--197},
}
@inproceedings{Eda96a,
author = {Edalat, Abbas},
title = {The {S}cott Topology Induces the Weak Topology},
booktitle = {LICS '96: Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science},
publisher = {IEEE Computer Society},
address = {Washington, DC, USA},
year = {1996},
pages = {372},
}
@article{Eda97,
author = {Edalat, Abbas},
title = {Domains for Computation in Mathematics, Physics and Exact Real Arithmetic},
journal = {Bulletin of Symbolic Logic},
volume = {3},
number = {4},
year = {1997},
pages = {401--452},
}
@article{EE01,
author = {Edalat, Abbas and Escard\'{o}, Mart\'{\i}n H\"otzel},
title = {Integration in real {PCF}},
journal = {Information and Computation},
volume = {160},
year = {2001},
pages = {128--166},
}
@article{EG05,
author = {Esposti, Mirko Degli and Galatolo, Stefano},
title = {Recurrence near given sets and the complexity of the {C}asati-{P}rosen map},
journal = {Chaos Solitons Fractals},
volume = {23},
number = {4},
year = {2005},
pages = {1275--1284},
}
@article{EH98,
author = {Edalat, Abbas and Heckmann, Reinhold},
title = {A computational model for metric spaces},
journal = {Theoretical Computer Science},
volume = {193},
year = {1998},
pages = {53--73},
}
@inproceedings{EK99,
author = {Edalat, Abbas and Krznari{\'{c}}, Marko},
title = {Numerical Integration with Exact Real Arithmetic},
editor = {Wiedermann, Ji{\v{r}}{\'{\i}} and van Emde Boas, Peter and Nielsen, Mogens},
booktitle = {Automata, Languages and Programming},
series = {Lecture Notes in Computer Science},
volume = {1644},
publisher = {Springer},
address = {Berlin},
year = {1999},
pages = {90--104},
note = {26th International Colloquium, ICALP'99, Prague, Czech Republic, July, 1999},
}
@inproceedings{EKL00,
author = {Edalat, Abbas and Kashefi, Elham and Lieutier, Andr\'{e}},
title = {The Convex Hull is Computable!},
editor = {Blanck, Jens and Brattka, Vasco and Hertling, Peter and Weihrauch, Klaus},
booktitle = {Computability and Complexity in Analysis},
series = {Informatik Berichte},
volume = {272},
publisher = {FernUniversit\"at Hagen},
year = {2000},
month = sep,
pages = {75--77},
note = {CCA 2000 Workshop, Swansea, Wales, September 17--19, 2000},
}
@inproceedings{EKL05,
author = {Edalat, Abbas and Khanban, Ali A. and Lieutier, Andr\'{e}},
title = {Computability in Computational Geometry},
editor = {Cooper, Barry S. and L{\"o}we, Benedikt and Torenvliet, Leen},
booktitle = {New Computational Paradigms},
series = {Lecture Notes in Computer Science},
volume = {3526},
publisher = {Springer},
address = {Berlin},
year = {2005},
pages = {117--127},
note = {First Conference on Computability in Europe, CiE 2005, Amsterdam, The Netherlands, June 2005},
}
@inproceedings{EL00,
author = {Edalat, Abbas and Lieutier, Andr\'{e}},
title = {Domain of Differentiable Functions},
editor = {Blanck, Jens and Brattka, Vasco and Hertling, Peter and Weihrauch, Klaus},
booktitle = {Computability and Complexity in Analysis},
series = {Informatik Berichte},
volume = {272},
publisher = {FernUniversit\"at Hagen},
year = {2000},
month = sep,
pages = {79},
note = {CCA 2000 Workshop, Swansea, Wales, September 17--19, 2000},
}
@article{EL02,
author = {Edalat, Abbas and Lieutier, Andr\'{e}},
title = {Foundation of a computable solid modelling},
journal = {Theoretical Computer Science},
volume = {284},
number = {2},
year = {2002},
pages = {319--345},
}
@article{ELP13,
author = {Edalat, Abbas and Lieutier, Andr{\'e} and Pattinson, Dirk},
title = {A computational model for multi-variable differential calculus},
journal = {Inform. and Comput.},
volume = {224},
year = {2013},
pages = {23--45},
doi = {10.1016/j.ic.2012.11.006},
}
@article{ELS04,
author = {Escard{\'o}, Mart{\'{\i}}n and Lawson, Jimmie and Simpson, Alex},
title = {Comparing {C}artesian closed categories of (core) compactly generated spaces},
journal = {Topology and its Applications},
volume = {143},
number = {1-3},
year = {2004},
pages = {105--145},
doi = {10.1016/j.topol.2004.02.011},
}
@inproceedings{EM17,
author = {Edalat, Abbas and Maleki, Mehrdad},
title = {Differentiation in logical form},
booktitle = {2017 32nd {A}nnual {ACM}/{IEEE} {S}ymposium on {L}ogic in {C}omputer {S}cience ({LICS})},
publisher = {IEEE},
address = {Piscataway, NJ},
year = {2017},
pages = {12},
}
@inproceedings{EM18,
author = {Edalat, Abbas and Maleki, Mehrdad},
title = {Differential calculus with imprecise input and its logical framework},
booktitle = {Foundations of software science and computation structures},
series = {Lecture Notes in Comput. Sci.},
volume = {10803},
publisher = {Springer},
address = {Cham},
year = {2018},
pages = {459--475},
}
@article{EM98,
author = {Esbelin, Henri-Alex and More, Malika},
title = {Rudimentary relations and primitive recursion: a toolbox},
journal = {Theoretical Computer Science},
volume = {193},
number = {1-2},
year = {1998},
pages = {129--148},
doi = {10.1016/S0304-3975(97)00002-9},
}
@article{EN02,
author = {Etesi, G{\'a}bor and N{\'e}meti, Istv{\'a}n},
title = {Non-{T}uring computations via {M}alament-{H}ogarth space-times},
journal = {International Journal of Theoretical Physics},
volume = {41},
number = {2},
year = {2002},
pages = {341--370},
}
@article{EO10,
author = {Escard{\'o}, Mart{\'{\i}}n and Oliva, Paulo},
title = {Selection functions, bar recursion and backward induction},
journal = {Math. Structures Comput. Sci.},
volume = {20},
number = {2},
year = {2010},
pages = {127--168},
doi = {10.1017/S0960129509990351},
}
@inproceedings{EO10a,
author = {Escard{\'o}, Mart{\'{\i}}n and Oliva, Paulo},
title = {Computational interpretations of analysis via products of selection functions},
booktitle = {Programs, proofs, processes},
series = {Lecture Notes in Comput. Sci.},
volume = {6158},
publisher = {Springer},
address = {Berlin},
year = {2010},
pages = {141--150},
doi = {10.1007/978-3-642-13962-8_16},
}
@inproceedings{EP03,
author = {Edalat, Abbas and Pattinson, Dirk},
title = {Initial value problems in domain theory},
editor = {Brattka, Vasco and Schr{\"{o}}der, Matthias and Weihrauch, Klaus and Zhong, Ning},
booktitle = {Computability and Complexity in Analysis},
series = {Informatik Berichte},
volume = {302},
publisher = {FernUniversit\"at in Hagen},
year = {2003},
month = aug,
pages = {211--227},
note = {International Conference, CCA 2003, Cincinnati, USA, August 28--30, 2003},
}
@article{EP07,
author = {Edalat, Abbas and Pattinson, Dirk},
title = {A domain-theoretic account of {P}icard's theorem},
journal = {LMS Journal of Computation and Mathematics},
volume = {10},
year = {2007},
pages = {83--118},
}
@article{EP97,
author = {Edalat, Abbas and Potts, Peter John},
title = {A new representation for exact real numbers},
journal = {Electronical Notes in Theoretical Computer Science},
volume = {6},
year = {1997},
pages = {14 pp.},
note = {Mathematical foundations of programming semantics (Pittsburgh, PA, 1997)},
}
@proceedings{EPSW14,
title = {Special issue: {S}elected papers of the {N}inth {I}nternational {C}onference on {C}omputability and {C}omplexity in {A}nalysis ({CCA}) 2012},
editor = {Escard{\'o}, Mart{\'\i}n and Pauly, Arno and Schr{\"o}der, Matthias and Weihrauch, Klaus},
series = {Logical Methods in Computer Science},
number = {The Ninth International Conference on Computability and Complexity in Analysis (CCA) 2012},
year = {2013/14},
note = {Held in Cambridge, June 24--27, 2012},
}
@inproceedings{ER98,
author = {Edalat, Abbas and Rico, Fabien},
title = {Root Finding in Exact Real Arithmetic Using Linear Fractional Transformations},
editor = {Chesneaux, J.-M. and J\'{e}z\'{e}quel, F. and Lamotte, J.-L. and Vignes, J.},
booktitle = {Third Real Numbers and Computers Conference},
publisher = {Universit\'{e} Pierre et Marie Curie, Paris},
year = {1998},
pages = {27--43},
note = {Paris, France, April 27--29, 1998},
}
@article{Ers72,
author = {Er{\v{s}}ov, Ju. L.},
title = {Computable functionals of finite type},
journal = {Algebra and Logic},
volume = {11},
number = {4},
year = {1972},
pages = {203--242},
}
@article{ES02,
author = {Escard\'{o}, Mart\'{\i}n H\"otzel and Streicher, Thomas},
title = {In Domain Realizability Not All Functionals on $C[-1,1]$ are Continuous},
journal = {Mathematical Logic Quarterly},
volume = {48},
number = {Suppl. 1},
year = {2002},
pages = {41--44},
}
@article{ES99,
author = {Edalat, Abbas and S{\"u}nderhauf, Philipp},
title = {A domain-theoretic approach to computability on the real line},
journal = {Theoretical Computer Science},
volume = {210},
year = {1999},
pages = {73--98},
}
@article{ES99b,
author = {Escard\'{o}, Mart\'{\i}n H\"otzel and Streicher, Thomas},
title = {Induction and recursion on the partial real line with applications to Real {PCF}},
journal = {Theoretical Computer Science},
volume = {210},
year = {1999},
pages = {121--157},
}
@article{ES99c,
author = {Edalat, Abbas and S{\"u}nderhauf, Philipp},
title = {Computable {B}anach spaces via domain theory},
journal = {Theoretical Computer Science},
volume = {219},
year = {1999},
pages = {169--184},
}
@incollection{Esb10,
author = {Esbelin, Henri-Alex},
title = {Rudimentarity of two famous real numbers},
booktitle = {Studies in weak arithmetics},
series = {CSLI Lecture Notes},
volume = {196},
publisher = {CSLI Publ.},
address = {Stanford, CA},
year = {2010},
pages = {121--126},
}
@article{Esb94,
author = {Esbelin, Henri Alex},
title = {Une classe minimale de fonctions r\'ecursives contenant les relations rudimentaires},
journal = {C. R. Acad. Sci. Paris S\'er. I Math.},
volume = {319},
number = {5},
year = {1994},
pages = {505--508},
}
@article{Esc04,
author = {Escard{\'o}, Mart{\'{\i}}n},
title = {Synthetic Topology of Data Types and Classical Spaces},
journal = {Electronic Notes in Theoretical Computer Science},
volume = {87},
year = {2004},
pages = {21--165},
doi = {10.1016/j.entcs.2004.09.017},
}
@article{Esc08,
author = {Escard{\'o}, Mart{\'{\i}}n},
title = {Exhaustible sets in higher-type computation},
journal = {Logical Methods in Computer Science},
volume = {4},
number = {3},
year = {2008},
pages = {3:3, 37},
doi = {10.2168/LMCS-4(3:3)2008},
}
@inproceedings{Esc09,
author = {Escard{\'o}, Mart{\'{\i}}n},
title = {Computability of continuous solutions of higher-type equations},
booktitle = {Mathematical theory and computational practice},
series = {Lecture Notes in Comput. Sci.},
volume = {5635},
publisher = {Springer},
address = {Berlin},
year = {2009},
pages = {188--197},
doi = {10.1007/978-3-642-03073-4_20},
}
@article{Esc13,
author = {Escard{\'o}, Mart{\'{\i}}n},
title = {Algorithmic solution of higher type equations},
journal = {J. Logic Comput.},
volume = {23},
number = {4},
year = {2013},
pages = {839--854},
doi = {10.1093/logcom/exr048},
}
@article{Esc15,
author = {Escard{\'o}, Mart{\'{\i}}n},
title = {Constructive decidability of classical continuity},
journal = {Mathematical Structures in Computer Science},
volume = {25},
year = {2015},
month = {10},
pages = {1578--1589},
doi = {10.1017/S096012951300042X},
}
@article{Esc96,
author = {Escard\'{o}, Mart\'{\i}n H\"otzel},
title = {{PCF} extended with real numbers},
journal = {Theoretical Computer Science},
volume = {162},
year = {1996},
pages = {79--115},
}
@phdthesis{Esc97,
author = {Escard\'{o}, Mart\'{\i}n H\"otzel},
title = {{PCF} extended with real numbers: a domain-theoretic approach to higher-order exact real number computation},
school = {Imperial College, University of London},
address = {London, Great Britain},
year = {1997},
}
@inproceedings{Esp98,
author = {Esbelin, Henri-Alex},
title = {Rudimentary computable reals},
editor = {Ko, Ker-I and Nerode, Anil and Pour-El, Marian B. and Weihrauch, Klaus and Wiedermann, Ji{\v{r}}{\'{\i}}},
booktitle = {Computability and Complexity in Analysis},
series = {Informatik Berichte},
volume = {235},
publisher = {FernUniversit\"at Hagen},
year = {1998},
month = aug,
pages = {21--30},
note = {CCA Workshop, Brno, Czech Republic, August, 1998},
}
@article{Far07,
author = {Farjudian, Amin},
title = {{SHRAD}: A Language for Sequential Real Number Computation},
journal = {Theory of Computing Systems},
volume = {41},
number = {1},
year = {2007},
pages = {49--105},
}
@inproceedings{Far11,
author = {Farjudian, Amin},
title = {On the {K}olmogorov complexity of continuous real functions},
booktitle = {Models of computation in context},
series = {Lecture Notes in Comput. Sci.},
volume = {6735},
publisher = {Springer},
address = {Heidelberg},
year = {2011},
pages = {81--91},
doi = {10.1007/978-3-642-21875-0_9},
}
@inproceedings{Far12,
author = {Farjudian, Amin},
title = {Polynomial-time solution of initial value problems using polynomial enclosures},
editor = {Ong, L. and de Queiroz, R.},
booktitle = {Logic, Language, Information and Computation},
series = {Lecture Notes in Computer Science},
volume = {7456},
publisher = {Springer},
address = {Heidelberg},
year = {2012},
pages = {232--245},
}
@article{Far13,
author = {Farjudian, Amin},
title = {On the {K}olmogorov complexity of continuous real functions},
journal = {Ann. Pure Appl. Logic},
volume = {164},
number = {5},
year = {2013},
pages = {566--576},
doi = {10.1016/j.apal.2012.11.003},
}
@inproceedings{Far19,
author = {Farjudian, Amin},
title = {Computable Analysis of Linear Rearrangement Optimization},
editor = {Gopal, T.V. and Watada, Junzo},
booktitle = {Theory and Applications of Models of Computation},
series = {Lecture Notes in Computer Science},
volume = {11436},
publisher = {Springer},
address = {Cham},
year = {2019},
pages = {172--187},
note = {15th Annual Conference, TAMC 2019, Kitakyushu, Japan, April 13--16, 2019},
doi = {10.1007/978-3-030-14812-6_11},
}
@article{Fef64,
author = {Feferman, S.},
title = {Systems of predicative analysis},
journal = {The Journal of Symbolic Logic},
volume = {29},
year = {1964},
pages = {1--30},
}
@inproceedings{Fef77,
author = {Feferman, S.},
title = {Theories of finite type related to mathematical practice},
editor = {Barwise, J.},
booktitle = {Handbook of {M}athematical {L}ogic},
series = {Studies in Logic and the Foundations of Mathematics},
volume = {90},
publisher = {North-Holland},
address = {Amsterdam},
year = {1977},
pages = {913--971},
}
@inproceedings{Fef79,
author = {Feferman, S.},
title = {Constructive Theories of Functions and Classes},
editor = {Boffa, D., van Dalen and McAloon, K.},
booktitle = {Proceedings Logic Colloquium '78},
series = {Studies in Logic and the Foundations of Mathematics},
volume = {97},
publisher = {North-Holland},
address = {Amsterdam},
year = {1979},
pages = {159--224},
note = {Mons, Aug. 24--Sept. 1., 1978},
}
@inproceedings{Fef84,
author = {Feferman, S.},
title = {Between constructive and classical mathematics},
editor = {Richter, M.M. and B\"orger, E. and Oberschelp, W. and Schinzel, B. and Thomas, W.},
booktitle = {Computation and Proof Theory},
series = {Lecture Notes in Mathematics},
volume = {1104},
year = {1984},
pages = {143--162},
note = {(Proc. Logic Colloq., Aachen, July 14--23, 1983, Part II)},
}
@article{Fer17,
author = {F{\'e}r{\'e}e, Hugo},
title = {Game semantics approach to higher-order complexity},
journal = {Journal of Computer and System Sciences},
volume = {87},
year = {2017},
pages = {1--15},
}
@inproceedings{Fer21,
author = {Ferreira, Fernando},
title = {On False {H}eine/{B}orel Compactness Principles in Proof Mining},
editor = {De Mol, Liesbeth and Weiermann, Andreas and Manea, Florin and Fern{\'a}ndez-Duque, David},
booktitle = {Connecting with Computability},
publisher = {Springer},
address = {Cham},
year = {2021},
pages = {199--203},
doi = {10.1007/978-3-030-80049-9_18},
}
@article{Fer21a,
author = {Ferreira, Fernando},
title = {The abstract type of the real numbers},
journal = {Archive for Mathematical Logic},
volume = {60},
number = {7--8},
year = {2021},
pages = {1005--1017},
doi = {10.1007/s00153-021-00772-9},
}
@article{FF06,
author = {Ferreira, Fernando and Ferreira, Gilda},
title = {Counting as integration in feasible analysis},
journal = {Mathematical Logic Quarterly},
volume = {52},
number = {3},
year = {2006},
pages = {315--320},
}
@article{FF08,
author = {Ferreira, Fernando and Ferreira, Gilda},
title = {The {R}iemann Integral in Weak Systems of Analysis},
journal = {Journal of Universal Computer Science},
volume = {14},
number = {6},
year = {2008},
pages = {908--937},
}
@article{FGH14,
author = {F{\'e}r{\'e}e, Hugo and Gomaa, Walid and Hoyrup, Mathieu},
title = {Analytical properties of resource-bounded real functionals},
journal = {Journal of Complexity},
volume = {30},
number = {5},
year = {2014},
pages = {647--671},
doi = {10.1016/j.jco.2014.02.008},
}
@article{FGMN12,
author = {Franklin, Johanna N. Y. and Greenberg, Noam and Miller, Joseph S. and Ng, Keng Meng},
title = {Martin-{L}\"of random points satisfy {B}irkhoff's ergodic theorem for effectively closed sets},
journal = {Proceedings of the American Mathematical Society},
volume = {140},
number = {10},
year = {2012},
pages = {3623--3628},
}
@incollection{FH79,
author = {Fourman, Michael and Hyland, John M. E.},
title = {Sheaf models for analysis},
editor = {Michael Fourman and Christopher Mulvey and Dana Scott},
booktitle = {Applications of Sheaves},
series = {Lecture Notes in Mathematics},
volume = {753},
publisher = {Springer},
address = {Berlin/Heidelberg},
year = {1979},
pages = {280--301},
}
@incollection{FHG13,
author = {F{\'e}r{\'e}e, Hugo and Hoyrup, Mathieu and Gomaa, Walid},
title = {On the query complexity of real functionals},
booktitle = {2013 28th {A}nnual {ACM}/{IEEE} {S}ymposium on {L}ogic in {C}omputer {S}cience ({LICS} 2013)},
publisher = {IEEE Computer Soc., Los Alamitos, CA},
year = {2013},
pages = {103--112},
}
@inproceedings{FHHP10,
author = {F{\'e}r{\'e}e, Hugo and Hainry, Emmanuel and Hoyrup, Mathieu and P{\'e}choux, Romain},
title = {Interpretation of stream programs: characterizing type 2 polynomial time complexity},
booktitle = {Algorithms and computation. {P}art {I}},
series = {Lecture Notes in Comput. Sci.},
volume = {6506},
publisher = {Springer},
address = {Berlin},
year = {2010},
pages = {291--303},
doi = {10.1007/978-3-642-17517-6_27},
}
@article{FHHP15,
author = {F{\'e}r{\'e}e, Hugo and Hainry, Emmanuel and Hoyrup, Mathieu and P{\'e}choux, Romain},
title = {Characterizing polynomial time complexity of stream programs using interpretations},
journal = {Theoretical Computer Science},
volume = {585},
year = {2015},
pages = {41--54},
}
@article{FHK14,
author = {Fujiwara, Makoto and Higuchi, Kojiro and Kihara, Takayuki},
title = {On the strength of marriage theorems and uniformity},
journal = {Mathematical Logic Quarterly},
volume = {60},
number = {3},
year = {2014},
pages = {136--153},
doi = {10.1002/malq.201300021},
}
@article{FHM+16,
author = {Frittaion, Emanuele and Hendtlass, Matthew and Marcone, Alberto and Shafer, Paul and Van der Meeren, Jeroen},
title = {Reverse mathematics, well-quasi-orders, and {N}oetherian spaces},
journal = {Archive for Mathematical Logic},
volume = {55},
number = {3-4},
year = {2016},
pages = {431--459},
doi = {10.1007/s00153-015-0473-4},
}
@article{FIN15,
author = {Fujiwara, Makoto and Ishihara, Hajime and Nemoto, Takako},
title = {Some principles weaker than {M}arkov's principle},
journal = {Archive for Mathematical Logic},
volume = {54},
number = {7-8},
year = {2015},
pages = {861--870},
}
@article{FK13,
author = {Freer, Cameron E. and Kjos-Hanssen, Bj{\o}rn},
title = {Randomness extraction and asymptotic {H}amming distance},
journal = {Logical Methods in Computer Science},
volume = {9},
year = {2013},
pages = {3:27, 14},
doi = {10.2168/LMCS-9(3:27)2013},
}
@article{FK21,
author = {Fujiwara, Makoto and Kawai, Tatsuji},
title = {Characterising {B}rouwer’s continuity by bar recursion on moduli of continuity},
journal = {Archive for Mathematical Logic},
volume = {60},
number = {1},
year = {2021},
pages = {241--263},
doi = {10.1007/s00153-020-00740-9},
}
@article{FKNS14,
author = {Freer, Cameron and Kjos-Hanssen, Bj{\o}rn and Nies, Andr{\'e} and Stephan, Frank},
title = {Algorithmic aspects of {L}ipschitz functions},
journal = {Computability},
volume = {3},
number = {1},
year = {2014},
pages = {45--61},
doi = {10.3233/COM-14025},
}
@article{FM20,
author = {Franklin, Johanna N. Y. and McNicholl, Timothy H.},
title = {Degrees of and lowness for isometric isomorphism},
journal = {Journal of Logic and Analysis},
volume = {12},
year = {2020},
pages = {Paper No. 6, 23},
doi = {10.4115/jla.2020.12.6},
}
@article{FM21,
author = {Fiori-Carones, Marta and Marcone, Alberto},
title = {To reorient is easier than to orient: an on-line algorithm for reorientation of graphs},
journal = {Computability},
volume = {10},
number = {3},
year = {2021},
pages = {215--233},
doi = {10.3233/com-190285},
}
@article{FMD14,
author = {Fouch{\'e}, Willem L. and Mukeru, Safari and Davie, George},
title = {Fourier spectra of measures associated with algorithmically random {B}rownian motion},
journal = {Logical Methods in Computer Science},
volume = {10},
number = {3},
year = {2014},
pages = {3:20, 24},
doi = {10.2168/LMCS-10(3:20)2014},
}
@article{FMR19,
author = {Franklin, Johanna N. Y. and McNicholl, Timothy H. and Rute, Jason},
title = {Algorithmic Randomness and Fourier Analysis},
journal = {Theory of Computing Systems},
volume = {63},
number = {3},
year = {2019},
month = {Apr},
pages = {567--586},
doi = {10.1007/s00224-018-9888-8},
}
@article{FNT14,
author = {Fritz, Tobias and Netzer, Tim and Thom, Andreas},
title = {Can you compute the operator norm?},
journal = {Proceedings of the American Mathematical Society},
volume = {142},
number = {12},
year = {2014},
month = {December},
pages = {4265--4276},
doi = {10.1090/S0002-9939-2014-12170-8},
}
@article{FO07,
author = {Ferreira, Fernando and Oliva, Paulo},
title = {Bounded functional interpretation and feasible analysis},
journal = {Annals of Pure and Applied Logic},
volume = {145},
number = {2},
year = {2007},
pages = {115--129},
}
@article{For20,
author = {Foreman, Matthew},
title = {G{\"o}del Diffeomorphisms},
journal = {The Bulletin of Symbolic Logic},
volume = {26},
number = {3--4},
publisher = {Cambridge University Press},
year = {2020},
pages = {219--223},
doi = {10.1017/bsl.2020.36},
}
@article{Fou00,
author = {Fouch{\'{e}}, Willem},
title = {Arithmetical Representation of {B}rownian Motion {I}},
journal = {The Journal of Symbolic Logic},
volume = {65},
year = {2000},
pages = {421--442},
}
@article{Fou00a,
author = {Fouch{\'{e}}, Willem},
title = {The Descriptive Complexity of {B}rownian Motion},
journal = {Advances in Mathematics},
volume = {155},
year = {2000},
pages = {317--343},
}
@article{Fou08,
author = {Fouch{\'{e}}, Willem},
title = {Dynamics of a generic {B}rownian motion: Recursive aspects},
journal = {Theoretical Computer Science},
volume = {394},
year = {2008},
pages = {175--186},
}
@inproceedings{Fou08a,
author = {Fouch{\'{e}}, Willem},
title = {An Algorithmic Construction of Quantum Circuits of High Descriptive Complexity},
editor = {Brattka, Vasco and Dillhage, Ruth and Grubba, Tanja and Klutsch, Angela},
booktitle = {{CCA} 2008, Fifth International Conference on Computability and Complexity in Analysis},
series = {Electronic Notes in Theoretical Computer Science},
volume = {221},
publisher = {Elsevier},
year = {2008},
pages = {61--69},
note = {{CCA} 2008, Fifth International Conference, Hagen, Germany, August 21--24, 2008},
}
@incollection{Fou08b,
author = {Fouch{\'e}, Willem L.},
title = {Subrecursive complexity of identifying the {R}amsey structure of posets},
booktitle = {Logic and theory of algorithms},
series = {Lecture Notes in Comput. Sci.},
volume = {5028},
publisher = {Springer, Berlin},
year = {2008},
pages = {196--205},
doi = {10.1007/978-3-540-69407-6_23},
}
@incollection{Fou09,
author = {Fouch{\'e}, Willem L.},
title = {Fractals generated by algorithmically random {B}rownian motion},
editor = {Klaus Ambos-Spies and Benedikt L{\"o}we and Wolfgang Merkle},
booktitle = {Mathematical Theory and Computational Practice},
series = {Lecture Notes in Computer Science},
volume = {5635},
publisher = {Springer},
address = {Berlin},
year = {2009},
pages = {208--217},
note = {5th Conference on Computability in Europe, CiE 2009, Heidelberg, Germany, July 19-24, 2009. Proceedings},
doi = {10.1007/978-3-642-03073-4_22},
}
@incollection{Fou12,
author = {Fouch{\'e}, Willem L.},
title = {Algorithmic randomness and {R}amsey properties of countable homogeneous structures},
booktitle = {Logic, language, information and computation},
series = {Lecture Notes in Comput. Sci.},
volume = {7456},
publisher = {Springer, Heidelberg},
year = {2012},
pages = {246--256},
doi = {10.1007/978-3-642-32621-9_18},
}
@article{Fou13,
author = {Fouch{\'e}, Willem L.},
title = {Martin-{L}\"of randomness, invariant measures and countable homogeneous structures},
journal = {Theory Comput. Syst.},
volume = {52},
number = {1},
year = {2013},
pages = {65--79},
doi = {10.1007/s00224-012-9419-y},
}
@incollection{Fou14,
author = {Fouch{\'e}, Willem L.},
title = {{D}iophantine properties of {B}rownian motion: recursive aspects},
editor = {Brattka, Vasco and Diener, Hannes and Spreen, Dieter},
booktitle = {Logic, Computation, Hierarchies},
series = {Ontos Mathematical Logic},
volume = {4},
publisher = {De Gruyter},
address = {Boston},
year = {2014},
pages = {139--156},
}
@article{Fou15,
author = {Fouch{\'e}, Willem L.},
title = {Kolmogorov complexity and the geometry of {B}rownian motion},
journal = {Mathematical Structures in Computer Science},
volume = {25},
number = {7},
year = {2015},
pages = {1590--1606},
doi = {10.1017/S0960129513000273},
}
@incollection{FP20,
author = {Franklin, Johanna N.Y. and Porter, Christopher P.},
title = {Key developments in algorithmic randomness},
editor = {Franklin, Johanna N.Y. and Porter, Christopher P.},
booktitle = {Algorithmic Randomness: Progress and Prospects},
series = {Lecture Notes in Logic},
volume = {50},
publisher = {Cambridge University Press},
year = {2020},
pages = {1--39},
doi = {10.1017/9781108781718.002},
}
@book{FP20a,
title = {Algorithmic Randomness: Progress and Prospects},
editor = {Franklin, Johanna N.Y. and Porter, Christopher P.},
series = {Lecture Notes in Logic},
volume = {50},
publisher = {Cambridge University Press},
year = {2020},
doi = {10.1017/9781108781718.001},
}
@inproceedings{FR09,
author = {Freer, Cameron E. and Roy, Daniel M.},
title = {Computable exchangeable sequences have computable de {F}inetti measures},
editor = {Klaus Ambos-Spies and Benedikt L{\"o}we and Wolfgang Merkle},
booktitle = {Mathematical Theory and Computational Practice},
series = {Lecture Notes in Computer Science},
volume = {5635},
publisher = {Springer},
address = {Berlin},
year = {2009},
pages = {218--231},
doi = {10.1007/978-3-642-03073-4_23},
}
@article{FR12,
author = {Freer, Cameron E. and Roy, Daniel M.},
title = {Computable de {F}inetti measures},
journal = {Annals of Pure and Applied Logic},
volume = {163},
number = {5},
year = {2012},
pages = {530--546},
doi = {10.1016/j.apal.2011.06.011},
}
@inproceedings{Fra07,
author = {Franklin, Johanna N.Y.},
title = {Schnorr trivial reals: a construction},
editor = {Cenzer, Douglas and Dillhage, Ruth and Grubba, Tanja and Weihrauch, Klaus},
booktitle = {Proceedings of the Third International Conference on Computability and Complexity in Analysis},
series = {Electronic Notes in Theoretical Computer Science},
volume = {167},
publisher = {Elsevier},
address = {Amsterdam},
year = {2007},
pages = {79--93},
note = {{CCA} 2006, Gainesville, Florida, USA, November 1--5, 2006},
}
@article{Fra08,
author = {Franklin, Johanna N.Y.},
title = {{S}chnorr trivial reals: a construction},
journal = {Archive for Mathematical Logic},
volume = {46},
number = {7--8},
year = {2008},
pages = {665--678},
}
@incollection{Fra20,
author = {Franklin, Johanna N.Y.},
title = {Relativization in randomness},
editor = {Franklin, Johanna N.Y. and Porter, Christopher P.},
booktitle = {Algorithmic Randomness: Progress and Prospects},
series = {Lecture Notes in Logic},
volume = {50},
publisher = {Cambridge University Press},
year = {2020},
pages = {134--174},
doi = {10.1017/9781108781718.006},
}
@inproceedings{Fra21,
author = {Franklin, Johanna N. Y.},
title = {A {C}hurch-{T}uring Thesis for Randomness?},
editor = {De Mol, Liesbeth and Weiermann, Andreas and Manea, Florin and Fern{\'a}ndez-Duque, David},
booktitle = {Connecting with Computability},
publisher = {Springer},
address = {Cham},
year = {2021},
pages = {217--226},
doi = {10.1007/978-3-030-80049-9_20},
}
@article{Fre83,
author = {Freund, Rudolf},
title = {Real Functions and Numbers Defined by {T}uring Machines},
journal = {Theoretical Computer Science},
volume = {23},
year = {1983},
pages = {287--304},
}
@inproceedings{Fri74,
author = {Friedman, Harvey},
title = {Some systems of second order arithmetic and their use},
booktitle = {Proceedings of the International Congress of Mathematicians, Vancouver},
volume = {1},
year = {1974},
pages = {235--242},
}
@article{Fri77,
author = {Friedman, H.M.},
title = {Set theoretic foundations for constructive analysis},
journal = {Ann. of Math.},
series = {2},
volume = {105},
year = {1977},
pages = {1--28},
}
@article{Fri84,
author = {Friedman, Harvey},
title = {The computational complexity of maximization and integration},
journal = {Advances in Mathematics},
volume = {53},
year = {1984},
pages = {80--98},
doi = {10.1016/0001-8708(84)90019-7},
}
@inproceedings{FS95,
author = {Freund, Rudolf and Staiger, Ludwig},
title = {Numbers defined via {T}uring machines},
editor = {Ko, Ker-I and Weihrauch, Klaus},
booktitle = {Computability and Complexity in Analysis},
series = {Informatik Berichte},
volume = {190},
publisher = {FernUniversit\"at Hagen},
year = {1995},
month = sep,
pages = {119--124},
note = {CCA Workshop, Hagen, August 19--20, 1995},
}
@article{FS96,
author = {Freund, Rudolf and Staiger, Ludwig},
title = {Numbers defined by {T}uring machines},
journal = {Collegium Logicum, Annals of the Kurt-G\"{o}del-Society},
volume = {2},
year = {1996},
pages = {118--137},
doi = {10.1007/978-3-7091-9461-4_8},
}
@article{FSS22,
author = {Fiori-Carones, Marta and Shafer, Paul and Sold{\`a}, Giovanni},
title = {An inside/outside {R}amsey theorem and recursion theory},
journal = {Transactions of the American Mathematical Society},
volume = {375},
year = {2022},
pages = {1977--2024},
doi = {10.1090/tran/8561},
}
@article{FSW06,
author = {Figueira, Santiago and Stephan, Frank and Wu, Guohua},
title = {Randomness and universal machines},
journal = {Journal of Complexity},
volume = {22},
number = {6},
year = {2006},
pages = {738--751},
}
@article{FT14,
author = {Franklin, Johanna N. Y. and Towsner, Henry},
title = {Randomness and non-ergodic systems},
journal = {Moscow Mathematical Journal},
volume = {14},
number = {4},
year = {2014},
pages = {711--744, 827},
}
@phdthesis{Fuj15,
author = {Fujiwara, Makoto},
title = {Intuitionistic and uniform provability in reverse mathematics},
school = {Tohoku University},
address = {Sendai, Japan},
year = {2015},
}
@inproceedings{Fuj20,
author = {Fujiwara, Makoto},
title = {Parallelizations in {W}eihrauch Reducibility and Constructive Reverse Mathematics},
editor = {Anselmo, Marcella and Della Vedova, Gianluca and Manea, Florin and Pauly, Arno},
booktitle = {Beyond the Horizon of Computability},
publisher = {Springer International Publishing},
address = {Cham},
year = {2020},
pages = {38--49},
doi = {10.1007/978-3-030-51466-2_4},
}
@article{Fuj21,
author = {Fujiwara, Makoto},
title = {Weihrauch and constructive reducibility between existence statements},
journal = {Computability},
volume = {10},
number = {1},
year = {2021},
doi = {10.3233/COM-190278},
}
@article{FZ15,
author = {Fu, Ming Quan and Zucker, Jeffery},
title = {Models of computation for partial functions on the reals},
journal = {Journal of Logical and Algebraic Methods in Programming},
volume = {84},
number = {2},
year = {2015},
pages = {218--237},
doi = {10.1016/j.jlamp.2014.11.001},
}
@incollection{FZ16,
author = {F{\'e}r{\'e}e, Hugo and Ziegler, Martin},
title = {On the computational complexity of positive linear functionals on {$C[0;1]$}},
editor = {Kotsireas, Ilias S. and Rump, Siegfried M. and Yap, Chee K.},
booktitle = {Mathematical Aspects of Computer and Information Sciences},
series = {Lecture Notes in Computer Science},
volume = {9582},
publisher = {Springer},
address = {Cham},
year = {2016},
pages = {489--504},
note = {6th International Conference, {MACIS} 2015, Berlin, Germany, November 11--13, 2015, Revised Selected Papers},
}
@article{Gac05,
author = {G{\'{a}}cs, Peter},
title = {Uniform test of algorithmic randomness over a general space},
journal = {Theoretical Computer Science},
volume = {341},
year = {2005},
pages = {91--137},
}
@inproceedings{GAC12,
author = {Gao, Sicun and Avigad, Jeremy and Clarke, Edmund M.},
title = {Delta-decidability over the reals},
booktitle = {Proceedings of the 2012 27th {A}nnual {ACM}/{IEEE} {S}ymposium on {L}ogic in {C}omputer {S}cience},
publisher = {IEEE Computer Soc., Los Alamitos, CA},
year = {2012},
pages = {305--314},
doi = {10.1109/LICS.2012.41},
}
@inproceedings{GAC12a,
author = {Gao, Sicun and Avigad, Jeremy and Clarke, Edmund M.},
title = {{$\delta$}-complete decision procedures for satisfiability over the reals},
booktitle = {Automated reasoning},
series = {Lecture Notes in Comput. Sci.},
volume = {7364},
publisher = {Springer},
address = {Heidelberg},
year = {2012},
pages = {286--300},
}
@book{Gai64,
author = {Gaier, D.},
title = {Konstruktive {M}ethoden der konformen {A}bbildung, {T}racts in {N}atural {P}hilosophy},
volume = {3},
publisher = {Springer},
address = {Berlin},
year = {1964},
}
@article{Gal00,
author = {Galatolo, Stefano},
title = {Orbit computability by computable structures},
journal = {Nonlinearity},
volume = {13},
year = {2000},
pages = {1531--1546},
}
@article{Gal03,
author = {Galatolo, Stefano},
title = {Complexity, initial condition sensitivity, dimension and weak chaos in dynamical systems},
journal = {Nonlinearity},
volume = {16},
number = {4},
year = {2003},
pages = {1219--1238},
}
@article{Gal03a,
author = {Galatolo, Stefano},
title = {Global and local complexity in weakly chaotic dynamical systems},
journal = {Discrete and Continuous Dynamical Systems},
volume = {9},
number = {6},
year = {2003},
pages = {1607--1624},
}
@inproceedings{Gal15,
author = {Galicki, Alex},
title = {Randomness and Differentiability of Convex Functions},
editor = {Beckmann, Arnold and Mitrana, Victor and Soskova, Mariya},
booktitle = {Evolving Computability},
series = {Lecture Notes in Computer Science},
volume = {9136},
publisher = {Springer},
address = {Cham},
year = {2015},
pages = {196--205},
note = {11th Conference on Computability in Europe, CiE 2015, Bucharest, Romania, June 29--July 3, 2015},
doi = {10.1007/978-3-319-20028-6_20},
}
@inproceedings{Gal16,
author = {Galeotti, Lorenzo},
title = {A Candidate for the Generalised Real Line},
editor = {Beckmann, Arnold and Bienvenu, Laurent and Jonoska, Nata\v{s}a},
booktitle = {Pursuit of the Universal},
series = {Lecture Notes in Computer Science},
volume = {9709},
publisher = {Springer},
address = {Switzerland},
year = {2016},
pages = {271--281},
note = {12th Conference on Computability in Europe, CiE 2016, Paris, France, June 27 - July 1, 2016},
doi = {10.1007/978-3-319-40189-8_28},
}
@incollection{Gal17,
author = {Galicki, Alex},
title = {Polynomial-time {R}ademacher theorem, porosity and randomness},
editor = {Chatzigiannakis, Ioannis and Indyk, Piotr and Kuhn, Fabian and Muscholl, Anca},
booktitle = {44th {I}nternational {C}olloquium on {A}utomata, {L}anguages, and {P}rogramming},
series = {LIPIcs. Leibniz Int. Proc. Inform.},
volume = {80},
publisher = {Schloss Dagstuhl. Leibniz-Zent. Inform., Wadern},
year = {2017},
pages = {Art. No. 30, 13},
doi = {10.4230/LIPIcs.ICALP.2017.30},
}
@phdthesis{Gal18,
author = {Galicki, Aleksander},
title = {Computable Randomness and Differentiability in $R^n$},
school = {Department of Computer Science, University of Auckland},
year = {2018},
}
@article{Gal99,
author = {Galatolo, Stefano},
title = {Pointwise information entropy for metric spaces},
journal = {Nonlinearity},
volume = {12},
year = {1999},
pages = {1289--1298},
}
@incollection{GB93,
author = {Garzon, Max and Botelho, Fernanda},
title = {Real computation with cellular automata},
booktitle = {Cellular automata and cooperative systems ({L}es {H}ouches, 1992)},
series = {NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci.},
volume = {396},
publisher = {Kluwer Acad. Publ., Dordrecht},
year = {1993},
pages = {191--202},
}
@inproceedings{GBC08,
author = {Gra\c{c}a, Daniel S. and Buescu, Jorge and Campagnolo, Manuel L.},
title = {Boundedness of the domain of definition is undecidable for polynomial {ODEs}},
editor = {Dillhage, Ruth and Grubba, Tanja and Sorbi, Andrea and Weihrauch, Klaus and Zhong, Ning},
booktitle = {Proceedings of the Fourth International Conference on Computability and Complexity in Analysis ({CCA} 2007)},
series = {Electronic Notes in Theoretical Computer Science},
volume = {202},
publisher = {Elsevier},
year = {2008},
pages = {49--57},
note = {{CCA} 2007, Siena, Italy, June 16--18, 2007},
}
@article{GBC09,
author = {Gra{\c{c}}a, Daniel S. and Buescu, Jorge and Campagnolo, Manuel L.},
title = {Computational bounds on polynomial differential equations},
journal = {Applied Mathematics and Computation},
volume = {215},
number = {4},
year = {2009},
pages = {1375--1385},
doi = {10.1016/j.amc.2009.04.055},
}
@article{GC03,
author = {Gra{\c{c}}a, Daniel Silva and Costa, Jos\'{e} F\'{e}lix},
title = {Analog computers and recursive functions over the reals},
journal = {Journal of Complexity},
volume = {19},
number = {5},
year = {2003},
pages = {644--664},
}
@inproceedings{GCB05,
author = {Gra{\c{c}}a, Daniel Silva and Campagnolo, Manuel L. and Buescu, Jorge},
title = {Robust Simulations of {T}uring Machines with Analytic Maps and Flows},
editor = {Cooper, S. Barry and L{\"o}we, Benedikt and Torenvliet, Leen},
booktitle = {New Computational Paradigms},
series = {Lecture Notes in Computer Science},
volume = {3526},
publisher = {Springer},
address = {Berlin},
year = {2005},
pages = {169--179},
note = {First Conference on Computability in Europe, CiE 2005, Amsterdam, The Netherlands, June 2005},
}
@article{GCB08,
author = {Gra{\c{c}}a, Daniel S. and Campagnolo, Manuel L. and Buescu, Jorge},
title = {Computability with polynomial differential equations},
journal = {Advances in Applied Mathematics},
volume = {40},
number = {3},
year = {2008},
pages = {330--349},
doi = {10.1016/j.aam.2007.02.003},
}
@phdthesis{Ge93,
author = {Ge, Xiaolin},
title = {Some Algorithms in {E}uclidean Space and Group Representations},
school = {University of Minnesota},
address = {Minneapolis},
year = {1993},
month = may,
}
@article{Gel69,
author = {Gelfond, Michael G.},
title = {Constructive pseudofunctions ({R}ussian)},
journal = {Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov.},
volume = {16},
year = {1969},
pages = {20--27},
}
@article{Gel72,
author = {Gelfond, Michael G.},
title = {The relation between the classical and constructive versions of the construction of mathematical analysis ({R}ussian)},
journal = {Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov.},
volume = {32},
year = {1972},
pages = {5--11},
}
@inproceedings{Gel81,
author = {Gelfond, Michael G.},
title = {A class of theorems with valid constructive counterparts},
editor = {Richman, Fred},
booktitle = {Constructive mathematics},
series = {Lecture Notes in Mathematics},
volume = {873},
publisher = {Springer},
address = {Berlin},
year = {1981},
pages = {314--320},
note = {Conference held at the New Mexico State University, Las Cruces, N.M., August 11--15, 1980},
}
@article{Geo15,
author = {Georgiev, Ivan},
title = {Continued fractions of primitive recursive real numbers},
journal = {Mathematical Logic Quarterly},
volume = {61},
number = {4-5},
year = {2015},
pages = {288--306},
doi = {10.1002/malq.201400013},
}
@article{Geo20,
author = {Georgiev, Ivan},
title = {On subrecursive complexity of integration},
journal = {Annals of Pure and Applied Logic},
volume = {171},
number = {4},
year = {2020},
pages = {102777},
doi = {10.1016/j.apal.2020.102777},
}
@inproceedings{Geo21,
author = {Georgiev, Ivan},
title = {Dedekind Cuts and Long Strings of Zeros in Base Expansions},
editor = {De Mol, Liesbeth and Weiermann, Andreas and Manea, Florin and Fern{\'a}ndez-Duque, David},
booktitle = {Connecting with Computability},
publisher = {Springer},
address = {Cham},
year = {2021},
pages = {248--259},
doi = {10.1007/978-3-030-80049-9_23},
}
@phdthesis{Ger06,
author = {Gerhardy, Philipp},
title = {Applications of Proof Interpretations},
school = {Department of Computer Science, University of Aarhus, Denmark},
address = {Aarhus},
year = {2006},
}
@article{Ger06a,
author = {Gerhardy, Philipp},
title = {A quantitative version of {K}irk's fixed point theorem for asymptotic contractions},
journal = {J. Math. Anal. Appl.},
volume = {316},
year = {2006},
pages = {339--345},
}
@article{Ger08,
author = {Gerhardy, Philipp},
title = {Proof mining in topological dynamics},
journal = {Notre Dame Journal of Formal Logic},
volume = {49},
number = {4},
year = {2008},
pages = {431--446},
doi = {10.1215/00294527-2008-022},
}
@article{GG23,
author = {Gozzi, Riccardo and Gra\c{c}a},
title = {Characterizing time computational complexity classes with polynomial differential equations},
journal = {Computability},
volume = {12},
number = {1},
year = {2023},
pages = {23--57},
doi = {10.3233/COM-210384},
}
@inproceedings{GH00,
author = {G{\"a}rtner, Tobias and Hotz, G{\"u}nter},
title = {Recursive Analytic Functions of a Complex Variable},
editor = {Blanck, Jens and Brattka, Vasco and Hertling, Peter and Weihrauch, Klaus},
booktitle = {Computability and Complexity in Analysis},
series = {Informatik Berichte},
volume = {272},
publisher = {FernUniversit\"at Hagen},
year = {2000},
month = sep,
pages = {81--97},
note = {CCA 2000 Workshop, Swansea, Wales, September 17--19, 2000},
}
@article{GH16,
author = {Goldbring, Isaac and Hart, Bradd},
title = {Computability and the {C}onnes embedding problem},
journal = {The Bulletin of Symbolic Logic},
volume = {22},
number = {2},
year = {2016},
pages = {238--248},
doi = {10.1017/bsl.2016.5},
}
@article{GH21,
author = {Goldbring, Isaac and Hart, Bradd},
title = {Operator algebras with hyperarithmetic theory},
journal = {Journal of Logic and Computation},
volume = {31},
number = {2},
year = {2021},
pages = {612--629},
doi = {10.1093/logcom/exaa059},
}
@article{GH60,
author = {Goodstein, R.L. and Hooley, J.},
title = {On recursive transcendence},
journal = {Notre Dame J. Formal Logic},
volume = {1},
year = {1960},
pages = {127--137},
}
@inproceedings{Ghe06,
author = {Gherardi, Guido},
title = {An Analysis of the Lemmas of {U}rysohn and {U}rysohn-{T}ietze According to Effective {B}orel Measurability},
editor = {Beckmann, A. and Berger, U. and L{\"o}we, B. and Tucker, J.V.},
booktitle = {Logical Approaches to Computational Barriers},
series = {Lecture Notes in Computer Science},
volume = {3988},
publisher = {Springer},
address = {Berlin},
year = {2006},
pages = {199--208},
note = {Second Conference on Computability in Europe, CiE 2006, Swansea, UK, June 30-July 5, 2006},
}
@article{Ghe06a,
author = {Gherardi, Guido},
title = {Effective {B}orel degrees of some topological functions},
journal = {Mathematical Logic Quarterly},
volume = {52},
number = {6},
year = {2006},
pages = {625--642},
}
@phdthesis{Ghe06b,
author = {Gherardi, Guido},
title = {Some Results in Computable Analysis and Effective {B}orel Measurability},
school = {University of Siena, Department of Mathematics and Computer Science},
address = {Siena},
year = {2006},
}
@inproceedings{Ghe07,
author = {Gherardi, Guido},
title = {Internal Computability},
editor = {Cooper, S. Barry and L{\"o}we, Benedikt and Sorbi, Andrea},
booktitle = {Computation and Logic in the Real World},
series = {Lecture Notes in Computer Science},
volume = {4497},
publisher = {Springer},
address = {Berlin},
year = {2007},
pages = {348--357},
note = {Third Conference on Computability in Europe, CiE 2007, Siena, Italy, June 18-23, 2007},
}
@incollection{Ghe08a,
author = {Gherardi, Guido},
title = {Computability and incomputability of differential equations},
editor = {Corsi, Giovanna and Lupacchini, Rossella},
booktitle = {Deduction, Computation, Experiment},
publisher = {Springer Verlag},
address = {Milano},
year = {2008},
pages = {223--242},
doi = {10.1007/978-88-470-0784-0_12},
}
@article{Ghe11,
author = {Gherardi, Guido},
title = {Alan {T}uring and the foundations of computable analysis},
journal = {Bull. Symbolic Logic},
volume = {17},
number = {3},
year = {2011},
pages = {394--430},
doi = {10.2178/bsl/1309952319},
}
@article{GHK+20,
author = {Gorman, Alexi Block and Hieronymi, Philipp and Kaplan, Elliot and Meng, Ruoyu and Walsberg, Erik and Wang, Zihe and Xiong, Ziqin and Yang, Hongru},
title = {Continuous Regular Functions},
journal = {Logical Methods in Computer Science},
volume = {16},
number = {1},
year = {2020},
month = Feb,
pages = {17:1-17:24},
doi = {10.23638/LMCS-16(1:17)2020},
}
@article{GHM15,
author = {Gura, Kirill and Hirst, Jeffry L. and Mummert, Carl},
title = {On the existence of a connected component of a graph},
journal = {Computability},
volume = {4},
number = {2},
year = {2015},
pages = {103--117},
doi = {10.3233/COM-150039},
}
@article{GHR09,
author = {Galatolo, Stefano and Hoyrup, Mathieu and Rojas, Crist{\'o}bal},
title = {A constructive {B}orel-{C}antelli lemma. {C}onstructing orbits with required statistical properties},
journal = {Theoretical Computer Science},
volume = {410},
year = {2009},
pages = {2207--2222},
}
@inproceedings{GHR09a,
author = {G{\'a}cs, Peter and Hoyrup, Mathieu and Rojas, Crist{\'o}bal},
title = {Randomness on computable probability spaces---a dynamical point of view},
editor = {Susanne Albers and Jean-Yves Marion},
booktitle = {S{TACS} 2009: 26th {I}nternational {S}ymposium on {T}heoretical {A}spects of {C}omputer {S}cience},
series = {LIPIcs. Leibniz Int. Proc. Inform.},
volume = {3},
publisher = {Schloss Dagstuhl. Leibniz-Zent. Inform., Wadern},
year = {2009},
pages = {469--480},
}
@article{GHR10,
author = {Galatolo, Stefano and Hoyrup, Mathieu and Rojas, Crist{\'o}bal},
title = {Effective symbolic dynamics, random points, statistical behavior, complexity and entropy},
journal = {Information and Computation},
volume = {208},
number = {1},
year = {2010},
pages = {23--41},
doi = {10.1016/j.ic.2009.05.001},
}
@inproceedings{GHR10a,
author = {Galatolo, Stefano and Hoyrup, Mathieu and Rojas, Crist{\'o}bal},
title = {Computing the speed of convergence of ergodic averages and pseudorandom points in computable dynamical systems},
editor = {Zheng, Xizhong and Zhong, Ning},
booktitle = {Proceedings Seventh International Conference on Computability and Complexity in Analysis 2010},
series = {Electronic Proceedings in Theoretical Computer Science},
volume = {24},
publisher = {Open Publishing Association},
year = {2010},
pages = {7--18},
note = {{Z}henjiang, China, 21-25th June 2010},
doi = {10.4204/EPTCS.24.6},
}
@article{GHR11,
author = {Galatolo, Stefano and Hoyrup, Mathieu and Rojas, Cristobal},
title = {Dynamics and abstract computability: computing invariant measures},
journal = {Discrete and Continuous Dynamical Systems. Series A},
volume = {29},
number = {1},
year = {2011},
pages = {193--212},
doi = {10.3934/dcds.2011.29.193},
}
@article{GHR11a,
author = {G{\'a}cs, Peter and Hoyrup, Mathieu and Rojas, Crist{\'o}bal},
title = {Randomness on computable probability spaces---a dynamical point of view},
journal = {Theory of Computing Systems},
volume = {48},
number = {3},
year = {2011},
pages = {465--485},
doi = {10.1007/s00224-010-9263-x},
}
@article{GHR12,
author = {Galatolo, Stefano and Hoyrup, Mathieu and Rojas, Crist{\'o}bal},
title = {Statistical properties of dynamical systems---simulation and abstract computation},
journal = {Chaos, Solitons and Fractals},
volume = {45},
number = {1},
year = {2012},
pages = {1--14},
doi = {10.1016/j.chaos.2011.09.011},
}
@article{GHRS20,
author = {Gangloff, Silv\'{e}re and Herrera, Alonso and Rojas, Cristobal and Sablik, Mathieu},
title = {Computability of topological entropy: from general systems to transformations on {C}antor sets and the interval},
journal = {Discrete and Continuous Dynamical Systems. Series A},
volume = {40},
number = {7},
year = {2020},
pages = {4259--4286},
doi = {10.3934/dcds.2020180},
}
@phdthesis{Gia93,
author = {Di Gianantonio, Pietro},
title = {A Functional Approach to Computability on Real Numbers},
school = {Universit\`{a} di Pisa-Genova-Udine},
address = {Udine},
year = {1993},
month = jun,
}
@article{Gia96,
author = {Di Gianantonio, Pietro},
title = {Real number computation and Domain Theory},
journal = {Information and Computation},
volume = {127},
year = {1996},
pages = {11--25},
}
@article{Gia99,
author = {Di Gianantonio, Pietro},
title = {An abstract data type for real numbers},
journal = {Theoretical Computer Science},
volume = {221},
year = {1999},
pages = {295--326},
}
@article{GK06,
author = {Gerhardy, Philipp and Kohlenbach, Ulrich},
title = {Strongly uniform bounds from semi-constructive proofs},
journal = {Annals of Pure and Applied Logic},
volume = {141},
number = {1--2},
year = {2006},
pages = {89--107},
}
@article{GK08,
author = {Gerhardy, Philipp and Kohlenbach, Ulrich},
title = {General logical metatheorems for functional analysis},
journal = {Transactions of the American Mathematical Society},
volume = {360},
number = {5},
year = {2008},
pages = {2615--2660},
doi = {10.1090/S0002-9947-07-04429-7},
}
@article{GK10,
author = {Gaspar, Jaime and Kohlenbach, Ulrich},
title = {On {T}ao's ``finitary'' infinite pigeonhole principle},
journal = {J. Symbolic Logic},
volume = {75},
number = {1},
year = {2010},
pages = {355--371},
doi = {10.2178/jsl/1264433926},
}
@article{GKN21,
author = {Gregoriades, Vassilios and Kihara, Takayuki and Ng, Keng Meng},
title = {Turing Degrees in {P}olish Spaces and Decomposibility of {B}orel Functions},
journal = {Journal of Mathematical Logic},
volume = {21},
number = {01},
year = {2021},
pages = {{2050021}},
doi = {10.1142/S021906132050021X},
}
@article{GKP17,
author = {Gregoriades, Vassilios and Kisp{\'e}ter, Tam{\'a}s and Pauly, Arno},
title = {A comparison of concepts from computable analysis and effective descriptive set theory},
journal = {Mathematical Structures in Computer Science},
volume = {27},
number = {8},
publisher = {Cambridge University Press},
year = {2017},
pages = {1414--1436},
doi = {10.1017/S0960129516000128},
}
@inproceedings{GKS18,
author = {Georgiev, Ivan and Kristiansen, Lars and Stephan, Frank},
title = {On General Sum Approximations of Irrational Numbers},
editor = {Manea, Florin and Miller, Russell G. and Nowotka, Dirk},
booktitle = {Sailing Routes in the World of Computation},
publisher = {Springer},
address = {Cham},
year = {2018},
pages = {194--203},
doi = {10.1007/978-3-319-94418-0_20},
}
@article{GKS21,
author = {Georgiev, Ivan and Kristiansen, Lars and Stephan, Frank},
title = {Computable irrational numbers with representations of surprising complexity},
journal = {Annals of Pure and Applied Logic},
volume = {172},
number = {2},
year = {2021},
pages = {102893},
doi = {10.1016/j.apal.2020.102893},
}
@article{GKT19,
author = {Greenberg, Noam and Kuyper, Rutger and Turetsky, Dan},
title = {Cardinal invariants, non-lowness classes, and {W}eihrauch reducibility},
journal = {Computability},
volume = {8},
number = {3, 4},
year = {2019},
pages = {305--346},
doi = {10.3233/COM-180219},
}
@inproceedings{GL01,
author = {Gowland, Paul and Lester, David},
title = {A Survey of Exact Arithmetic Implementations},
editor = {Blanck, Jens and Brattka, Vasco and Hertling, Peter},
booktitle = {Computability and Complexity in Analysis},
series = {Lecture Notes in Computer Science},
volume = {2064},
publisher = {Springer},
address = {Berlin},
year = {2001},
pages = {30--47},
note = {4th International Workshop, CCA 2000, Swansea, UK, September 2000},
}
@inproceedings{GL08,
author = {Gu, Xiaoyang and Lutz, Jack H.},
title = {Effective dimensions and relative frequencies},
booktitle = {Logic and theory of algorithms},
series = {Lecture Notes in Comput. Sci.},
volume = {5028},
publisher = {Springer},
address = {Berlin},
year = {2008},
pages = {231--240},
doi = {10.1007/978-3-540-69407-6_27},
}
@article{GL11,
author = {Gu, Xiaoyang and Lutz, Jack H.},
title = {Effective dimensions and relative frequencies},
journal = {Theoret. Comput. Sci.},
volume = {412},
number = {48},
year = {2011},
pages = {6696--6711},
doi = {10.1016/j.tcs.2011.08.023},
}
@article{Gli28,
author = {Glivenko, V.I.},
title = {Sur la logique de {M}. {B}rouwer},
journal = {Roy. Belg. Bull. Cl. Sci.},
series = {5},
volume = {14},
year = {1928},
pages = {225--228},
}
@article{Gli29,
author = {Glivenko, V.I.},
title = {Sur quelques points de la logique de {M}. {B}rouwer},
journal = {Roy. Belg. Bull. Cl. Sci.},
series = {5},
volume = {15},
year = {1929},
pages = {183--188},
}
@inproceedings{GLM06,
author = {Gu, Xiaoyang and Lutz, Jack H. and Mayordomo, Elvira},
title = {Points on computable curves},
booktitle = {47th Annual IEEE Symposium on Foundations of Computer Science},
publisher = {IEEE Computer Society Press},
year = {2006},
pages = {469--474},
note = {Proceedings of FOCS 2006, Berkeley, CA, October 22--24, 2006},
}
@article{GLM11,
author = {Gu, Xiaoyang and Lutz, Jack H. and Mayordomo, Elvira},
title = {Curves that must be retraced},
journal = {Information and Computation},
volume = {209},
number = {6},
year = {2011},
pages = {992--1006},
doi = {10.1016/j.ic.2011.01.004},
}
@article{GLMM14,
author = {Gu, Xiaoyang and Lutz, Jack H. and Mayordomo, Elvira and Moser, Philippe},
title = {Dimension spectra of random subfractals of self-similar fractals},
journal = {Annals of Pure and Applied Logic},
volume = {165},
number = {11},
year = {2014},
pages = {1707--1726},
doi = {10.1016/j.apal.2014.07.001},
}
@article{GM02,
author = {Gori, Marco and Meer, Klaus},
title = {A Step towards a Complexity Theory for Analog Systems},
journal = {Mathematical Logic Quarterly},
volume = {48},
number = {Suppl. 1},
year = {2002},
pages = {45--58},
}
@inproceedings{GM08,
author = {Gherardi, Guido and Marcone, Alberto},
title = {How Incomputable is the Separable {H}ahn-{B}anach Theorem?},
editor = {Brattka, Vasco and Dillhage, Ruth and Grubba, Tanja and Klutsch, Angela},
booktitle = {{CCA} 2008, Fifth International Conference on Computability and Complexity in Analysis},
series = {Electronic Notes in Theoretical Computer Science},
volume = {221},
publisher = {Elsevier},
year = {2008},
pages = {85--102},
note = {{CCA} 2008, Fifth International Conference, Hagen, Germany, August 21--24, 2008},
}
@article{GM09,
author = {Gherardi, Guido and Marcone, Alberto},
title = {How Incomputable is the Separable {H}ahn-{B}anach Theorem?},
journal = {Notre Dame Journal of Formal Logic},
volume = {50},
number = {4},
year = {2009},
pages = {393--425},
doi = {10.1215/00294527-2009-018},
}
@inproceedings{GM72,
author = {Goodman, N.D. and Myhill, J.},
title = {The formalization of {B}ishop's constructive mathematics},
editor = {Lawvere, F. W.},
booktitle = {Toposes, Algebraic Geometry and Logic},
series = {Lecture Notes in Mathematics},
volume = {274},
year = {1972},
pages = {83--96},
note = {(Partial Report Conf. Connections between Category Theory, Algebraic Geometry and Intuitionistic Logic, Dalhousie Univ., Halifax, Nova Scotia, Jan. 16--19, 1971)},
}
@article{GMN21,
author = {Greenberg, Noam and Miller, Joseph S. and Nies, An},
title = {Highness properties close to {PA} completeness},
journal = {Israel Journal of Mathematics},
volume = {244},
year = {2021},
pages = {419--465},
doi = {10.1007/s11856-021-2200-7},
}
@article{GMP19,
author = {Gherardi, Guido and Marcone, Alberto and Pauly, Arno},
title = {Projection operators in the {W}eihrauch lattice},
journal = {Computability},
volume = {8},
number = {3, 4},
year = {2019},
pages = {281--304},
doi = {10.3233/COM-180207},
}
@inproceedings{GN02,
author = {Geuvers, Herman and Niqui, Milad},
title = {Constructive reals in {C}oq: axioms and categoricity},
booktitle = {Types for proofs and programs ({D}urham, 2000)},
series = {Lecture Notes in Comput. Sci.},
volume = {2277},
publisher = {Springer},
address = {Berlin},
year = {2002},
pages = {79--95},
doi = {10.1007/3-540-45842-5_6},
}
@article{GN14,
author = {Gavruskin, A. and Nies, A.},
title = {Universality for left-computably enumerable metric spaces},
journal = {Lobachevskii Journal of Mathematics},
volume = {35},
number = {4},
year = {2014},
pages = {292--294},
doi = {10.1134/S1995080214040179},
}
@inproceedings{GN16,
author = {Galicki, Aleksander and Nies, Andr\'{e}},
title = {A Computational Approach to the {B}orwein-{D}itor Theorem},
editor = {Beckmann, Arnold and Bienvenu, Laurent and Jonoska, Nata\v{s}a},
booktitle = {Pursuit of the Universal},
series = {Lecture Notes in Computer Science},
volume = {9709},
publisher = {Springer},
address = {Switzerland},
year = {2016},
pages = {99--104},
note = {12th Conference on Computability in Europe, CiE 2016, Paris, France, June 27 - July 1, 2016},
doi = {10.1007/978-3-319-40189-8_10},
}
@inproceedings{GN17,
author = {Galeotti, Lorenzo and Nobrega, Hugo},
title = {Towards Computable Analysis on the Generalized Real Line},
editor = {Kari, Jarkko and Manea, Florin and Petre, Ion},
booktitle = {Unveiling Dynamics and Complexity},
series = {Lecture Notes in Computer Science},
volume = {10307},
publisher = {Springer},
address = {Cham},
year = {2017},
pages = {246--257},
note = {13th Conference on Computability in Europe, CiE 2017, Turku, Finland, June 12-16, 2017},
doi = {10.1007/978-3-319-58741-7_24},
}
@inproceedings{GN94,
author = {Ge, Xiaolin and Nerode, Anil},
title = {On extreme points of convex compact {T}uring located sets},
editor = {Nerode, Anil and Matiyasevich, Yu. V.},
booktitle = {Logical Foundations of Computer Science},
series = {Lecture Notes in Computer Science},
volume = {813},
publisher = {Springer},
address = {Berlin},
year = {1994},
pages = {114--128},
note = {Third International Symposium, LFCS'94, St. Petersburg, Russia, July 11--14, 1994},
}
@article{GN96,
author = {Ge, Xiaolin and Nerode, Anil},
title = {Effective content of the calculus of variations {I}: semi-continuity and the chattering lemma},
journal = {Annals of Pure and Applied Logic},
volume = {78},
year = {1996},
pages = {127--146},
}
@article{GNR14,
author = {Galatolo, Stefano and Nisoli, Isaia and Rojas, Crist{\'o}bal},
title = {Probability, statistics and computation in dynamical systems},
journal = {Mathematical Structures in Computer Science},
volume = {24},
number = {3},
year = {2014},
pages = {e240304, 25},
doi = {10.1017/S0960129512000758},
}
@article{GNSW07,
author = {Geuvers, Herman and Niqui, Milad and Spitters, Bas and Wiedijk, Freek},
title = {Constructive analysis, types and exact real numbers},
journal = {Mathematical Structures in Computer Science},
volume = {17},
year = {2007},
pages = {3--36},
}
@phdthesis{Goh19a,
author = {Goh, Jun Le},
title = {Measuring the Relative Complexity of Mathematical Constructions and Theorems},
school = {Cornell University},
year = {2019},
month = {August},
doi = {10.7298/0h3c-x173},
}
@article{Goh20,
author = {Goh, Jun Le},
title = {Compositions of multivalued functions},
journal = {Computability},
volume = {9},
number = {3-4},
year = {2020},
pages = {231--247},
doi = {10.3233/com-180235},
}
@article{Goh20a,
author = {Goh, Jun Le},
title = {Embeddings between well-orderings: Computability-theoretic reductions},
journal = {Annals of Pure and Applied Logic},
volume = {171},
number = {6},
year = {2020},
pages = {102789},
doi = {10.1016/j.apal.2020.102789},
}
@article{Gom12,
author = {Gomaa, Walid},
title = {A survey of recursive analysis and {M}oore's notion of real computation},
journal = {Natural Computing},
volume = {11},
number = {1},
year = {2012},
pages = {37--49},
}
@article{Goo49,
author = {Goodstein, R.L.},
title = {Missing value theorems},
journal = {Math. Gaz.},
volume = {33},
year = {1949},
pages = {19--25},
}
@article{Goo50,
author = {Goodstein, R.L.},
title = {Mean value theorems in recursive function theory {I}. {D}ifferential mean value theorems},
journal = {Proc. London Math. Soc.},
volume = {52},
year = {1950},
pages = {81--106},
}
@article{Goo54,
author = {Goodstein, R.L.},
title = {The recursive irrationality of $\pi$},
journal = {The Journal of Symbolic Logic},
volume = {19},
year = {1954},
pages = {267--274},
}
@article{Goo56,
author = {Goodstein, R.L.},
title = {On non-constructive theorems of analysis and the decision problem},
journal = {Math. Scand.},
volume = {3},
year = {1956},
pages = {261--263},
}
@inproceedings{Goo59,
author = {Goodstein, R.L.},
title = {Recursive analysis},
editor = {Heyting, A.},
booktitle = {Constructivity in Mathematics},
series = {Studies in Logic and the Foundations of Mathematics},
publisher = {North-Holland},
address = {Amsterdam},
year = {1959},
pages = {37--42},
note = {Proc. Colloq., Amsterdam, Aug. 26--31, 1957},
}
@book{Goo61,
author = {Goodstein, R.L.},
title = {Recursive Analysis},
series = {Studies in Logic and the Foundations of Mathematics},
publisher = {North-Holland},
address = {Amsterdam},
year = {1961},
}
@article{Goo68,
author = {Goodstein, R.L.},
title = {Existence in mathematics},
journal = {Compositio Math.},
volume = {20},
year = {1968},
pages = {70--82},
}
@inproceedings{Goo69,
author = {Goodstein, R.L.},
title = {A constructive form for the second {G}auss proof of the fundamental theorem of algebra},
booktitle = {Constructive Aspects of the Fundamental Theorem of Algebra},
publisher = {Willey-Interscience},
address = {NY},
year = {1969},
pages = {69--76},
note = {Proc. Sympos. Z\"urich-R\"uschlikon, June 5--7, 1967},
}
@article{Goo70,
author = {Goodstein, R.L.},
title = {Polynomials with computable coefficients},
journal = {Notre Dame J. Formal Logic},
volume = {11},
year = {1970},
pages = {447--448},
}
@article{Got15,
author = {Gottwald, Siegfried},
title = {Dieter {K}laua---obituary},
journal = {Fuzzy Sets and Systems},
volume = {259},
year = {2015},
pages = {126--127},
doi = {10.1016/j.fss.2014.09.017},
}
@article{Gou15,
author = {Goubault-Larrecq, Jean},
title = {A short proof of the {S}chr{\"o}der-{S}impson Theorem},
journal = {Mathematical Structures in Computer Science},
volume = {25},
number = {01},
year = {2015},
month = {January},
pages = {1--5},
doi = {10.1017/S0960129513000467},
}
@incollection{GPS21,
author = {Ga{\ss}ner, Christine and Pauly, Arno and Steinberg, Florian},
title = {Computing measure as a primitive operation in real number computation},
booktitle = {29th {EACSL} {A}nnual {C}onference on {C}omputer {S}cience {L}ogic},
series = {LIPIcs. Leibniz Int. Proc. Inform.},
volume = {183},
publisher = {Schloss Dagstuhl. Leibniz-Zent. Inform., Wadern},
year = {2021},
pages = {Art. No. 22, 22},
}
@article{GPV21,
author = {Goh, Jun Le and Pauly, Arno and Valenti, Manlio},
title = {Finding descending sequences through ill-founded linear orders},
journal = {The Journal of Symbolic Logic},
volume = {86},
number = {2},
year = {2021},
pages = {817--854},
doi = {10.1017/jsl.2021.15},
}
@inproceedings{GR93,
author = {Ge, Xiaolin and Richards, J. Ian},
title = {Computability in unitary representations of compact groups},
editor = {Crossley, John N. and Remmel, Jefferey B. and Shore, Richard A. and Sweedler, Moss E.},
booktitle = {Logical Methods in Honor of Anil Nerode's Sixtieth Birthday},
series = {Progress in Computer Science and Applied Logic},
volume = {12},
publisher = {Birkh\"auser},
address = {Boston},
year = {1993},
pages = {386--421},
}
@inproceedings{Gra03,
author = {Gra{\c{c}}a, Daniel Silva},
title = {Computability via analog circuits},
editor = {Brattka, Vasco and Schr{\"{o}}der, Matthias and Weihrauch, Klaus and Zhong, Ning},
booktitle = {Computability and Complexity in Analysis},
series = {Informatik Berichte},
volume = {302},
publisher = {FernUniversit\"at in Hagen},
year = {2003},
month = aug,
pages = {229--240},
note = {International Conference, CCA 2003, Cincinnati, USA, August 28--30, 2003},
}
@article{Gra04,
author = {Gra{\c{c}}a, Daniel Silva},
title = {Some recent developments on {S}hannon's General Purpose Analog Computer},
journal = {Mathematical Logic Quarterly},
volume = {50},
number = {4,5},
year = {2004},
pages = {473--485},
}
@article{Gra16,
author = {Gra\c{c}a, Daniel S.},
title = {Calculability of the asymptotic behavior of dynamical systems},
journal = {Boletim da Sociedade Portuguesa de Matem\'{a}tica},
number = {Special issue},
year = {2016},
pages = {95--98},
}
@incollection{Gra84,
author = {Grayson, Robin J.},
title = {Heyting-Valued Semantics},
editor = {Lolli, G. and Longo, G. and Marcja, A.},
booktitle = {Logic Colloquium '82},
series = {Studies in Logic and the Foundations of Mathematics},
volume = {112},
publisher = {Elsevier},
year = {1984},
pages = {181--208},
}
@article{Gre11,
author = {Gregoriades, Vassilios},
title = {The descriptive set-theoretic complexity of the set of points of continuity of a multi-valued function},
journal = {Logical Methods in Computer Science},
volume = {7},
year = {2011},
pages = {4:2, 42},
doi = {10.2168/LMCS-7(4:2)2011},
}
@article{Gri71,
author = {Grilliot, Thomas J.},
title = {On effectively discontinuous type-{$2$} objects},
journal = {The Journal of Symbolic Logic},
volume = {36},
year = {1971},
pages = {245--248},
}
@article{GRZ18,
author = {Gra\c{c}a, Daniel and Rojas, Cristobal and Zhong, Ning},
title = {Computing geometric {L}orenz attractors with arbitrary precision},
journal = {Transactions of the American Mathematical Society},
volume = {370},
number = {4},
year = {2018},
pages = {2955--2970},
doi = {10.1090/tran/7228},
}
@article{Grz51,
author = {Grzegorczyk, Andrzej},
title = {Undecidability of some topological theories},
journal = {Fund. Math.},
volume = {38},
year = {1951},
pages = {137--152},
}
@article{Grz55,
author = {Grzegorczyk, Andrzej},
title = {Computable functionals},
journal = {Fundamenta Mathematicae},
volume = {42},
year = {1955},
pages = {168--202},
}
@article{Grz55a,
author = {Grzegorczyk, Andrzej},
title = {On the definition of computable functionals},
journal = {Fundamenta Mathematicae},
volume = {42},
year = {1955},
pages = {232--239},
}
@article{Grz57,
author = {Grzegorczyk, Andrzej},
title = {On the definitions of computable real continuous functions},
journal = {Fundamenta Mathematicae},
volume = {44},
year = {1957},
pages = {61--71},
}
@inproceedings{Grz59,
author = {Grzegorczyk, Andrzej},
title = {Some approaches to constructive analysis},
editor = {Heyting, A.},
booktitle = {Constructivity in Mathematics},
series = {Studies in Logic and the Foundations of Mathematics},
publisher = {North-Holland},
address = {Amsterdam},
year = {1959},
pages = {43--61},
note = {Colloquium at Amsterdam, 1957},
}
@inproceedings{Grz77,
author = {Grzegorczyk, Andrzej},
title = {Mathematical and empirical verifiability},
booktitle = {Twenty-five Years of logic. Methodol. in Poland},
year = {1977},
pages = {165--169},
}
@article{GS07,
author = {Gambino, Nicola and Schuster, Peter},
title = {Spatiality for formal topologies},
journal = {Mathematical Structures in Computer Science},
volume = {17},
year = {2007},
pages = {65--80},
}
@article{GS13,
author = {Georgiev, Ivan and Skordev, Dimiter},
title = {Conditional computability of real functions with respect to a class of operators},
journal = {Ann. Pure Appl. Logic},
volume = {164},
number = {5},
year = {2013},
pages = {550--565},
doi = {10.1016/j.apal.2012.11.004},
}
@article{GS83,
author = {Gordon, Dan and Shamir, Eliahu},
title = {Computation of recursive functionals using minimal initial segments},
journal = {Theoretical Computer Science},
volume = {23},
year = {1983},
pages = {305--315},
}
@article{GSW07,
author = {Grubba, Tanja and Schr{\"o}der, Matthias and Weihrauch, Klaus},
title = {Computable metrization},
journal = {Mathematical Logic Quarterly},
volume = {53},
number = {4--5},
year = {2007},
pages = {381--395},
}
@inproceedings{GW05a,
author = {Grubba, Tanja and Weihrauch, Klaus},
title = {A computable version of {D}ini's Theorem for topological spaces},
editor = {Yolum, Pinar and G{\"u}ng{\"o}r, Tunga and G{\"u}rgen, Fikret and {\"O}zturan, Can},
booktitle = {Computer and Information Sciences - ISCIS 2005},
series = {Lecture Notes in Computer Science},
volume = {3733},
publisher = {Springer},
address = {Berlin},
year = {2005},
pages = {927--936},
note = {20th International Symposium, ISCIS, Istanbul, Turkey, October 2005},
}
@inproceedings{GW07,
author = {Grubba, Tanja and Weihrauch, Klaus},
title = {On computable metrization},
editor = {Cenzer, Douglas and Dillhage, Ruth and Grubba, Tanja and Weihrauch, Klaus},
booktitle = {Proceedings of the Third International Conference on Computability and Complexity in Analysis},
series = {Electronic Notes in Theoretical Computer Science},
volume = {167},
publisher = {Elsevier},
address = {Amsterdam},
year = {2007},
pages = {345--364},
note = {{CCA} 2006, Gainesville, Florida, USA, November 1--5, 2006},
}
@inproceedings{GWX08,
author = {Grubba, Tanja and Weihrauch, Klaus and Xu, Yatao},
title = {Effectivity on Continuous Functions in Topological Spaces},
editor = {Dillhage, Ruth and Grubba, Tanja and Sorbi, Andrea and Weihrauch, Klaus and Zhong, Ning},
booktitle = {Proceedings of the Fourth International Conference on Computability and Complexity in Analysis ({CCA} 2007)},
series = {Electronic Notes in Theoretical Computer Science},
volume = {202},
publisher = {Elsevier},
year = {2008},
pages = {237--254},
note = {{CCA} 2007, Siena, Italy, June 16--18, 2007},
}
@inproceedings{GZ09,
author = {Gra{\c{c}}a, Daniel S. and Zhong, Ning},
title = {Computing domains of attraction for planar dynamics},
booktitle = {Unconventional computation},
series = {Lecture Notes in Comput. Sci.},
volume = {5715},
publisher = {Springer},
address = {Berlin},
year = {2009},
pages = {179--190},
doi = {10.1007/978-3-642-03745-0_22},
}
@article{GZ11,
author = {G{\"a}rtner, Tobias and Ziegler, Martin},
title = {Real analytic machines and degrees: a topological view on algebraic limiting computation},
journal = {Log. Methods Comput. Sci.},
volume = {7},
number = {3},
year = {2011},
pages = {3:11, 20},
doi = {10.2168/LMCS-7 (3:11) 2011},
}
@article{GZ11a,
author = {Gra{\c{c}}a, Daniel and Zhong, Ning},
title = {Computability in planar dynamical systems},
journal = {Nat. Comput.},
volume = {10},
number = {4},
year = {2011},
pages = {1295--1312},
doi = {10.1007/s11047-010-9230-0},
}
@article{GZ15,
author = {Gra{\c{c}}a, Daniel and Zhong, Ning},
title = {An analytic System with a Computable Hyperbolic Sink Whose Basin of Attraction is Non-Computable},
journal = {Theory of Computing Systems},
volume = {57},
number = {2},
year = {2015},
pages = {478--520},
doi = {10.1007/s00224-015-9609-5},
}
@inproceedings{GZ18,
author = {Gra{\c{c}}a, Daniel S. and Zhong, Ning},
title = {Computability of ordinary differential equations},
booktitle = {Sailing routes in the world of computation},
series = {Lecture Notes in Computer Science},
volume = {10936},
publisher = {Springer},
address = {Cham},
year = {2018},
pages = {204--213},
doi = {10.1007/978-3-319-94418-0_21},
}
@incollection{GZ21,
author = {Gra{\c{c}}a, Daniel S. and Zhong, Ning},
title = {Computability of Differential Equations},
editor = {Brattka, Vasco and Hertling, Peter},
booktitle = {Handbook of Computability and Complexity in Analysis},
series = {Theory and Applications of Computability},
publisher = {Springer},
address = {Cham},
year = {2021},
pages = {71--99},
doi = {10.1007/978-3-030-59234-9_3},
}
@inproceedings{GZ21a,
author = {Gra{\c{c}}a, Daniel S. and Zhong, Ning},
title = {Computability of Limit Sets for Two-Dimensional Flows},
editor = {De Mol, Liesbeth and Weiermann, Andreas and Manea, Florin and Fern{\'a}ndez-Duque, David},
booktitle = {Connecting with Computability},
publisher = {Springer},
address = {Cham},
year = {2021},
pages = {494--503},
doi = {10.1007/978-3-030-80049-9_48},
}
@article{GZ21b,
author = {Gra\c{c}a, Daniel S. and Zhong, Ning},
title = {The set of hyperbolic equilibria and of invertible zeros on the unit ball is computable},
journal = {Theoretical Computer Science},
volume = {895},
year = {2021},
pages = {48--54},
doi = {10.1016/j.tcs.2021.09.028},
}
@article{GZ22,
author = {Gra\c{c}a, Daniel and Zhong, Ning},
title = {Computing the exact number of periodic orbits for planar flows},
journal = {Transactions of the American Mathematical Society},
volume = {375},
year = {2022},
pages = {5491--5538},
doi = {10.1090/tran/8644},
}
@article{GZB09,
author = {Gra{\c{c}}a, D. S. and Zhong, N. and Buescu, J.},
title = {Computability, noncomputability and undecidability of maximal intervals of {IVP}s},
journal = {Transactions of the American Mathematical Society},
volume = {361},
number = {6},
year = {2009},
pages = {2913--2927},
doi = {10.1090/S0002-9947-09-04929-0},
}
@article{GZB12,
author = {Gra{\c{c}}a, Daniel S. and Zhong, Ning and Buescu, Jorge},
title = {Computability, noncomputability, and hyperbolic systems},
journal = {Appl. Math. Comput.},
volume = {219},
number = {6},
year = {2012},
pages = {3039--3054},
doi = {10.1016/j.amc.2012.09.031},
}
@article{GZD12,
author = {Gra{\c{c}}a, Daniel S. and Zhong, Ning and Dumas, H. S.},
title = {The connection between computability of a nonlinear problem and its linearization: {T}he {H}artman-{G}robman theorem revisited},
journal = {Theoret. Comput. Sci.},
volume = {457},
year = {2012},
pages = {101--110},
doi = {10.1016/j.tcs.2012.07.013},
}
@article{GZZ01,
author = {Gay, William and Zhang, Bing-Yu and Zhong, Ning},
title = {Computability of Solutions of the {K}orteweg-de {V}ries Equation},
journal = {Mathematical Logic Quarterly},
volume = {47},
number = {1},
year = {2001},
pages = {93--110},
}
@article{HA01,
author = {Hirowatari, Eiju and Arikawa, Setsuo},
title = {A comparison of identification criteria for inductive inference of recursive real-valued functions},
journal = {Theoretical Computer Science},
volume = {268},
year = {2001},
pages = {351--366},
}
@phdthesis{Hai06,
author = {Hainry, Emmanuel},
title = {Mod\`eles de calcul sur les r\'eels r\'esultats de comparaisons},
school = {l'Institut National Polytechnique de Lorraine},
year = {2006},
}
@inproceedings{Har93,
author = {Harrison, John},
title = {Constructing the real numbers in {HOL}},
booktitle = {Higher order logic theorem proving and its applications ({L}euven, 1992)},
series = {IFIP Trans. A Comput. Sci. Tech., A-20},
publisher = {North-Holland},
address = {Amsterdam},
year = {1993},
pages = {145--164},
}
@phdthesis{Har96,
author = {Harrison, John Robert},
title = {Theorem Proving with the Real Numbers},
school = {University of Cambridge},
address = {Cambridge, UK},
year = {1996},
}
@book{Har98a,
author = {Harrison, John},
title = {Theorem proving with the real numbers},
series = {CPHC/BCS Distinguished Dissertations},
publisher = {Springer-Verlag London Ltd.},
address = {London},
year = {1998},
pages = {xii+186},
doi = {10.1007/978-1-4471-1591-5},
}
@article{Hau71,
author = {Hauck, J\"urgen},
title = {{E}in {K}riterium f\"{u}r die {A}nnahme des {M}aximums in der {B}erechenbaren {A}nalysis},
journal = {Zeitschrift f\"ur Mathematische Logik und Grundlagen der Mathematik},
volume = {17},
year = {1971},
pages = {193--196},
}
@article{Hau71a,
author = {Hauck, J\"urgen},
title = {{Z}ur {P}r\"{a}zisierung des {B}egriffes berechenbare reelle {F}unktion},
journal = {Zeitschrift f\"ur Mathematische Logik und Grundlagen der Mathematik},
volume = {17},
year = {1971},
pages = {295--300},
}
@article{Hau72,
author = {Hauck, J\"urgen},
title = {{F}unktional-{R}ekursion},
journal = {Zeitschrift f\"ur Mathematische Logik und Grundlagen der Mathematik},
volume = {18},
year = {1972},
pages = {31--36},
}
@article{Hau72a,
author = {Hauck, J\"urgen},
title = {Berechenbare gleichm\"a\ss{}ige {S}tetigkeit in der konstruktiven {A}nalysis von {K}laua},
journal = {Wissenschaftliche Zeitschrift der Humboldt-Universit\"at zu Berlin Math.-Nat. R.},
volume = {21},
number = {5},
year = {1972},
pages = {523--526},
}
@article{Hau72b,
author = {Hauck, J\"urgen},
title = {Berechenbare gleichm\"a\ss{}ige {F}initheit rekursiver Funktionale},
journal = {Wissenschaftliche Zeitschrift der Humboldt-Universit\"at zu Berlin Math.-Nat. R.},
volume = {21},
number = {5},
year = {1972},
pages = {527--529},
}
@article{Hau73,
author = {Hauck, J\"urgen},
title = {{B}erechenbare reelle {F}unktionen},
journal = {Zeitschrift f\"ur Mathematische Logik und Grundlagen der Mathematik},
volume = {19},
year = {1973},
pages = {121--140},
}
@article{Hau75,
author = {Hauck, J\"urgen},
title = {Turingmaschinen und berechenbare reelle {F}unktionen},
journal = {Wissenschaftliche Zeitschrift der Humboldt-Universit\"at zu Berlin Math.-Nat. R.},
volume = {24},
number = {6},
year = {1975},
pages = {797--798},
}
@article{Hau75a,
author = {Hauck, J\"urgen},
title = {Iterationsverfahren in der konstruktiven {A}nalysis},
journal = {Wissenschaftliche Zeitschrift der Humboldt-Universit\"at zu Berlin Math.-Nat. R.},
volume = {24},
number = {6},
year = {1975},
pages = {799--800},
}
@article{Hau76,
author = {Hauck, J\"urgen},
title = {{B}erechenbare reelle {F}unktionenfolgen},
journal = {Zeitschrift f\"ur Mathematische Logik und Grundlagen der Mathematik},
volume = {22},
year = {1976},
pages = {265--282},
}
@article{Hau77,
author = {Hauck, J\"urgen},
title = {Zum {Z}wischenwertsatz in der konstruktiven {A}nalysis},
journal = {Wissenschaftliche Zeitschrift der Humboldt-Universit\"at zu Berlin Math.-Nat. R.},
volume = {26},
number = {5},
year = {1977},
pages = {623--627},
}
@article{Hau77a,
author = {Hauck, J\"urgen},
title = {Rekursive {F}unktionale und der {F}ixpunksatz von {B}anach},
journal = {Wissenschaftliche Zeitschrift der Humboldt-Universit\"at zu Berlin Math.-Nat. R.},
volume = {26},
number = {5},
year = {1977},
pages = {635--636},
}
@article{Hau78,
author = {Hauck, J\"urgen},
title = {{K}onstruktive {D}arstellungen reeller {Z}ahlen und {F}olgen},
journal = {Zeitschrift f\"ur Mathematische Logik und Grundlagen der Mathematik},
volume = {24},
year = {1978},
pages = {365--374},
}
@article{Hau80,
author = {Hauck, J\"urgen},
title = {{S}tetigkeitseigenschaften berechenbarer reeller {F}unktionen},
journal = {Zeitschrift f\"ur Mathematische Logik und Grundlagen der Mathematik},
volume = {26},
year = {1980},
pages = {69--76},
}
@article{Hau80a,
author = {Hauck, J\"urgen},
title = {{K}onstruktive {D}arstellungen in topologischen {R}\"{a}umen mit rekursiver {B}asis},
journal = {Zeitschrift f\"ur Mathematische Logik und Grundlagen der Mathematik},
volume = {26},
year = {1980},
pages = {565--576},
}
@article{Hau81,
author = {Hauck, J\"urgen},
title = {{B}erechenbarkeit in topologischen {R}\"{a}umen mit rekursiver {B}asis},
journal = {Zeitschrift f\"ur Mathematische Logik und Grundlagen der Mathematik},
volume = {27},
year = {1981},
pages = {473--480},
}
@article{Hau82,
author = {Hauck, J\"urgen},
title = {{S}tetigkeitseigenschaften berechenbarer {F}unktionale},
journal = {Zeitschrift f\"ur Mathematische Logik und Grundlagen der Mathematik},
volume = {28},
year = {1982},
pages = {377--383},
}
@article{Hau83,
author = {Hauck, J\"urgen},
title = {Konstruktive reelle {F}unktionale und {O}peratoren},
journal = {Zeitschrift f\"ur Mathematische Logik und Grundlagen der Mathematik},
volume = {29},
year = {1983},
pages = {213--218},
}
@article{Hau84,
author = {Hauck, J\"urgen},
title = {{E}ine neue {D}efinition berechenbarer reeller {F}unktionen},
journal = {Zeitschrift f\"ur Mathematische Logik und Grundlagen der Mathematik},
volume = {30},
year = {1984},
pages = {259--268},
}
@article{Hau84a,
author = {Hauck, J\"urgen},
title = {{Z}ur {W}ellengleichung mit konstruktiven {R}andbedingungen},
journal = {Zeitschrift f\"ur Mathematische Logik und Grundlagen der Mathematik},
volume = {30},
year = {1984},
pages = {561--566},
}
@article{Hau85,
author = {Hauck, J\"urgen},
title = {{E}in {K}riterium f\"{u}r die konstruktive {L}\"{o}sbarkeit der {D}ifferentialgleichung $y'=f(x,y)$},
journal = {Zeitschrift f\"ur Mathematische Logik und Grundlagen der Mathematik},
volume = {31},
year = {1985},
pages = {357--362},
}
@article{Hau87,
author = {Hauck, J\"urgen},
title = {{E}ine berechenbare {F}unktion mit rationalen {W}erten, die nicht rekursiv ist},
journal = {Zeitschrift f\"ur Mathematische Logik und Grundlagen der Mathematik},
volume = {33},
year = {1987},
pages = {255--256},
}
@phdthesis{Hav01,
author = {Havea, Robin Siale},
title = {Constructive Spectral and Numerical Range Theory},
school = {Department of Mathematics \& Statistics, University of Canterbury},
address = {Christchurch},
year = {2001},
}
@article{Hav05,
author = {Havea, Robin Siale},
title = {On Firmness of the State Space and Positive Elements of a {B}anach Algebra},
journal = {Journal of Universal Computer Science},
volume = {11},
number = {12},
year = {2005},
pages = {1963--1969},
}
@article{Hay06,
author = {Hayashi, Susumu},
title = {Mathematics based on incremental learning--Excluded middle and inductive inference},
journal = {Theoretical Computer Science},
volume = {350},
year = {2006},
pages = {125--139},
}
@inproceedings{HD01,
author = {Hur, Namhyun and Davenport, James H.},
title = {A Generic Root Operation for Exact Real Arithmetic},
editor = {Blanck, Jens and Brattka, Vasco and Hertling, Peter},
booktitle = {Computability and Complexity in Analysis},
series = {Lecture Notes in Computer Science},
volume = {2064},
publisher = {Springer},
address = {Berlin},
year = {2001},
pages = {82--87},
note = {4th International Workshop, CCA 2000, Swansea, UK, September 2000},
}
@article{Hec02,
author = {Heckmann, Reinhold},
title = {Contractivity of linear fractional transformations},
journal = {Theoretical Computer Science},
volume = {279},
year = {2002},
pages = {65--82},
}
@article{Hem00a,
author = {Hemmerling, Armin},
title = {On the Time Complexity of Partial Real Functions},
journal = {Journal of Complexity},
volume = {16},
year = {2000},
pages = {363--376},
}
@inproceedings{Hem00b,
author = {Hemmerling, Armin},
title = {Berechenbarkeit {\"{u}}ber den reellen {Z}ahlen, der approximative und der algebraische {Z}ugang},
editor = {Flachsmeyer, J{\"{u}}rgen and Fritsch, Rudolph and Reichel, Hans-Christian},
booktitle = {Mathematik-interdisziplin{\"{a}}r},
publisher = {Shaker Verlag},
address = {Aachen},
year = {2000},
pages = {167--176},
}
@inproceedings{Hem01,
author = {Hemmerling, Armin},
title = {Standard Representations of Effective Metric Spaces},
editor = {Blanck, Jens and Brattka, Vasco and Hertling, Peter},
booktitle = {Computability and Complexity in Analysis},
series = {Lecture Notes in Computer Science},
volume = {2064},
publisher = {Springer},
address = {Berlin},
year = {2001},
pages = {48--68},
note = {4th International Workshop, CCA 2000, Swansea, UK, September 2000},
}
@article{Hem02,
author = {Hemmerling, Armin},
title = {Effective metric spaces and representations of the reals},
journal = {Theoretical Computer Science},
volume = {284},
number = {2},
year = {2002},
pages = {347--372},
}
@article{Hem03,
author = {Hemmerling, Armin},
title = {Approximate decidability in {E}uclidean spaces},
journal = {Mathematical Logic Quarterly},
volume = {49},
number = {1},
year = {2003},
pages = {34--56},
}
@article{Hem03a,
author = {Hemmerling, Armin},
title = {The discrete parts of approximately decidable sets in {E}uclidean spaces},
journal = {Mathematical Logic Quarterly},
volume = {49},
number = {4},
year = {2003},
pages = {428--432},
}
@inproceedings{Hem03b,
author = {Hemmerling, Armin},
title = {Characterizations of the class $\Delta_2^{ta}$ over {E}uclidean spaces},
editor = {Brattka, Vasco and Schr{\"{o}}der, Matthias and Weihrauch, Klaus and Zhong, Ning},
booktitle = {Computability and Complexity in Analysis},
series = {Informatik Berichte},
volume = {302},
publisher = {FernUniversit\"at in Hagen},
year = {2003},
month = aug,
pages = {241--254},
note = {International Conference, CCA 2003, Cincinnati, USA, August 28--30, 2003},
}
@article{Hem04,
author = {Hemmerling, Armin},
title = {Characterizations of the class {$\Delta_2^{ta}$} over {E}uclidean spaces},
journal = {Mathematical Logic Quarterly},
volume = {50},
number = {4,5},
year = {2004},
pages = {507--519},
}
@inproceedings{Hem05,
author = {Hemmerling, Armin},
title = {Hierarchies of Function Classes Defined by the First-Value Operator (Extended Abstract)},
editor = {Brattka, Vasco and Staiger, Ludwig and Weihrauch, Klaus},
booktitle = {Proceedings of the 6th Workshop on Computability and Complexity in Analysis},
series = {Electronic Notes in Theoretical Computer Science},
volume = {120},
publisher = {Elsevier},
address = {Amsterdam},
year = {2005},
pages = {59--72},
note = {6th International Workshop, {CCA} 2004, Wittenberg, Germany, August 16--20, 2004},
}
@article{Hem06,
author = {Hemmerling, Armin},
title = {The {H}ausdorff-{E}rshov Hierarchy in {E}uclidean Spaces},
journal = {Archive for Mathematical Logic},
volume = {45},
year = {2006},
pages = {323--350},
}
@article{Hem08,
author = {Hemmerling, Armin},
title = {Hierarchies of function classes defined by the first-value operator},
journal = {Theoretical Informatics and Applications},
volume = {42},
number = {2},
year = {2008},
pages = {253--270},
}
@inproceedings{Hem98,
author = {Hemmerling, Armin},
title = {On the Time Complexity of Partial Real Functions},
editor = {Ko, Ker-I and Nerode, Anil and Pour-El, Marian B. and Weihrauch, Klaus and Wiedermann, Ji{\v{r}}{\'{\i}}},
booktitle = {Computability and Complexity in Analysis},
series = {Informatik Berichte},
volume = {235},
publisher = {FernUniversit\"at Hagen},
year = {1998},
month = aug,
pages = {31--40},
note = {CCA Workshop, Brno, Czech Republic, August, 1998},
}
@article{Hem99,
author = {Hemmerling, Armin},
title = {On Approximative and Algebraic Computability over the Real Numbers},
journal = {Theoretical Computer Science},
volume = {219},
year = {1999},
pages = {185--223},
}
@article{Hen11,
author = {Hendtlass, Matthew},
title = {The computational content of {W}alras' existence theorem},
journal = {Appl. Math. Comput.},
volume = {217},
number = {13},
year = {2011},
pages = {6185--6191},
doi = {10.1016/j.amc.2010.12.102},
}
@article{Hen12,
author = {Hendtlass, Matthew},
title = {The intermediate value theorem in constructive mathematics without choice},
journal = {Annals of Pure and Applied Logic},
volume = {163},
number = {8},
year = {2012},
pages = {1050--1056},
doi = {10.1016/j.apal.2011.12.026},
}
@article{Hen12a,
author = {Hendtlass, Matthew},
title = {Fixed point theorems in constructive mathematics},
journal = {Journal of Logic and Analysis},
volume = {4},
year = {2012},
pages = {Paper 10, 20},
}
@article{Hen12b,
author = {Hendtlass, Matthew},
title = {Constructing the minimal period of homomorphisms into {${R}^n$}},
journal = {Indagationes Mathematicae},
volume = {23},
number = {3},
year = {2012},
pages = {479--486},
doi = {10.1016/j.indag.2012.02.010},
}
@phdthesis{Hen13,
author = {Hendtlass, Matthew},
title = {Constructing fixed points and economic equilibria},
school = {Department of Pure Mathematics, University of Leeds},
address = {Leeds, UK},
year = {2013},
month = {April},
note = {{Ph.D.} thesis},
}
@inproceedings{Her01a,
author = {Hertling, Peter},
title = {Banach-{M}azur Computable Functions on Metric Spaces},
editor = {Blanck, Jens and Brattka, Vasco and Hertling, Peter},
booktitle = {Computability and Complexity in Analysis},
series = {Lecture Notes in Computer Science},
volume = {2064},
publisher = {Springer},
address = {Berlin},
year = {2001},
pages = {69--81},
note = {4th International Workshop, CCA 2000, Swansea, UK, September 2000},
}
@inproceedings{Her02b,
author = {Hertling, Peter},
title = {A Comparison of Certain Representations of Regularly Closed Sets},
editor = {Brattka, Vasco and Schr{\"{o}}der, Matthias and Weihrauch, Klaus},
booktitle = {{CCA} 2002 Computability and Complexity in Analysis},
series = {Electronic Notes in Theoretical Computer Science},
volume = {66},
publisher = {Elsevier},
address = {Amsterdam},
year = {2002},
note = {5th International Workshop, {CCA} 2002, M{\'{a}}laga, Spain, July 12--13, 2002},
}
@inproceedings{Her02c,
author = {Hertling, Peter},
title = {A {B}anach-{M}azur Computable But Not {M}arkov Computable Function on the Computable Real Numbers},
editor = {Widmayer, Peter and Triguero, Francisco and Morales, Rafael and Hennessy, Matthew and Eidenbenz, Stephan and Conejo, Ricardo},
booktitle = {Automata, Languages and Programming},
series = {Lecture Notes in Computer Science},
volume = {2380},
publisher = {Springer},
address = {Berlin},
year = {2002},
pages = {962--972},
note = {29th International Colloquium, ICALP, M{\'{a}}laga, Spain, July 8--13, 2002},
}
@article{Her02d,
author = {Hertling, Peter},
title = {Topological Complexity of Zero Finding with Algebraic Operations},
journal = {Journal of Complexity},
volume = {18},
number = {4},
year = {2002},
pages = {912--942},
}
@inproceedings{Her03a,
author = {Hertling, Peter},
title = {Topological complexity of zero finding for continuous functions (Abstract)},
editor = {Brattka, Vasco and Schr{\"{o}}der, Matthias and Weihrauch, Klaus and Zhong, Ning},
booktitle = {Computability and Complexity in Analysis},
series = {Informatik Berichte},
volume = {302},
publisher = {FernUniversit\"at in Hagen},
year = {2003},
month = aug,
pages = {13},
note = {International Conference, CCA 2003, Cincinnati, USA, August 28--30, 2003},
}
@article{Her05,
author = {Hertling, Peter},
title = {Is the {M}andelbrot set computable?},
journal = {Mathematical Logic Quarterly},
volume = {51},
number = {1},
year = {2005},
pages = {5--18},
}
@article{Her05a,
author = {Hertling, Peter},
title = {A {B}anach-{M}azur computable but not {M}arkov computable function on the computable real numbers},
journal = {Annals of Pure and Applied Logic},
volume = {132},
number = {2-3},
year = {2005},
pages = {227--246},
doi = {10.1016/j.apal.2004.08.001},
}
@article{Her05c,
author = {Hertling, Peter},
title = {Nonrandom sequences between random sequences},
journal = {Journal of Universal Computer Science},
volume = {11},
number = {12},
year = {2005},
pages = {1970--1985 (electronic)},
}
@article{Her06,
author = {Hertling, Peter},
title = {A sequentially computable function that is not effectively continuous at any point},
journal = {Journal of Complexity},
volume = {22},
number = {6},
year = {2006},
pages = {752--767},
doi = {10.1016/j.jco.2006.05.004},
}
@article{Her17,
author = {Hertling, Peter},
title = {{C}larke's Generalized Gradient and {E}dalat's {L}-derivative},
journal = {Journal of Logic \& Analysis},
volume = {9},
number = {c1},
year = {2017},
pages = {1--21},
doi = {10.4115/jla.2017.9.c1},
}
@article{Her20,
author = {Hertling, Peter},
title = {Forests describing {W}adge degrees and topological {W}eihrauch degrees of certain classes of functions and relations},
journal = {Computability},
volume = {9},
number = {3-4},
year = {2020},
pages = {249--307},
doi = {10.3233/com-190255},
}
@article{Her96b,
author = {Hertling, Peter},
title = {Topological complexity with continuous operations},
journal = {Journal of Complexity},
volume = {12},
year = {1996},
pages = {315--338},
doi = {10.1006/jcom.1996.0021},
}
@article{Her96c,
author = {Hertling, Peter},
title = {Disjunctive Omega-words und real numbers},
journal = {Journal of Universal Computer Science},
volume = {2},
number = {7},
year = {1996},
pages = {549--568},
}
@phdthesis{Her96d,
author = {Hertling, Peter},
title = {{U}nstetigkeitsgrade von {F}unktionen in der effektiven {A}nalysis},
school = {Fachbereich Informatik},
address = {FernUniversit\"{a}t Hagen},
year = {1996},
note = {{D}issertation},
}
@inproceedings{Her97,
author = {Hertling, Peter},
title = {Effectivity and Effective Continuity of Functions between Computable Metric Spaces},
editor = {Bridges, Douglas S. and Calude, Cristian S. and Gibbons, Jeremy and Reeves, Steve and Witten, Ian H.},
booktitle = {Combinatorics, Complexity, and Logic},
series = {Discrete Mathematics and Theoretical Computer Science},
publisher = {Springer},
address = {Singapore},
year = {1997},
pages = {264--275},
note = {Proceedings of DMTCS'96},
}
@article{Her97f,
author = {Hertling, Peter},
title = {Surjective Functions on Computably Growing {C}antor Sets},
journal = {Journal of Universal Computer Science},
volume = {3},
number = {11},
year = {1997},
pages = {1226--1240},
}
@article{Her99,
author = {Hertling, Peter},
title = {Standard Representations of Real Numbers},
journal = {Chaos, Solitons \& Fractals},
volume = {10},
number = {6},
year = {1999},
pages = {1087--1101},
}
@article{Her99a,
author = {Hertling, Peter},
title = {A Real Number Structure that is Effectively Categorical},
journal = {Mathematical Logic Quarterly},
volume = {45},
number = {2},
year = {1999},
pages = {147--182},
}
@article{Her99b,
author = {Hertling, Peter},
title = {An effective {R}iemann {M}apping {T}heorem},
journal = {Theoretical Computer Science},
volume = {219},
year = {1999},
pages = {225--265},
}
@article{Hey51,
author = {Heyting, A.},
title = {Note on the {R}iesz-{F}ischer theorem},
journal = {Indagationes Mathematicae},
volume = {13},
year = {1951},
pages = {35--40},
}
@book{Hey56,
author = {Heyting, A.},
title = {Intuitionism: {A}n {I}ntroduction},
publisher = {North-Holland},
address = {Amsterdam},
year = {1956},
}
@book{Hey71,
author = {Arend Heyting},
title = {Intuitionism: An Introduction},
edition = {3rd},
publisher = {North-Holland},
year = {1971},
}
@inproceedings{HG17,
author = {Hoyrup, Mathieu and Gomaa, Walid},
title = {On the extension of computable real functions},
booktitle = {2017 32nd {A}nnual {ACM}/{IEEE} {S}ymposium on {L}ogic in {C}omputer {S}cience ({LICS})},
publisher = {IEEE},
address = {Piscataway, NJ},
year = {2017},
pages = {12},
}
@inproceedings{Hig10,
author = {Higuchi, Kojiro},
title = {{$P_w$} is not a {H}eyting algebra},
booktitle = {Programs, proofs, processes},
series = {Lecture Notes in Comput. Sci.},
volume = {6158},
publisher = {Springer},
address = {Berlin},
year = {2010},
pages = {190--194},
doi = {10.1007/978-3-642-13962-8_21},
}
@article{Hig12,
author = {Higuchi, Kojiro},
title = {Effectively closed mass problems and intuitionism},
journal = {Annals of Pure and Applied Logic},
volume = {163},
number = {6},
year = {2012},
pages = {693--697},
doi = {10.1016/j.apal.2011.11.003},
}
@phdthesis{Hig12a,
author = {Higuchi, Kojiro},
title = {Degree Structures of Mass Problems and Choice Functions},
school = {Mathematical Institute, Tohoku University},
address = {Sendai, Japan},
year = {2012},
month = {January},
}
@article{HIP20,
author = {Horvat, Marko and Iljazovi{\'c}, Zvonko and Pa{\v{z}}ek, Bojan},
title = {Computability of pseudo-cubes},
journal = {Annals of Pure and Applied Logic},
volume = {171},
number = {8},
year = {2020},
pages = {102823},
doi = {10.1016/j.apal.2020.102823},
}
@book{Hir15,
author = {Hirschfeldt, Denis R.},
title = {Slicing the Truth: On the Computable and Reverse Mathematics of Combinatorial Principles},
series = {Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore},
volume = {28},
publisher = {World Scientific},
address = {Singapore},
year = {2015},
}
@incollection{Hir17,
author = {Hirschfeldt, Denis R.},
title = {Some Questions in Computable Mathematics},
editor = {Day, Adam and Fellows, Michael and Greenberg, Noam and Khoussainov, Bakhadyr and Melnikov, Alexander and Rosamond, Frances},
booktitle = {Computability and Complexity: Essays Dedicated to Rodney G. Downey on the Occasion of His 60th Birthday},
series = {Lecture Notes in Computer Science},
volume = {10010},
publisher = {Springer},
address = {Cham},
year = {2017},
pages = {22--55},
doi = {10.1007/978-3-319-50062-1_4},
}
@article{Hir20,
author = {Hirst, Jeffry L.},
title = {Leaf management},
journal = {Computability},
volume = {9},
number = {3-4},
year = {2020},
pages = {309--314},
doi = {10.3233/com-180243},
}
@phdthesis{Hir90,
author = {Hirsch, Michael David},
title = {Applications of topology to lower bound estimates in computer science},
school = {University of California, Berkeley},
year = {1990},
pages = {39},
note = {{Ph.D.} thesis},
}
@inproceedings{Hit02,
author = {Hitchcock, John M.},
title = {Correspondence Principles for Effective Dimensions},
editor = {Widmayer, Peter and Triguero, Francisco and Morales, Rafael and Hennessy, Matthew and Eidenbenz, Stephan and Conejo, Ricardo},
booktitle = {Automata, Languages and Programming},
series = {Lecture Notes in Computer Science},
volume = {2380},
publisher = {Springer},
address = {Berlin},
year = {2002},
pages = {561--572},
note = {29th International Colloquium, ICALP, M{\'{a}}laga, Spain, July 8--13, 2002},
}
@article{HIV08,
author = {Havea, Robin and Ishihara, Hajime and V{\^{\i}}{\c{t}}{\u{a}}, Lumini{\c{t}}a},
title = {Separation properties in neighbourhood and quasi-apartness spaces},
journal = {Mathematical Logic Quarterly},
volume = {54},
number = {1},
year = {2008},
pages = {58--64},
doi = {10.1002/malq.200710025},
}
@article{HJ16,
author = {Hirschfeldt, Denis R. and Jockusch, Carl G.},
title = {On notions of computability-theoretic reduction between {$\Pi_2^1$} principles},
journal = {Journal of Mathematical Logic},
volume = {16},
number = {1},
year = {2016},
pages = {1650002, 59},
doi = {10.1142/S0219061316500021},
}
@inproceedings{HK12,
author = {Higuchi, Kojiro and Kihara, Takayuki},
title = {Effective strong nullness and effectively closed sets},
editor = {Cooper, S. Barry and Dawar, Anuj and L{\"o}we, Benedikt},
booktitle = {How the World Computes},
series = {Lecture Notes in Computer Science},
volume = {7318},
publisher = {Springer},
address = {Heidelberg},
year = {2012},
pages = {303--312},
}
@article{HK14,
author = {Higuchi, Kojiro and Kihara, Takayuki},
title = {Inside the {M}uchnik degrees {I}: Discontinuity, learnability and constructivism},
journal = {Annals of Pure and Applied Logic},
volume = {165},
number = {5},
year = {2014},
pages = {1058--1114},
doi = {10.1016/j.apal.2014.01.003},
}
@article{HK14a,
author = {Higuchi, Kojiro and Kihara, Takayuki},
title = {Inside the {M}uchnik Degrees {II}: The degree structures induced by the arithmetical hierarchy of countably continuous functions},
journal = {Annals of Pure and Applied Logic},
volume = {165},
number = {6},
year = {2014},
pages = {1201--1241},
doi = {10.1016/j.apal.2014.03.001},
}
@inproceedings{HKL+17,
author = {Huang, Xiang and Klinge, Titus H and Lathrop, James I and Li, Xiaoyuan and Lutz, Jack H},
title = {Real-Time Computability of Real Numbers by Chemical Reaction Networks},
booktitle = {International Conference on Unconventional Computation and Natural Computation},
year = {2017},
pages = {29--40},
}
@article{HKL+19,
author = {Huang, Xiang and Klinge, Titus H. and Lathrop, James I. and Li, Xiaoyuan and Lutz, Jack H.},
title = {Real-time computability of real numbers by chemical reaction networks},
journal = {Natural Computing},
volume = {18},
number = {1},
year = {2019},
pages = {63--73},
doi = {10.1007/s11047-018-9706-x},
}
@article{HKL08,
author = {Hoyrup, Mathieu and Kol{\c{c}}ak, Arda and Longo, Giuseppe},
title = {Computability and the morphological complexity of some dynamics on continuous domains},
journal = {Theoretical Computer Science},
volume = {398},
number = {1-3},
year = {2008},
pages = {170--182},
doi = {10.1016/j.tcs.2008.01.048},
}
@inproceedings{HKP19,
author = {Hirvonen, Asa and Kontinen, Juha and Pauly, Arno},
title = {Continuous Team Semantics},
editor = {Gopal, T.V. and Watada, Junzo},
booktitle = {Theory and Applications of Models of Computation},
series = {Lecture Notes in Computer Science},
volume = {11436},
publisher = {Springer},
address = {Cham},
year = {2019},
pages = {262--278},
note = {15th Annual Conference, TAMC 2019 Kitakyushu, Japan, April 13-16, 2019 Proceedings},
doi = {10.1007/978-3-030-14812-6_16},
}
@article{HKR02,
author = {Heindl, Gerhard and Kreinovich, Vladik and Rifqi, Maria},
title = {In Case of Interval (or More General) Uncertainty, No Algorithm Can Choose the Simplest Representative},
journal = {Reliable Computing},
volume = {8},
year = {2002},
pages = {213--227},
}
@inproceedings{HKS20,
author = {Hoyrup, Mathieu and Kihara, Takayuki and Selivanov, Victor},
title = {Degrees of Non-computability of Homeomorphism Types of {P}olish Spaces},
editor = {Anselmo, Marcella and Della Vedova, Gianluca and Manea, Florin and Pauly, Arno},
booktitle = {Beyond the Horizon of Computability},
publisher = {Springer International Publishing},
address = {Cham},
year = {2020},
pages = {189--192},
doi = {10.1007/978-3-030-51466-2_16},
}
@inproceedings{HL02,
author = {Hitchcock, John M. and Lutz, Jack H.},
title = {Why Computational Complexity Requires Stricter Martingales},
editor = {Widmayer, Peter and Triguero, Francisco and Morales, Rafael and Hennessy, Matthew and Eidenbenz, Stephan and Conejo, Ricardo},
booktitle = {Automata, Languages and Programming},
series = {Lecture Notes in Computer Science},
volume = {2380},
publisher = {Springer},
address = {Berlin},
year = {2002},
pages = {549--560},
note = {29th International Colloquium, ICALP, M{\'{a}}laga, Spain, July 8--13, 2002},
}
@article{HL16,
author = {Hendtlass, Matthew and Lubarsky, Robert},
title = {Separating Fragments of {WLEM}, {LPO}, and {MP}},
journal = {Journal of Symbolic Logic},
volume = {81},
number = {4},
year = {2016},
month = {12},
doi = {10.1017/jsl.2016.38},
}
@article{HM13,
author = {Hitchcock, John M. and Mayordomo, Elvira},
title = {Base invariance of feasible dimension},
journal = {Inform. Process. Lett.},
volume = {113},
number = {14-16},
year = {2013},
pages = {546--551},
doi = {10.1016/j.ipl.2013.04.004},
}
@incollection{HM17,
author = {Hirst, Jeffry L. and Mummert, Carl},
title = {Reverse Mathematics of Matroids},
editor = {Day, Adam and Fellows, Michael and Greenberg, Noam and Khoussainov, Bakhadyr and Melnikov, Alexander and Rosamond, Frances},
booktitle = {Computability and Complexity: Essays Dedicated to Rodney G. Downey on the Occasion of His 60th Birthday},
series = {Lecture Notes in Computer Science},
volume = {10010},
publisher = {Springer},
address = {Cham},
year = {2017},
pages = {143--159},
doi = {10.1007/978-3-319-50062-1_12},
}
@article{HM19,
author = {Hirst, Jeffry L. and Mummert, Carl},
title = {Using {R}amsey's theorem once},
journal = {Archive for Mathematical Logic},
volume = {58},
number = {7-8},
year = {2019},
pages = {857--866},
doi = {10.1007/s00153-019-00664-z},
}
@article{HMM20,
author = {Harrison-Trainor, Matthew and Melnikov, Alexander and Ng, Keng Meng},
title = {Computability of {P}olish spaces up to homeomorphism},
journal = {The Journal of Symbolic Logic},
volume = {85},
number = {4},
publisher = {Cambridge University Press},
year = {2020},
pages = {1664--1686},
doi = {10.1017/jsl.2020.67},
}
@article{HN06,
author = {Hughes, Jesse and Niqui, Milad},
title = {Admissible digit sets},
journal = {Theoretical Computer Science},
volume = {351},
number = {1},
year = {2006},
pages = {61--73},
}
@inproceedings{HNSS18,
author = {Hoyrup, Mathieu and Nava Saucedo, Diego and Stull, Don M.},
title = {Semicomputable geometry},
booktitle = {45th {I}nternational {C}olloquium on {A}utomata, {L}anguages, and {P}rogramming},
series = {LIPIcs. Leibniz Int. Proc. Inform.},
volume = {107},
publisher = {Schloss Dagstuhl. Leibniz-Zent. Inform.},
year = {2018},
pages = {Art. No. 129, 13},
}
@article{Ho96,
author = {Ho, Chun-Kuen},
title = {Beyond recursive real functions},
journal = {Information and Computation},
volume = {124},
number = {2},
year = {1996},
pages = {113--126},
}
@article{Ho99,
author = {Ho, Chun-Kuen},
title = {Relatively recursive reals and real functions},
journal = {Theoretical Computer Science},
volume = {210},
number = {1},
year = {1999},
pages = {99--120},
}
@article{Hoc12,
author = {Hochman, Michael},
title = {Rohlin properties for {$\Bbb{Z}^{d}$} actions on the {C}antor set},
journal = {Trans. Amer. Math. Soc.},
volume = {364},
number = {3},
year = {2012},
pages = {1127--1143},
doi = {10.1090/S0002-9947-2011-05319-5},
}
@article{Hoe06,
author = {van der Hoeven, Joris},
title = {Computations with effective real numbers},
journal = {Theoretical Computer Science},
volume = {351},
number = {1},
year = {2006},
pages = {52--60},
}
@inproceedings{Hoe06a,
author = {van der Hoeven, Joris},
title = {Effective Real Numbers in {M}mxlib},
editor = {Dumas, Jean-Guillaume},
booktitle = {International Conference on Symbolic and Algebraic Computation},
publisher = {ACM Press},
year = {2006},
pages = {138--145},
note = {Proceedings of the International Symposium on Symbolic and Algebraic Computations ISSAC, Genoa, Italy, July 9--12, 2006},
}
@phdthesis{Hog96,
author = {Hogarth, Mark},
title = {Predictability, Computability and Spacetime},
school = {Sidney Sussex College, Cambridge University},
year = {1996},
note = {{Ph.D.} thesis},
}
@phdthesis{Hoo87,
author = {Hoover, H. James},
title = {Feasible Constructive Analysis},
school = {Dept.\ of Computer Science, University of Toronto},
address = {Toronto, Canada},
year = {1987},
}
@inproceedings{Hoo89,
author = {Hoover, H. James},
title = {Why integration is hard},
editor = {Kaltofen, Erich and Watt, Stephen M.},
booktitle = {Computers and mathematics},
publisher = {Springer},
year = {1989},
pages = {172--181},
note = {Conference held at the Massachusetts Institute of Technology, Cambridge, Massachusetts, June 13--17, 1989},
}
@article{Hoo90,
author = {Hoover, H. James},
title = {Feasible real functions and arithmetic circuits},
journal = {SIAM Journal on Computing},
volume = {19},
number = {1},
year = {1990},
pages = {182--204},
}
@article{Hoo91,
author = {Hoover, H. James},
title = {Real functions, contraction mappings, and {P}-completeness},
journal = {Information and Computation},
volume = {93},
number = {2},
year = {1991},
pages = {333--349},
}
@inproceedings{Hoo93,
author = {Hoover, H. James},
title = {Computational models for feasible real analysis},
editor = {Buss, Samuel R. and Scott, Philip J.},
booktitle = {Feasible mathematics},
series = {Progress in Computer Science and Applied Logic},
volume = {9},
publisher = {Birkh\"auser},
year = {1993},
pages = {221--237},
note = {Proceedings of the workshop held at Cornell University, Ithaca, New York, June 26--28, 1989},
}
@inproceedings{Hou06,
author = {Hou, Tie},
title = {Coinductive Proofs for Basic Real Computation},
editor = {Beckmann, A. and Berger, U. and L{\"o}we, B. and Tucker, J.V.},
booktitle = {Logical Approaches to Computational Barriers},
series = {Lecture Notes in Computer Science},
volume = {3988},
publisher = {Springer},
address = {Berlin},
year = {2006},
pages = {221--230},
note = {Second Conference on Computability in Europe, CiE 2006, Swansea, UK, June 30-July 5, 2006},
}
@inproceedings{Hoy11,
author = {Hoyrup, Mathieu},
title = {Randomness and the ergodic decomposition},
editor = {Benedikt L{\"o}we and Dag Normann and Ivan N. Soskov and Alexandra A. Soskova},
booktitle = {Models of Computation in Context},
series = {Lecture Notes in Computer Science},
volume = {6735},
publisher = {Springer},
address = {Heidelberg},
year = {2011},
pages = {122--131},
doi = {10.1007/978-3-642-21875-0_13},
}
@inproceedings{Hoy12,
author = {Hoyrup, Mathieu},
title = {The dimension of ergodic random sequences},
editor = {Christoph D{\"u}rr and Thomas Wilke},
booktitle = {29th {I}nternational {S}ymposium on {T}heoretical {A}spects of {C}omputer {S}cience},
series = {LIPIcs. Leibniz Int. Proc. Inform.},
volume = {14},
publisher = {Schloss Dagstuhl. Leibniz-Zent. Inform., Wadern},
year = {2012},
pages = {567--576},
}
@article{Hoy13,
author = {Hoyrup, Mathieu},
title = {Computability of the ergodic decomposition},
journal = {Annals of Pure and Applied Logic},
volume = {164},
number = {5},
year = {2013},
pages = {542--549},
doi = {10.1016/j.apal.2012.11.005},
}
@inproceedings{Hoy14,
author = {Hoyrup, Mathieu},
title = {Irreversible computable functions},
editor = {Ernst W. Mayr and Natacha Portier},
booktitle = {31st International Symposium on Theoretical Aspects of Computer Science (STACS 2014)},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
volume = {25},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
year = {2014},
pages = {362--373},
doi = {10.4230/LIPIcs.STACS.2014.362},
}
@inproceedings{Hoy16,
author = {Hoyrup, Mathieu},
title = {The Typical Constructible Object},
editor = {Beckmann, Arnold and Bienvenu, Laurent and Jonoska, Nata\v{s}a},
booktitle = {Pursuit of the Universal},
series = {Lecture Notes in Computer Science},
volume = {9709},
publisher = {Springer},
address = {Switzerland},
year = {2016},
pages = {115--123},
note = {12th Conference on Computability in Europe, CiE 2016, Paris, France, June 27 - July 1, 2016},
doi = {10.1007/978-3-319-40189-8_12},
}
@incollection{Hoy16a,
author = {Hoyrup, Mathieu},
title = {The decidable properties of subrecursive functions},
booktitle = {43rd {I}nternational {C}olloquium on {A}utomata, {L}anguages, and {P}rogramming},
series = {LIPIcs. Leibniz Int. Proc. Inform.},
volume = {55},
publisher = {Schloss Dagstuhl. Leibniz-Zent. Inform., Wadern},
year = {2016},
pages = {Art. No. 108, 13},
}
@article{Hoy17,
author = {Hoyrup, Mathieu},
title = {Genericity of Weakly Computable Objects},
journal = {Theory of Computing Systems},
volume = {60},
number = {3},
year = {2017},
pages = {396--420},
doi = {10.1007/s00224-016-9737-6},
}
@inproceedings{Hoy18,
author = {Hoyrup, Mathieu},
title = {Topological analysis of representations},
booktitle = {Sailing routes in the world of computation},
series = {Lecture Notes in Computer Science},
volume = {10936},
publisher = {Springer},
address = {Cham},
year = {2018},
pages = {214--223},
doi = {10.1007/978-3-319-94418-0_22},
}
@inproceedings{Hoy20,
author = {Hoyrup, Mathieu},
title = {Descriptive Complexity on Non-{P}olish Spaces {II}},
editor = {Czumaj, Artur and Dawar, Anuj and Merelli, Emanuela},
booktitle = {47th International Colloquium on Automata, Languages, and Programming ({ICALP} 2020)},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
volume = {168},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
year = {2020},
pages = {132:1--132:17},
doi = {10.4230/LIPIcs.ICALP.2020.132},
}
@incollection{Hoy20a,
author = {Hoyrup, Mathieu},
title = {Algorithmic randomness and layerwise computability},
editor = {Franklin, Johanna N.Y. and Porter, Christopher P.},
booktitle = {Algorithmic Randomness: Progress and Prospects},
series = {Lecture Notes in Logic},
volume = {50},
publisher = {Cambridge University Press},
year = {2020},
pages = {115--133},
doi = {10.1017/9781108781718.005},
}
@article{Hoy22,
author = {Hoyrup, Mathieu},
title = {The fixed-point property for represented spaces},
journal = {Annals of Pure and Applied Logic},
volume = {173},
number = {5},
year = {2022},
pages = {Paper No. 103090, 29},
doi = {10.1016/j.apal.2022.103090},
}
@article{HP13,
author = {Higuchi, Kojiro and Pauly, Arno},
title = {The degree structure of {W}eihrauch reducibility},
journal = {Log. Methods Comput. Sci.},
volume = {9},
number = {2},
year = {2013},
pages = {2:02, 17},
doi = {10.2168/LMCS-9(2:2)2013},
}
@article{HP22,
author = {H{\"o}lzl, Rupert and Porter, Christoph P.},
title = {Degrees of randomized computability},
journal = {Bulletin of Symbolic Logic},
volume = {28},
number = {1},
year = {2022},
pages = {27--70},
doi = {10.1017/bsl.2021.46},
}
@article{HR09,
author = {Hoyrup, Mathieu and Rojas, Crist{\'o}bal},
title = {Computability of probability measures and {M}artin-{L}\"of randomness over metric spaces},
journal = {Information and Computation},
volume = {207},
number = {7},
year = {2009},
pages = {830--847},
doi = {10.1016/j.ic.2008.12.009},
}
@inproceedings{HR09a,
author = {Hoyrup, Mathieu and Rojas, Crist{\'o}bal},
title = {An application of {M}artin-{L}\"of randomness to effective probability theory},
editor = {Klaus Ambos-Spies and Benedikt L{\"o}we and Wolfgang Merkle},
booktitle = {Mathematical Theory and Computational Practice},
series = {Lecture Notes in Computer Science},
volume = {5635},
publisher = {Springer},
address = {Berlin},
year = {2009},
pages = {260--269},
doi = {10.1007/978-3-642-03073-4_27},
}
@inproceedings{HR09b,
author = {Hoyrup, Mathieu and Rojas, Crist{\'o}bal},
title = {Applications of effective probability theory to {M}artin-{L}\"of randomness},
editor = {Susanne Albers and Alberto Marchetti-Spaccamela and Yossi Matias and Sotiris E. Nikoletseas and Wolfgang Thomas},
booktitle = {Automata, Languages and Programming. {P}art {I}},
series = {Lecture Notes in Comput. Sci.},
volume = {5555},
publisher = {Springer},
address = {Berlin},
year = {2009},
pages = {549--561},
doi = {10.1007/978-3-642-02927-1_46},
}
@inproceedings{HR15,
author = {Hoyrup, Mathieu and Rojas, Crist{\'o}bal},
title = {On the Information Carried by Programs about the Objects They Compute},
editor = {Mayr, Ernst W. and Ollinger, Nicolas},
booktitle = {32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
volume = {30},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
year = {2015},
pages = {447--459},
doi = {10.4230/LIPIcs.STACS.2015.447},
}
@article{HR17,
author = {Hoyrup, Mathieu and Rojas, Crist{\'o}bal},
title = {On the Information Carried by Programs About the Objects they Compute},
journal = {Theory of Computing Systems},
volume = {61},
number = {4},
year = {2017},
pages = {1214--1236},
doi = {10.1007/s00224-016-9726-9},
}
@incollection{HR21,
author = {Hoyrup, Mathieu and Rute, Jason},
title = {Computable Measure Theory and Algorithmic Randomness},
editor = {Brattka, Vasco and Hertling, Peter},
booktitle = {Handbook of Computability and Complexity in Analysis},
series = {Theory and Applications of Computability},
publisher = {Springer},
address = {Cham},
year = {2021},
pages = {227--270},
doi = {10.1007/978-3-030-59234-9_7},
}
@inproceedings{HRSS19,
author = {Hoyrup, Mathieu and Rojas, Crist\'{o}bal and Selivanov, Victor and Stull, Donald M.},
title = {Computability on quasi-{P}olish spaces},
booktitle = {Descriptional complexity of formal systems},
series = {Lecture Notes in Computer Science},
volume = {11612},
publisher = {Springer},
address = {Cham},
year = {2019},
pages = {171--183},
}
@inproceedings{HRW11,
author = {Hoyrup, Mathieu and Rojas, Crist{\'o}bal and Weihrauch, Klaus},
title = {Computability of the {R}adon-{N}ikodym derivative},
editor = {L{\"o}we, Benedikt and Normann, Dag and Soskov, Ivan and Soskova, Alexandra},
booktitle = {Models of Computation in Context},
series = {Lecture Notes in Computer Science},
volume = {6735},
publisher = {Springer},
address = {Heidelberg},
year = {2011},
pages = {132--141},
doi = {10.1007/978-3-642-21875-0_14},
}
@article{HRW12,
author = {Hoyrup, Mathieu and Rojas, Crist{\'o}bal and Weihrauch, Klaus},
title = {Computability of the {R}adon-{N}ikodym Derivative},
journal = {Computability},
volume = {1},
number = {1},
year = {2012},
pages = {3--13},
doi = {10.3233/COM-2012-005},
}
@article{HS08a,
author = {Hertling, Peter and Spandl, Christoph},
title = {Computability theoretic properties of the entropy of gap shifts},
journal = {Fundamenta Informaticae},
volume = {83},
number = {1-2},
year = {2008},
pages = {141--157},
}
@article{HS08b,
author = {Hertling, Peter and Spandl, Christoph},
title = {Shifts with decidable language and non-computable entropy},
journal = {Discrete Mathematics and Theoretical Computer Science},
volume = {10},
number = {3},
year = {2008},
pages = {75--93},
}
@inproceedings{HS11,
author = {Hertling, Peter and Selivanov, Victor},
title = {Complexity issues for preorders on finite labeled forests},
editor = {L{\"o}we, Benedikt and Normann, Dag and Soskov, Ivan and Soskova, Alexandra},
booktitle = {Models of computation in context},
series = {Lecture Notes in Computer Science},
volume = {6735},
publisher = {Springer},
address = {Heidelberg},
year = {2011},
pages = {112--121},
note = {7th Conference on Computability in Europe, CiE 2011, Sofia, Bulgaria, June 27--July 2, 2011},
doi = {10.1007/978-3-642-21875-0_12},
}
@article{HS11a,
author = {Hendtlass, Matthew and Schuster, Peter},
title = {Minima and best approximations in constructive analysis},
journal = {J. Log. Anal.},
volume = {3},
year = {2011},
pages = {Paper 5, 17},
doi = {10.4115/jla.2011.3.5},
}
@inproceedings{HS12,
author = {Hendtlass, Matthew and Schuster, Peter},
title = {A direct proof of {W}iener's theorem},
editor = {Cooper, S. Barry and Dawar, Anuj and L{\"o}we, Benedikt},
booktitle = {How the World Computes},
series = {Lecture Notes in Computer Science},
volume = {7318},
publisher = {Springer},
address = {Heidelberg},
year = {2012},
pages = {293--302},
}
@article{HS14,
author = {Hertling, Peter and Spandl, Christoph},
title = {Computing a solution of {F}eigenbaum's functional equation in polynomial time},
journal = {Logical Methods in Computer Science},
volume = {10},
number = {4},
year = {2014},
pages = {4:7, 9},
doi = {10.2168/LMCS-10(4:7)2014},
}
@incollection{HS14a,
author = {Hertling, Peter and Selivanov, Victor},
title = {Complexity issues for preorders on finite labeled forests},
editor = {Brattka, Vasco and Diener, Hannes and Spreen, Dieter},
booktitle = {Logic, Computation, Hierarchies},
series = {Ontos Mathematical Logic},
publisher = {Walter de Gruyter},
address = {Boston},
year = {2014},
pages = {165--190},
}
@article{HS15,
author = {H{\"o}lzl, Rupert and Shafer, Paul},
title = {Universality, optimality, and randomness deficiency},
journal = {Annals of Pure and Applied Logic},
volume = {166},
number = {10},
year = {2015},
pages = {1049--1069},
doi = {j.apal.2015.05.006},
}
@inproceedings{HS16,
author = {Huang, Xiang and Stull, Donald M.},
title = {Polynomial Space Randomness in Analysis},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science ({MFCS} 2016)},
series = {Leibniz International Proceedings in Informatics ({LIPI}cs)},
volume = {58},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
year = {2016},
pages = {86:1--86:13},
doi = {10.4230/LIPIcs.MFCS.2016.86},
}
@inproceedings{HS19,
author = {Hoyrup, Mathieu and Stull, Donald M.},
title = {Semicomputable Points in {E}uclidean Spaces},
editor = {Rossmanith, Peter and Heggernes, Pinar and Katoen, Joost-Pieter},
booktitle = {44th International Symposium on Mathematical Foundations of Computer Science ({MFCS} 2019)},
series = {Leibniz International Proceedings in Informatics ({LIPI}cs)},
volume = {138},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
year = {2019},
pages = {48:1--48:13},
doi = {10.4230/LIPIcs.MFCS.2019.48},
}
@inproceedings{HT08,
author = {Hirschfeldt, Denis R. and Terwijn, Sebastiaan A.},
title = {Limit computability and constructive measure},
booktitle = {Computational prospects of infinity. {P}art {II}. {P}resented talks},
series = {Lect. Notes Ser. Inst. Math. Sci. Natl. Univ. Singap.},
volume = {15},
publisher = {World Sci. Publ., Hackensack, NJ},
year = {2008},
pages = {131--141},
doi = {10.1142/9789812796554_0007},
}
@phdthesis{Hud62,
author = {Hudes, L.},
title = {Hyperarithmetical real numbers and hyperarithmetical analysis},
school = {Massachusetts Institute of Technology},
address = {Cambridge, Mass.},
year = {1962},
}
@article{HW03,
author = {Hertling, Peter and Weihrauch, Klaus},
title = {Random elements in effective topological spaces with measure},
journal = {Information and Computation},
volume = {181},
number = {1},
year = {2003},
pages = {32--56},
}
@inproceedings{HW94,
author = {Hertling, Peter and Weihrauch, Klaus},
title = {Levels of degeneracy and exact lower complexity bounds for geometric algorithms},
booktitle = {Proceedings of the Sixth Canadian Conference on Computational Geometry},
year = {1994},
pages = {237--242},
note = {{S}askatoon, Saskatchewan, August 2--6, 1994},
}
@inproceedings{HW98,
author = {Hertling, Peter and Weihrauch, Klaus},
title = {Randomness Spaces},
editor = {Kim G. Larsen and Sven Skyum and Glynn Winskel},
booktitle = {Automata, Languages and Programming},
series = {Lecture Notes in Computer Science},
volume = {1443},
publisher = {Springer},
address = {Berlin},
year = {1998},
pages = {796--807},
note = {25th International Colloquium, ICALP'98, Aalborg, Denmark, July 1998},
}
@article{Hyl79,
author = {Hyland, J.M.E.},
title = {Filter Spaces and Continuous Functionals},
journal = {Annals of Mathematical Logic},
volume = {16},
year = {1979},
pages = {101--143},
}
@inproceedings{Hyl82,
author = {Hyland, J.M.E.},
title = {Application of constructivity},
editor = {Cohen, L.J. and Lo\'s, G. and Pfeiffer, H. and and Podewski, K.-P.},
booktitle = {Methodology and Philos. Sci. VI},
series = {Studies in Logic and the Foundations of Mathematics},
volume = {104},
publisher = {North-Holland},
address = {Amsterdam},
year = {1982},
pages = {145--152},
note = {(Proc. 6th. Internatl. Congr. Logic, Methodology, and Philos. Sci., Hannover, Aug. 22--29, 1979)},
}
@article{IC21,
author = {{\v{C}}elar, Matea and Iljazovi{\'c}, Zvonko},
title = {Computability of Products of Chainable Continua},
journal = {Theory of Computing Systems},
volume = {65},
year = {2021},
pages = {410--427},
doi = {10.1007/s00224-020-10017-6},
}
@article{Iiz06,
author = {Iizuka, Shinji},
title = {Effective continuities on effective topological spaces},
journal = {Journal of Complexity},
volume = {22},
number = {6},
year = {2006},
pages = {894--908},
}
@article{IK15,
author = {Ishihara, Hajime and Kawai, Tatsuji},
title = {Completeness and cocompleteness of the categories of basic pairs and concrete spaces},
journal = {Mathematical Structures in Computer Science},
volume = {25},
year = {2015},
month = {12},
pages = {1626--1648},
doi = {10.1017/S0960129513000285},
}
@incollection{IK21,
author = {Iljazovi{\'c}, Zvonko and Takayuki Kihara},
title = {Computability of Subsets of Metric Spaces},
editor = {Brattka, Vasco and Hertling, Peter},
booktitle = {Handbook of Computability and Complexity in Analysis},
series = {Theory and Applications of Computability},
publisher = {Springer},
address = {Cham},
year = {2021},
pages = {29--69},
doi = {10.1007/978-3-030-59234-9\_2},
}
@proceedings{IKP+17,
title = {Special issue: {C}ontinuity, computability, constructivity: from logic to algorithms 2013},
editor = {Ishihara, Hajime and Korovina, Margarita and Pauly, Arno and Seisenberger, Monika and Spreen, Dieter},
series = {Mathematical Structures in Computer Science},
volume = {27},
number = {8},
publisher = {Cambridge University Press},
year = {2017},
pages = {1285--1286},
doi = {10.1017/S0960129516000086},
}
@article{Ilj09,
author = {Iljazovi{\'c}, Zvonko},
title = {Chainable and circularly chainable co-r.e. sets in computable metric spaces},
journal = {Journal of Universal Computer Science},
volume = {15},
number = {6},
year = {2009},
pages = {1206--1235},
doi = {10.3217/jucs-015-06-1206},
}
@article{Ilj10,
author = {Iljazovi{\'c}, Zvonko},
title = {Isometries and computability structures},
journal = {Journal of Universal Computer Science},
volume = {16},
number = {18},
year = {2010},
pages = {2569--2596},
doi = {10.3217/jucs-016-18-2569},
}
@article{Ilj11,
author = {Iljazovi{\'c}, Zvonko},
title = {Co-c.e. spheres and cells in computable metric spaces},
journal = {Logical Methods in Computer Science},
volume = {7},
number = {3},
year = {2011},
pages = {3:05, 21},
}
@article{Ilj12,
author = {Iljazovi{\'c}, Zvonko},
title = {Local computability of computable metric spaces and computability of co-c.e. continua},
journal = {Glas. Mat. Ser. III},
volume = {47(67)},
number = {1},
year = {2012},
pages = {1--20},
doi = {10.3336/gm.47.1.01},
}
@article{Ilj13,
author = {Iljazovi{\'c}, Zvonko},
title = {Compact manifolds with computable boundaries},
journal = {Logical Methods in Computer Science},
volume = {9},
number = {4},
year = {2013},
pages = {4:19, 22},
doi = {10.2168/LMCS-9(4:19)2013},
}
@article{Ilj20,
author = {Iljazovi{\'c}, Zvonko},
title = {Computability of graphs},
journal = {Mathematical Logic Quarterly},
volume = {66},
number = {1},
year = {2020},
pages = {51--64},
doi = {10.1002/malq.201900025},
}
@article{Ils65,
author = {Ilse, Dieter},
title = {Zur {S}tetigkeit berechenbarer reeller {F}unktionen},
journal = {Zeitschrift f\"ur Mathematische Logik und Grundlagen der Mathematik},
volume = {11},
year = {1965},
pages = {297--342},
}
@article{IMSV04,
author = {Ishihara, Hajime and Mines, Ray and Schuster, Peter and V{\^{\i}}{\c{t}}{\u{a}}, Lumini{\c{t}}a},
title = {Quasi-apartness and neighbourhood spaces},
journal = {Annals of Pure and Applied Logic},
volume = {141},
number = {1--2},
year = {2006},
pages = {296--306},
}
@article{IP06,
author = {Ishihara, Hajime and Palmgren, Erik},
title = {Quotient topologies in constructive set theory and type theory},
journal = {Annals of Pure and Applied Logic},
volume = {141},
number = {1--2},
year = {2006},
pages = {257--265},
}
@article{IP18,
author = {Iljazovi{\'c}, Zvonko and Pa{\v{z}}ek, Bojan},
title = {Warsaw discs and semicomputability},
journal = {Topology and its Applications},
volume = {239},
year = {2018},
pages = {308--323},
doi = {10.1016/j.topol.2018.02.014},
}
@article{IP18a,
author = {Iljazovi{\'c}, Zvonko and Pa{\v{z}}ek, Bojan},
title = {Computable intersection points},
journal = {Computability},
volume = {7},
number = {3},
year = {2018},
pages = {57--99},
doi = {10.3233/COM-170079},
}
@article{IP18b,
author = {Iljazovi{\'c}, Zvonko and Pa{\v{z}}ek, Bojan},
title = {Co-c.e. Sets with Disconnected Complements},
journal = {Theory of Computing Systems},
volume = {62},
number = {5},
year = {2018},
month = {Jul},
pages = {1109--1124},
doi = {10.1007/s00224-017-9781-x},
}
@article{IS04,
author = {Ishihara, Hajime and Schuster, Peter},
title = {Compactness under constructive scrutiny},
journal = {Mathematical Logic Quarterly},
volume = {50},
number = {6},
year = {2004},
pages = {540--550},
}
@article{IS08,
author = {Ishihara, Hajime and Schuster, Peter},
title = {A continuity principle, a version of {B}aire's theorem and a boundedness principle},
journal = {Journal of Symbolic Logic},
volume = {73},
number = {4},
year = {2008},
pages = {1354--1360},
doi = {10.2178/jsl/1230396924},
}
@article{IS10,
author = {Ishihara, Hajime and Schuster, Peter},
title = {Kronecker's density theorem and irrational numbers in constructive reverse mathematics},
journal = {Math. Semesterber.},
volume = {57},
number = {1},
year = {2010},
pages = {57--72},
doi = {10.1007/s00591-009-0062-x},
}
@article{IS18,
author = {Iljazovi{\'c}, Zvonko and Su{\v{s}}i{\'c}, Igor},
title = {Semicomputable manifolds in computable topological spaces},
journal = {Journal of Complexity},
volume = {45},
year = {2018},
pages = {83--114},
doi = {10.1016/j.jco.2017.11.004},
}
@article{Ish00,
author = {Ishihara, Hajime},
title = {Feasibly constructive analysis},
journal = {S\={u}rikaisekikenky\={u}sho K\={o}ky\={u}roku},
volume = {1169},
year = {2000},
pages = {76--83},
note = {Research Institute for Mathematical Sciences Kyoto},
}
@article{Ish01,
author = {Ishihara, Hajime},
title = {Locating subsets of a Hilbert space},
journal = {Proceedings of the American Mathematical Society},
volume = {129},
year = {2001},
pages = {1385--1390},
}
@inproceedings{Ish01a,
author = {Ishihara, Hajime},
title = {Sequentially Continuity in Constructive Mathematics},
editor = {Calude, C.S. and Dinneen, M.J. and Sburlan, S.},
booktitle = {Combinatorics, Computability and Logic},
series = {Discrete Mathematics and Theoretical Computer Science},
publisher = {Springer},
address = {London},
year = {2001},
pages = {5--12},
note = {Proceedings of DMTCS 2001},
}
@incollection{Ish05,
author = {Ishihara, Hajime},
title = {Constructive reverse mathematics: compactness properties},
editor = {Crosilla, Laura and Schuster, Peter},
booktitle = {From Sets and Types to Topology and Analysis: Towards Practicable Foundations for Constructive Mathematics},
publisher = {Oxford University Press},
year = {2005},
pages = {245--267},
}
@article{Ish06,
author = {Ishihara, Hajime},
title = {Reverse mathematics in {B}ishop's constructive mathematics},
journal = {Philosophia Scientiae, Cahier special},
volume = {6},
year = {2006},
pages = {43-59},
}
@article{Ish06a,
author = {Ishihara, Hajime},
title = {Weak {K}{\"o}nig's Lemma Implies {B}rouwer's Fan Theorem: A Direct Proof},
journal = {Notre Dame Journal of Formal Logic},
volume = {47},
number = {2},
year = {2006},
pages = {249--252},
}
@inproceedings{Ish07,
author = {Ishihara, Hajime},
title = {Unique Existence and Computability in Constructive Reverse Mathematics},
editor = {Cooper, S. Barry and L{\"o}we, Benedikt and Sorbi, Andrea},
booktitle = {Computation and Logic in the Real World},
series = {Lecture Notes in Computer Science},
volume = {4497},
publisher = {Springer},
address = {Berlin},
year = {2007},
pages = {368--377},
note = {Third Conference on Computability in Europe, CiE 2007, Siena, Italy, June 18-23, 2007},
}
@incollection{Ish09,
author = {Ishihara, Hajime},
title = {Relativization of real numbers to a universe},
booktitle = {Logicism, intuitionism, and formalism},
series = {Synth. Libr.},
volume = {341},
publisher = {Springer},
address = {Dordrecht},
year = {2009},
pages = {189--207},
doi = {10.1007/978-1-4020-8926-8_9},
}
@article{Ish12,
author = {Ishihara, Hajime},
title = {Two subcategories of apartness spaces},
journal = {Annals of Pure and Applied Logic},
volume = {163},
number = {2},
year = {2012},
pages = {132--139},
doi = {10.1016/j.apal.2011.06.022},
}
@article{Ish12a,
author = {Ishihara, Hajime},
title = {The uniform boundedness theorem and a boundedness principle},
journal = {Annals of Pure and Applied Logic},
volume = {163},
number = {8},
year = {2012},
pages = {1057--1061},
doi = {10.1016/j.apal.2011.12.027},
}
@article{Ish13,
author = {Ishihara, Hajime},
title = {Relating {B}ishop's function spaces to neighbourhood spaces},
journal = {Annals of Pure and Applied Logic},
volume = {164},
number = {4},
year = {2013},
pages = {482--490},
doi = {10.1016/j.apal.2012.10.009},
}
@article{Ish18,
author = {Ishihara, Hajime},
title = {On {B}rouwer's continuity principle},
journal = {Indagationes Mathematicae},
volume = {29},
number = {6},
year = {2018},
pages = {1511--1524},
doi = {10.1016/j.indag.2018.01.012},
}
@article{Ish88,
author = {Ishihara, Hajime},
title = {Constructive reflexivity of a uniformly convex {B}anach space},
journal = {Proc. Amer. Math. Soc.},
volume = {104},
number = {3},
year = {1988},
pages = {735--740},
}
@article{Ish89,
author = {Ishihara, Hajime},
title = {On the constructive {H}ahn-{B}anach theorem},
journal = {Bull. London Math. Soc.},
volume = {21},
number = {1},
year = {1989},
pages = {79--81},
}
@article{Ish89a,
author = {Ishihara, Hajime},
title = {Constructive compact linear mappings},
journal = {Bull. London Math. Soc.},
volume = {21},
year = {1989},
pages = {577--584},
}
@article{Ish90,
author = {Ishihara, Hajime},
title = {An omniscience principle, the {K}{\"{o}}nig lemma and the {H}ahn-{B}anach theorem},
journal = {Zeitschrift f\"ur Mathematische Logik und Grundlagen der Mathematik},
volume = {36},
year = {1990},
pages = {237--240},
}
@phdthesis{Ish90a,
author = {Ishihara, Hajime},
title = {Boundedness, normability and compactness of constructive linear mappings},
school = {Tokyo Institute of Technology},
address = {Tokyo},
year = {1990},
month = {mar},
}
@article{Ish91,
author = {Ishihara, Hajime},
title = {Constructive compact operators on a {H}ilbert space},
journal = {Annals of Pure and Applied Logic},
volume = {52},
year = {1991},
pages = {31--37},
}
@article{Ish91a,
author = {Ishihara, Hajime},
title = {Continuity and nondiscontinuity in constructive mathematics},
journal = {The Journal of Symbolic Logic},
volume = {56},
number = {4},
year = {1991},
pages = {1349--1354},
}
@article{Ish92,
author = {Ishihara, Hajime},
title = {Continuity properties in constructive mathematics},
journal = {The Journal of Symbolic Logic},
volume = {57},
number = {2},
year = {1992},
pages = {557--565},
}
@article{Ish92a,
author = {Ishihara, Hajime},
title = {Constructive existence of {M}inkowski functionals},
journal = {Proc. Amer. Math. Soc.},
volume = {116},
number = {1},
year = {1992},
pages = {79--84},
}
@article{Ish93,
author = {Ishihara, Hajime},
title = {{M}arkov's principle, {C}hurch's thesis and {L}indel{\"{o}}f's theorem},
journal = {Indagationes Mathematicae},
volume = {4},
year = {1993},
pages = {321--325},
}
@article{Ish94,
author = {Ishihara, Hajime},
title = {A constructive version of {B}anach's inverse mapping theorem},
journal = {New Zealand Journal of Mathematics},
volume = {23},
year = {1994},
pages = {71--75},
}
@article{Ish97,
author = {Ishihara, Hajime},
title = {Sequential continuity of linear mappings in constructive mathematics},
journal = {Journal of Universal Computer Science},
volume = {3},
year = {1997},
pages = {1250--1254},
}
@article{IV16,
author = {Iljazovi{\'c}, Zvonko and Valid{\v{z}}i{\'c}, Lucija},
title = {Maximal computability structures},
journal = {Bulletin of Symbolic Logic},
volume = {22},
number = {04},
year = {2016},
month = {12},
doi = {10.1017/bsl.2016.26},
}
@article{IV17,
author = {Iljazovi{\'c}, Zvonko and Valid{\v{z}}i{\'c}, Lucija},
title = {Computable neighbourhoods of points in semicomputable manifolds},
journal = {Annals of Pure and Applied Logic},
volume = {168},
number = {4},
year = {2017},
pages = {840--859},
doi = {10.1016/j.apal.2016.10.015},
}
@article{IV23,
author = {Iljazovi{\'c}, Zvonko and Valid{\v{z}}i{\'c}, Lucija},
title = {Effective compactness and orbits of points under the isometry group},
journal = {Annals of Pure and Applied Logic},
volume = {174},
number = {2},
year = {2023},
pages = {103198},
doi = {10.1016/j.apal.2022.103198},
}
@article{IY02,
author = {Hajime Ishihara and Satoru Yoshida},
title = {A constructive look at the completeness of the space $\mathcal{D} (\textbf{R})$},
journal = {Journal of Symbolic Logic},
volume = {67},
number = {4},
year = {2002},
pages = {1511---1519},
}
@article{JES06,
author = {De Jaeger, Fr{\'{e}}d{\'{e}}ric and Escard{\'{o}}, Mart{\'{\i}}n and Santini, Gabriele},
title = {On the computational content of the {L}awson topology},
journal = {Theoretical Computer Science},
volume = {357},
number = {1--3},
year = {2006},
pages = {230--240},
}
@article{JR84,
author = {Julian, William and Richman, Fred},
title = {A uniformly continuous function on $[0,1]$ that is everywhere different from its infimum},
journal = {Pacific Journal of Mathematics},
volume = {111},
number = {2},
publisher = {Pacific Journal of Mathematics},
year = {1984},
pages = {333--340},
}
@inproceedings{JS20,
author = {Jakobsen, Sune Kristian and Simonsen, Jakob Grue},
title = {Liouville Numbers and the Computational Complexity of Changing Bases},
editor = {Anselmo, Marcella and Della Vedova, Gianluca and Manea, Florin and Pauly, Arno},
booktitle = {Beyond the Horizon of Computability},
publisher = {Springer International Publishing},
address = {Cham},
year = {2020},
pages = {50--62},
doi = {https://doi.org/10.1007/978-3-030-51466-2_5},
}
@article{JW13,
author = {Jafarikhah, Tahereh and Weihrauch, Klaus},
title = {The {R}iesz representation operator on the dual of {$C[0;1]$} is computable},
journal = {Journal of Universal Computer Science},
volume = {19},
number = {6},
year = {2013},
pages = {750--770},
}
@article{JW14,
author = {Jafarikhah, Tahereh and Weihrauch, Klaus},
title = {Computable {J}ordan Decomposition of Linear Continuous Functionals on $C[0;1]$},
journal = {Logical Methods in Computer Science},
volume = {10},
year = {2014},
pages = {3:13,13},
doi = {10.2168/LMCS-10(3:13)2014},
}
@article{JWZ07,
author = {Jiang, Wei and Wang, Yuan and Zucker, Jeffery},
title = {Universality and semicomputability for nondeterministic programming languages over abstract algebras},
journal = {The Journal of Logic and Algebraic Programming},
volume = {71},
number = {1},
year = {2007},
pages = {44--78},
}
@inproceedings{Kal03,
author = {Kalantari, Iraj},
title = {Density \& {B}aire category in recursive topology},
editor = {Brattka, Vasco and Schr{\"{o}}der, Matthias and Weihrauch, Klaus and Zhong, Ning},
booktitle = {Computability and Complexity in Analysis},
series = {Informatik Berichte},
volume = {302},
publisher = {FernUniversit\"at in Hagen},
year = {2003},
month = aug,
pages = {15--18},
note = {International Conference, CCA 2003, Cincinnati, USA, August 28--30, 2003},
}
@inproceedings{Kal82,
author = {Kalantari, Iraj},
title = {Major subsets in effective topology},
editor = {Metakides, G.},
booktitle = {Patras Logic Symposion},
series = {Studies in Logic and the Foundations of Mathematics},
publisher = {North-Holland},
address = {Amsterdam},
year = {1982},
pages = {77--94},
note = {Proc. Logic Sympos. Patras, Greece, Aug. 18--22, 1980},
}
@inproceedings{Kam01,
author = {Kamo, Hiroyasu},
title = {Effective Contraction Theorem and Its Application},
editor = {Blanck, Jens and Brattka, Vasco and Hertling, Peter},
booktitle = {Computability and Complexity in Analysis},
series = {Lecture Notes in Computer Science},
volume = {2064},
publisher = {Springer},
address = {Berlin},
year = {2001},
pages = {88--100},
note = {4th International Workshop, CCA 2000, Swansea, UK, September 2000},
}
@inproceedings{Kam05,
author = {Kamo, Hiroyasu},
title = {Effective {D}ini's Theorem on Effectively Compact Metric Spaces},
editor = {Brattka, Vasco and Staiger, Ludwig and Weihrauch, Klaus},
booktitle = {Proceedings of the 6th Workshop on Computability and Complexity in Analysis},
series = {Electronic Notes in Theoretical Computer Science},
volume = {120},
publisher = {Elsevier},
address = {Amsterdam},
year = {2005},
pages = {73--82},
note = {6th International Workshop, {CCA} 2004, Wittenberg, Germany, August 16--20, 2004},
}
@inproceedings{Kam05a,
author = {Kamo, Hiroyasu},
title = {Computability and computable uniqueness of {U}rysohn's universal metric space},
editor = {Grubba, Tanja and Hertling, Peter and Tsuiki, Hideki and Weihrauch, Klaus},
booktitle = {Computability and Complexity in Analysis},
series = {Informatik Berichte},
volume = {326},
publisher = {FernUniversit\"at in Hagen},
year = {2005},
month = jul,
pages = {149--159},
note = {Proccedings, Second International Conference, CCA 2005, Kyoto, Japan, August 25--29, 2005},
}
@phdthesis{Kam06,
author = {Kamo, Hiroyasu},
title = {Computability in some fundamental theorems in functional analysis and general topology},
school = {Kyoto University},
year = {2006},
doi = {10.14989/doctor.r11863},
}
@inproceedings{Kap01,
author = {Kapoulas, George},
title = {Polynomially Time Computable Functions over $p$-Adic Fields},
editor = {Blanck, Jens and Brattka, Vasco and Hertling, Peter},
booktitle = {Computability and Complexity in Analysis},
series = {Lecture Notes in Computer Science},
volume = {2064},
publisher = {Springer},
address = {Berlin},
year = {2001},
pages = {101--118},
note = {4th International Workshop, CCA 2000, Swansea, UK, September 2000},
}
@article{Kap99a,
author = {Kapron, Bruce M.},
title = {Feasibly continuous type-two functionals},
journal = {Computational Complexity},
volume = {8},
number = {2},
year = {1999},
pages = {188--201},
}
@inproceedings{Kas03,
author = {Kashefi, Elham},
title = {Quantum domain theory -- definitions and applications},
editor = {Brattka, Vasco and Schr{\"{o}}der, Matthias and Weihrauch, Klaus and Zhong, Ning},
booktitle = {Computability and Complexity in Analysis},
series = {Informatik Berichte},
volume = {302},
publisher = {FernUniversit\"at in Hagen},
year = {2003},
month = aug,
pages = {255--274},
note = {International Conference, CCA 2003, Cincinnati, USA, August 28--30, 2003},
}
@inproceedings{Kaw05,
author = {Kawamura, Akitoshi},
title = {Type-2 Computability and {M}oore's Recursive Functions},
editor = {Brattka, Vasco and Staiger, Ludwig and Weihrauch, Klaus},
booktitle = {Proceedings of the 6th Workshop on Computability and Complexity in Analysis},
series = {Electronic Notes in Theoretical Computer Science},
volume = {120},
publisher = {Elsevier},
address = {Amsterdam},
year = {2005},
pages = {83--95},
note = {6th International Workshop, {CCA} 2004, Wittenberg, Germany, August 16--20, 2004},
}
@article{Kaw09,
author = {Kawamura, Akitoshi},
title = {Differential recursion},
journal = {ACM Transactions on Computational Logic},
volume = {10},
number = {3},
year = {2009},
pages = {Art. 22, 22},
doi = {10.1145/1507244.1507252},
}
@inproceedings{Kaw09a,
author = {Kawamura, Akitoshi},
title = {Lipschitz continuous ordinary differential equations are polynomial-space complete},
booktitle = {24th {A}nnual {IEEE} {C}onference on {C}omputational {C}omplexity},
publisher = {IEEE Computer Soc., Los Alamitos, CA},
year = {2009},
pages = {149--160},
doi = {10.1109/CCC.2009.34},
}
@article{Kaw10,
author = {Kawamura, Akitoshi},
title = {{L}ipschitz Continuous Ordinary Differential Equations are Polynomial-Space Complete},
journal = {Computational Complexity},
volume = {19},
number = {2},
year = {2010},
pages = {305--332},
doi = {10.1007/s00037-010-0286-0},
}
@phdthesis{Kaw11,
author = {Kawamura, Akitoshi},
title = {Computational Complexity in Analysis and Geometry},
school = {Department of Computer Science, University of Toronto},
year = {2011},
note = {{Ph.D.} thesis},
}
@article{Kaw17,
author = {Kawai, Tatsuji},
title = {A point-free characterisation of {B}ishop locally compact metric spaces},
journal = {Journal of Logic \& Analysis},
volume = {9},
number = {c2},
year = {2017},
pages = {1--44},
doi = {10.4115/jla.2017.9.c2},
}
@article{Kaw17a,
author = {Kawai, Tatsuji},
title = {Point-free characterisation of {B}ishop compact metric spaces},
journal = {Journal of Logic \& Analysis},
volume = {9},
number = {5},
year = {2017},
pages = {1--30},
doi = {10.4115/jla.2017.9.5},
}
@article{Kaw18,
author = {Kawai, Tatsuji},
title = {Formally continuous functions on {B}aire space},
journal = {Mathematical Logic Quarterly},
volume = {64},
number = {3},
year = {2018},
pages = {192--200},
doi = {10.1002/malq.201700015},
}
@inproceedings{KC10,
author = {Kawamura, Akitoshi and Cook, Stephen},
title = {Complexity theory for operators in analysis},
booktitle = {Proceedings of the 42nd ACM Symposium on Theory of Computing},
series = {STOC '10},
publisher = {ACM},
address = {New York},
year = {2010},
pages = {495--502},
doi = {10.1145/1806689.1806758},
}
@article{KC12,
author = {Kawamura, Akitoshi and Cook, Stephen A.},
title = {Complexity Theory for Operators in Analysis},
journal = {{ACM} Transactions on Computation Theory},
volume = {4},
number = {2},
year = {2012},
pages = {5:1--5:24},
doi = {10.1145/2189778.2189780},
}
@article{KCG94,
author = {Koiran, Pascal and Cosnard, Michel and Garzon, Max},
title = {Computability with low-dimensional dynamical systems},
journal = {Theoretical Computer Science},
volume = {132},
number = {1-2},
year = {1994},
pages = {113--128},
doi = {10.1016/0304-3975(94)90229-1},
}
@article{Kei12,
author = {Keimel, Klaus},
title = {Locally convex cones and the {S}chr{\"o}der-{S}impson theorem},
journal = {Quaestiones Mathematicae},
volume = {35},
year = {2012},
month = {09},
pages = {353--390},
}
@inproceedings{Kel00,
author = {Kelsey, Tom},
title = {Exact Numerical Computation via Symbolic Computation},
editor = {Blanck, Jens and Brattka, Vasco and Hertling, Peter and Weihrauch, Klaus},
booktitle = {Computability and Complexity in Analysis},
series = {Informatik Berichte},
volume = {272},
publisher = {FernUniversit\"at Hagen},
year = {2000},
month = sep,
pages = {187--197},
note = {CCA 2000 Workshop, Swansea, Wales, September 17--19, 2000},
}
@inproceedings{KEL02,
author = {Khanban, Ali Asghar and Edalat, Abbas and Lieutier, Andr{\'e}},
title = {Computability of {D}elaunay Triangulation and {V}oronoi Diagram},
editor = {Brattka, Vasco and Schr{\"{o}}der, Matthias and Weihrauch, Klaus},
booktitle = {{CCA} 2002 Computability and Complexity in Analysis},
series = {Electronic Notes in Theoretical Computer Science},
volume = {66},
publisher = {Elsevier},
address = {Amsterdam},
year = {2002},
note = {5th International Workshop, {CCA} 2002, M{\'{a}}laga, Spain, July 12--13, 2002},
}
@inproceedings{Ken05,
author = {Kenny, Robert},
title = {Orbit Complexity and Entropy for Group Endomorphisms},
editor = {Brattka, Vasco and Staiger, Ludwig and Weihrauch, Klaus},
booktitle = {Proceedings of the 6th Workshop on Computability and Complexity in Analysis},
series = {Electronic Notes in Theoretical Computer Science},
volume = {120},
publisher = {Elsevier},
address = {Amsterdam},
year = {2005},
pages = {97--110},
note = {6th International Workshop, {CCA} 2004, Wittenberg, Germany, August 16--20, 2004},
}
@article{Ken15,
author = {Kenny, Robert},
title = {Effective zero-dimensionality for computable metric spaces},
journal = {Logical Methods in Computer Science},
volume = {11},
year = {2015},
pages = {1:11,25},
doi = {10.2168/LMCS-11(1:11)2015},
}
@article{KF82,
author = {Ko, Ker-I and Friedman, H.},
title = {Computational complexity of real functions},
journal = {Theoretical Computer Science},
volume = {20},
year = {1982},
pages = {323--352},
}
@article{KF88,
author = {Ko, Ker-I and Friedman, H.},
title = {Computing power series in polynomial time},
journal = {Advances in Applied Math.},
volume = {9},
year = {1988},
pages = {40--50},
}
@inproceedings{Kie05,
author = {Kieu, Tien D.},
title = {Mathematical computability questions for some classes of linear and non-linear differential equations originated from {H}ilbert's Tenth Problem},
editor = {Grubba, Tanja and Hertling, Peter and Tsuiki, Hideki and Weihrauch, Klaus},
booktitle = {Computability and Complexity in Analysis},
series = {Informatik Berichte},
volume = {326},
publisher = {FernUniversit\"at in Hagen},
year = {2005},
month = jul,
pages = {161--168},
note = {Proccedings, Second International Conference, CCA 2005, Kyoto, Japan, August 25--29, 2005},
}
@phdthesis{Kih11,
author = {Kihara, Takayuki},
title = {Effectively closed sets and degrees of unsolvability},
school = {Mathematical Institute, Tohoku University},
year = {2011},
}
@article{Kih12,
author = {Kihara, Takayuki},
title = {Incomputability of simply connected planar continua},
journal = {Computability},
volume = {1},
number = {2},
year = {2012},
pages = {131--152},
doi = {10.3233/COM-12012},
}
@inproceedings{Kih12a,
author = {Kihara, Takayuki},
title = {A hierarchy of immunity and density for sets of reals},
editor = {Cooper, S. Barry and Dawar, Anuj and L{\"o}we, Benedikt},
booktitle = {How the World Computes},
series = {Lecture Notes in Computer Science},
volume = {7318},
publisher = {Springer},
address = {Heidelberg},
year = {2012},
pages = {384--394},
}
@article{Kih15,
author = {Kihara, Takayuki},
title = {Decomposing {B}orel functions using the {S}hore-{S}laman join theorem},
journal = {Fundamenta Mathematicae},
volume = {230},
year = {2015},
pages = {1--13},
doi = {10.4064/fm230-1-1},
}
@article{Kih15a,
author = {Kihara, Takayuki},
title = {Comparing the {M}edvedev and {T}uring degrees of $\Pi^0_1$ classes},
journal = {Mathematical Structures in Computer Science},
volume = {25},
year = {2015},
month = {12},
pages = {1649--1668},
doi = {10.1017/S0960129513000303},
}
@article{Kih16,
author = {Kihara, Takayuki},
title = {{B}orel-piecewise continuous reducibility for uniformization problems},
journal = {Logical Methods in Computer Science},
volume = {12},
number = {4},
year = {2016},
month = Oct,
doi = {10.2168/LMCS-12(4:4)2016},
}
@article{Kih19,
author = {Kihara, Takayuki},
title = {On a metric generalization of the {$tt$}-degrees and effective dimension theory},
journal = {The Journal of Symbolic Logic},
volume = {84},
number = {2},
year = {2019},
pages = {726--749},
doi = {10.1017/jsl.2019.18},
}
@article{Kih20a,
author = {Kihara, Takayuki},
title = {The {B}rouwer invariance theorems in reverse mathematics},
journal = {Forum of Mathematics. Sigma},
volume = {8},
year = {2020},
pages = {Paper No. e51, 12},
doi = {10.1017/fms.2020.52},
}
@article{Kih22,
author = {Kihara, Takayuki},
title = {Topological reducibilities for discontinuous functions and their structures},
journal = {Israel Journal of Mathematics},
year = {2022},
doi = {10.1007/s11856-022-2367-6},
}
@article{Kih23,
author = {Kihara, Takayuki},
title = {Lawvere-{T}ierney Topologies for Computability Theorists},
journal = {Transactions of the American Mathematical Society, Series B},
volume = {10},
number = {2},
year = {2023},
pages = {48--85},
doi = {10.1090/btran/134},
}
@article{Kjo10,
author = {Kjos-Hanssen, Bj{\o}rn},
title = {The probability distribution as a computational resource for randomness testing},
journal = {Journal of Logic and Analysis},
volume = {2},
year = {2010},
pages = {Paper 10, 13},
}
@inproceedings{KK01,
author = {Korovina, Margarita V. and Kudinov, Oleg V.},
title = {Formalisation of Computability of Operators and Real-Valued Functionals via Domain Theory},
editor = {Blanck, Jens and Brattka, Vasco and Hertling, Peter},
booktitle = {Computability and Complexity in Analysis},
series = {Lecture Notes in Computer Science},
volume = {2064},
publisher = {Springer},
address = {Berlin},
year = {2001},
pages = {146--168},
note = {4th International Workshop, CCA 2000, Swansea, UK, September 2000},
}
@inproceedings{KK01a,
author = {Korovina, Margarita V. and Kudinov, Oleg V.},
title = {Semantic Characterisations of Second-Order Computability over the Real Numbers},
editor = {Fribourg, Laurent},
booktitle = {Computer Science Logic},
series = {Lecture Notes in Computer Science},
volume = {2142},
publisher = {Springer},
address = {Berlin},
year = {2001},
pages = {160--172},
note = {15th International Workshop, CSL 2001, 10th Annual Conference of the EACSL, Paris, France, September 10--13, 2001},
}
@inproceedings{KK05,
author = {Korovina, Margarita and Kudinov, Oleg},
title = {Towards Computability of Higher Type Continuous Data},
editor = {Cooper, Barry S. and L{\"o}we, Benedikt and Torenvliet, Leen},
booktitle = {New Computational Paradigms},
series = {Lecture Notes in Computer Science},
volume = {3526},
publisher = {Springer},
address = {Berlin},
year = {2005},
pages = {235--241},
note = {First Conference on Computability in Europe, CiE 2005, Amsterdam, The Netherlands, June 2005},
}
@inproceedings{KK07,
author = {Korovina, Margarita and Kudinov, Oleg},
title = {The Uniformity Principle for {$\Sigma$}-Definability with Applications to Computable Analysis},
editor = {Cooper, S. Barry and L{\"o}we, Benedikt and Sorbi, Andrea},
booktitle = {Computation and Logic in the Real World},
series = {Lecture Notes in Computer Science},
volume = {4497},
publisher = {Springer},
address = {Berlin},
year = {2007},
pages = {416--425},
note = {Third Conference on Computability in Europe, CiE 2007, Siena, Italy, June 18-23, 2007},
}
@inproceedings{KK08,
author = {Korovina, Margarita and Kudinov, Oleg},
title = {Towards Computability over Effectively Enumerable Topological Spaces},
editor = {Brattka, Vasco and Dillhage, Ruth and Grubba, Tanja and Klutsch, Angela},
booktitle = {{CCA} 2008, Fifth International Conference on Computability and Complexity in Analysis},
series = {Electronic Notes in Theoretical Computer Science},
volume = {221},
publisher = {Elsevier},
year = {2008},
pages = {115--125},
note = {{CCA} 2008, Fifth International Conference, Hagen, Germany, August 21--24, 2008},
}
@article{KK09,
author = {Korovina, Margarita and Kudinov, Oleg},
title = {The Uniformity Principle for {$\Sigma$}-Definability},
journal = {Journal of Logic and Computation},
volume = {19},
number = {1},
year = {2009},
pages = {159--174},
}
@article{KK09a,
author = {Kreuzer, Alexander and Kohlenbach, Ulrich},
title = {Ramsey's theorem for pairs and provably recursive functions},
journal = {Notre Dame Journal of Formal Logic},
volume = {50},
number = {4},
year = {2009},
pages = {427--444 (2010)},
doi = {10.1215/00294527-2009-019},
}
@article{KK11,
author = {K{\"o}rnlein, Daniel and Kohlenbach, Ulrich},
title = {Effective rates of convergence for {L}ipschitzian pseudocontractive mappings in general {B}anach spaces},
journal = {Nonlinear Anal.},
volume = {74},
number = {16},
year = {2011},
pages = {5253--5267},
doi = {10.1016/j.na.2011.04.028},
}
@article{KK12,
author = {Kreuzer, Alexander P. and Kohlenbach, Ulrich},
title = {Term extraction and {R}amsey's theorem for pairs},
journal = {Journal of Symbolic Logic},
volume = {77},
number = {3},
year = {2012},
pages = {853--895},
doi = {10.2178/jsl/1344862165},
}
@article{KK13,
author = {Khan, Muhammad Aqeel Ahmad and Kohlenbach, Ulrich},
title = {Bounds on {K}uhfittig's iteration schema in uniformly convex hyperbolic spaces},
journal = {J. Math. Anal. Appl.},
volume = {403},
number = {2},
year = {2013},
pages = {633--642},
doi = {10.1016/j.jmaa.2013.02.058},
}
@inproceedings{KK15,
author = {Korovina, Margarita and Kudinov, Oleg},
title = {Rice's Theorem in Effectively Enumerable Topological Spaces},
editor = {Beckmann, Arnold and Mitrana, Victor and Soskova, Mariya},
booktitle = {Evolving Computability},
series = {Lecture Notes in Computer Science},
volume = {9136},
publisher = {Springer},
address = {Cham},
year = {2015},
pages = {226--235},
note = {11th Conference on Computability in Europe, CiE 2015, Bucharest, Romania, June 29--July 3, 2015},
doi = {10.1007/978-3-319-20028-6_23},
}
@article{KK15a,
author = {Korovina, Margarita and Kudinov, Oleg},
title = {Positive predicate structures for continuous data},
journal = {Mathematical Structures in Computer Science},
volume = {25},
year = {2015},
month = {12},
pages = {1669--1684},
doi = {10.1017/S0960129513000315},
}
@inproceedings{KK15b,
author = {Korovina, Margarita and Kudinov, Oleg},
title = {Index sets as a measure of continuous constraint complexity},
editor = {Voronkov, Andrei and Virbitskaite, Irina},
booktitle = {Perspectives of system informatics},
series = {Lecture Notes in Computer Science},
volume = {8974},
publisher = {Springer},
address = {Heidelberg},
year = {2015},
pages = {201--215},
note = {9th International Ershov Informatics Conference, PSI 2014, St. Petersburg, Russia, June 24-27, 2014. Revised Selected Papers},
doi = {10.1007/978-3-662-46823-4_17},
}
@article{KK16,
author = {Korovina, M. V. and Kudinov, O. V.},
title = {Spectrum of the field of computable real numbers},
journal = {Algebra Logic},
volume = {55},
number = {6},
year = {2016},
pages = {485--500},
doi = {0.1007/s10469-017-9419-8},
}
@inproceedings{KK17,
author = {Korovina, Margarita and Kudinov, Oleg},
title = {On Higher Effective Descriptive Set Theory},
editor = {Kari, Jarkko and Manea, Florin and Petre, Ion},
booktitle = {Unveiling Dynamics and Complexity},
series = {Lecture Notes in Computer Science},
volume = {10307},
publisher = {Springer},
address = {Cham},
year = {2017},
pages = {282--291},
note = {13th Conference on Computability in Europe, CiE 2017, Turku, Finland, June 12-16, 2017},
doi = {10.1007/978-3-319-58741-7_27},
}
@inproceedings{KK17a,
author = {Korovina, Margarita and Kudinov, Oleg},
title = {Outline of Partial Computability in Computable Topology},
editor = {Kari, Jarkko and Manea, Florin and Petre, Ion},
booktitle = {Unveiling Dynamics and Complexity},
series = {Lecture Notes in Computer Science},
volume = {10307},
publisher = {Springer},
address = {Cham},
year = {2017},
pages = {64--76},
note = {13th Conference on Computability in Europe, CiE 2017, Turku, Finland, June 12-16, 2017},
doi = {10.1007/978-3-319-58741-7_7},
}
@article{KK17b,
author = {Korovina, Margarita and Kudinov, Oleg},
title = {Computable elements and functions in effectively enumerable topological spaces},
journal = {Mathematical Structures in Computer Science},
volume = {27},
number = {8},
publisher = {Cambridge University Press},
year = {2017},
pages = {1466--1494},
doi = {10.1017/S0960129516000141},
}
@article{KK17c,
author = {Korovina, M. V. and Kudinov, O. V.},
title = {On images of partial computable functions over computable {P}olish spaces},
journal = {Sib. {\`E}lektron. Mat. Izv.},
volume = {14},
year = {2017},
pages = {418--432},
doi = {DOI 10.17377/semi.2017.14.035},
}
@article{KK17d,
author = {Korovina, Margarita and Kudinov, Oleg},
title = {The {R}ice-{S}hapiro theorem in computable topology},
journal = {Logical Methods in Computer Science},
volume = {13},
number = {4},
year = {2017},
pages = {Paper No. 30, 13},
}
@article{KK18,
author = {Korovina, Margarita and Kudinov, Oleg},
title = {Complexity for partial computable functions over computable {P}olish spaces},
journal = {Mathematical Structures in Computer Science},
volume = {28},
number = {3},
year = {2018},
pages = {429--447},
doi = {10.1017/S0960129516000438},
}
@inproceedings{KK18a,
author = {Korovina, Margarita and Kudinov, Oleg},
title = {Weak Reduction Principle and Computable Metric Spaces},
editor = {Manea, Florin and Miller, Russell G. and Nowotka, Dirk},
booktitle = {Sailing Routes in the World of Computation},
publisher = {Springer},
address = {Cham},
year = {2018},
pages = {234--243},
doi = {10.1007/978-3-319-94418-0_24},
}
@inproceedings{KK76,
author = {Kanovi\v{c}, M.I. and Kushner, B.A.},
title = {Complexity of algorithms, and {S}pecker sequences ({R}ussian)},
booktitle = {Studies in the {T}heory of {A}lgorithms and {M}athematical {L}ogic},
volume = {Vol. 2},
publisher = {Vy\v{c}isl. Centr. Akad. Nauk SSSR},
year = {1976},
pages = {77--63,160},
}
@article{KK78,
author = {Ku\v{c}era , A. and and Kushner, B.},
title = {A type of recursive isomorphism of certain concepts of constructive analysis ({R}ussian)},
journal = {Comment. Math. Univ. Carolin{\ae}},
volume = {19},
year = {1978},
pages = {97--105},
}
@inproceedings{KK98,
author = {Korovina, M.V. and Kudinov, O.V.},
title = {Majorant-computability and definability over the reals},
editor = {Chesneaux, J.-M. and J\'{e}z\'{e}quel, F. and Lamotte, J.-L. and Vignes, J.},
booktitle = {Third Real Numbers and Computers Conference},
publisher = {Universit\'{e} Pierre et Marie Curie, Paris},
year = {1998},
pages = {61--80},
note = {Paris, France, April 27--29, 1998},
}
@article{KK98a,
author = {Korovina, M.V. and Kudinov, O.V.},
title = {A new approach to computability over the reals},
journal = {Siberian Advances in Mathematics},
volume = {8},
number = {3},
year = {1998},
pages = {59--73},
}
@article{KK99,
author = {Kamo, Hiroyasu and Kawamura, Kiko},
title = {Computability of Self-Similar Sets},
journal = {Mathematical Logic Quarterly},
volume = {45},
year = {1999},
pages = {23--30},
}
@inproceedings{KK99a,
author = {Korovina, M.V. and Kudinov, O.V.},
title = {Some properties of majorant-computability},
editor = {Arslanov, Marat M. and Lempp, Steffen},
booktitle = {Recursion Theory and Complexity},
series = {Logic and Its Applications},
volume = {2},
publisher = {de Gruyter},
address = {Berlin},
year = {1999},
pages = {97--114},
note = {Proceedings of the Kazan Workshop, Kazan, Russia, July 14--19, 1997},
}
@inproceedings{KK99b,
author = {Korovina, M.V. and Kudinov, O.V.},
title = {Characteristic properties of majorant-computability over the reals},
editor = {Gottlob, Georg and Grandjean, Etienne and Seyr, Katrin},
booktitle = {Computer Science Logic},
series = {Lecture Notes in Computer Science},
volume = {1584},
publisher = {Springer},
address = {Berlin},
year = {1999},
pages = {188--203},
note = {Proceedings of the 12th International Workshop (CSL '98) (7th Annual Conference of the European Association for Computer Science Logic (EACSL)) held in Brno, August 24--28, 1998},
}
@article{KKT01,
author = {Kamo, Hiroyasu and Kawamura, Kiko and Takeuti, Izumi},
title = {Computational complexity of fractal sets},
journal = {Real Analysis Exchange},
volume = {26},
number = {2},
year = {2000/01},
pages = {773--793},
}
@inproceedings{KKT98,
author = {Kamo, Hiroyasu and Kawamura, Kiko and Takeuti, Izumi},
title = {Hausdorff Dimension and Computational Complexity},
editor = {Ko, Ker-I and Nerode, Anil and Pour-El, Marian B. and Weihrauch, Klaus and Wiedermann, Ji{\v{r}}{\'{\i}}},
booktitle = {Computability and Complexity in Analysis},
series = {Informatik Berichte},
volume = {235},
publisher = {FernUniversit\"at Hagen},
year = {1998},
month = aug,
pages = {41--50},
note = {CCA Workshop, Brno, Czech Republic, August, 1998},
}
@article{KL03,
author = {Kohlenbach, Ulrich and Leu{\c{s}}tean, Lauren{\c{t}}iu},
title = {Mann iterates of directionally nonexpansive mappings in hyperbolic spaces},
journal = {Abstract and Applied Analysis},
volume = {2003},
number = {8},
year = {2003},
pages = {449--477},
}
@inproceedings{KL03a,
author = {Kreinovich, Vladik and Longpr\'{e}, Luc},
title = {Computational complexity and feasibility of data processing and interval computations, with extension to cases when we have partial information about probabilities},
editor = {Brattka, Vasco and Schr{\"{o}}der, Matthias and Weihrauch, Klaus and Zhong, Ning},
booktitle = {Computability and Complexity in Analysis},
series = {Informatik Berichte},
volume = {302},
publisher = {FernUniversit\"at in Hagen},
year = {2003},
month = aug,
pages = {19--54},
note = {International Conference, CCA 2003, Cincinnati, USA, August 28--30, 2003},
}
@article{KL04,
author = {Kreinovich, Vladik and Longpr\'{e}, Luc},
title = {Fast quantum algorithms for handling probabilistic and interval uncertainty},
journal = {Mathematical Logic Quarterly},
volume = {50},
number = {4,5},
year = {2004},
pages = {405--416},
}
@inproceedings{KL04a,
author = {Kohlenbach, Ulrich and Lambov, Branimir},
title = {Bounds on iterations of asymptotically quasi-nonexpansive mappings},
editor = {Falset, J.G. and Fuster, E.L. and Sims, B.},
booktitle = {Proceedings of the International Conference on Fixed Point Theory and Applications},
publisher = {Yokohama Publishers},
year = {2004},
pages = {143--172},
note = {Valencia 2003},
}
@article{KL07,
author = {Kohlenbach, Ulrich and Leu{\c{s}}tean, Lauren{\c{t}}iu},
title = {The approximate fixed point property in product spaces},
journal = {Nonlinear Analysis},
volume = {66},
year = {2007},
pages = {806--818},
}
@article{KL09,
author = {Kohlenbach, U. and Leu{\c{s}}tean, L.},
title = {A quantitative mean ergodic theorem for uniformly convex {B}anach spaces},
journal = {Ergodic Theory and Dynamical Systems},
volume = {29},
number = {6},
year = {2009},
pages = {1907--1915},
doi = {10.1017/S0143385708001004},
}
@article{KL10,
author = {Kohlenbach, U. and Leu{\c{s}}tean, L.},
title = {Asymptotically nonexpansive mappings in uniformly convex hyperbolic spaces},
journal = {J. Eur. Math. Soc. (JEMS)},
volume = {12},
number = {1},
year = {2010},
pages = {71--92},
doi = {10.4171/JEMS/190},
}
@article{KL12,
author = {Kohlenbach, U. and Leu{\c{s}}tean, L.},
title = {On the computational content of convergence proofs via {B}anach limits},
journal = {Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci.},
volume = {370},
number = {1971},
year = {2012},
pages = {3449--3463},
doi = {10.1098/rsta.2011.0329},
}
@article{KL12a,
author = {Kohlenbach, U. and Leu{\c{s}}tean, L.},
title = {Effective metastability of {H}alpern iterates in {CAT}(0) spaces},
journal = {Adv. Math.},
volume = {231},
number = {5},
year = {2012},
pages = {2526--2556},
doi = {10.1016/j.aim.2012.06.028},
}
@article{KL57,
author = {Kreisel, Georg and Lacombe, Daniel},
title = {Ensembles r\'{e}cursivement mesurables et ensembles r\'{e}cursivement ouverts et ferm\'{e}s},
journal = {Comptes Rendus Acad\'emie des Sciences Paris},
volume = {245},
year = {1957},
pages = {1106--1109},
}
@article{KL82,
author = {Kalantari, I. and Leggett, A.},
title = {Simplicity in effective topology},
journal = {The Journal of Symbolic Logic},
volume = {47},
year = {1982},
pages = {169--183},
}
@article{KL83,
author = {Kalantari, I. and Leggett, A.},
title = {Maximality in effective topology},
journal = {The Journal of Symbolic Logic},
volume = {48},
year = {1983},
pages = {100--112},
}
@article{Kla56,
author = {Klaua, Dieter},
title = {Berechenbare {A}nalysis},
journal = {Zeitschrift f\"ur Mathematische Logik und Grundlagen der Mathematik},
volume = {2},
year = {1956},
pages = {265--303},
}
@phdthesis{Kla58,
author = {Klaua, Dieter},
title = {Berechenbare Analysis},
school = {Humboldt Universität Berlin},
address = {Berlin},
year = {1958},
month = {February},
}
@article{Kla59,
author = {Klaua, Dieter},
title = {Die {P}r\"azisierung des {B}erechenbarkeitsbegriffes in der {A}nalysis mit {H}ilfe rationaler {F}unktionale},
journal = {Zeitschrift f\"ur Mathematische Logik und Grundlagen der Mathematik},
volume = {5},
year = {1959},
pages = {33--96},
}
@article{Kla60,
author = {Klaua, Dieter},
title = {Berechenbare {R}eihen},
journal = {Zeitschrift f\"ur Mathematische Logik und Grundlagen der Mathematik},
volume = {6},
year = {1960},
pages = {143--161},
}
@book{Kla61,
author = {Klaua, Dieter},
title = {Konstruktive {A}nalysis},
publisher = {Deutscher Verlag der Wissenschaften},
address = {Berlin},
year = {1961},
}
@inproceedings{Kla94,
author = {Klaua, Dieter},
title = {Rational and real ordinal numbers},
booktitle = {Real Numbers, Generalizations of the Reals, and Theories of Continua},
series = {Synthese Lib.},
volume = {242},
year = {1994},
pages = {259--276},
}
@article{KLL99,
author = {Khalouani, Mohamed and Labhalla, Salah and Lombardi, Henri},
title = {\'Etude constructive de probl\`emes de topologie pour les r\'eels irrationnels},
journal = {Mathematical Logic Quarterly},
volume = {45},
number = {2},
year = {1999},
pages = {257--288},
}
@article{KLS57,
author = {Kreisel, G. and Lacombe, D. and Shoenfield, J.R.},
title = {Fonctionnelles r\'ecursivement d\'efinissables et fonctionnelles r\'ecursives},
journal = {C.R. Acad. Sci. Paris},
volume = {245},
year = {1957},
pages = {399--402},
}
@inproceedings{KLS59,
author = {Kreisel, G. and Lacombe, D. and Shoenfield, J.R.},
title = {Partial recursive functionals and effective operations},
editor = {Heyting, A.},
booktitle = {Constructivity in Mathematics},
series = {Studies in Logic and the Foundations of Mathematics},
publisher = {North-Holland},
address = {Amsterdam},
year = {1959},
pages = {290--297},
note = {Proc. Colloq., Amsterdam, Aug. 26--31, 1957},
}
@article{KM14,
author = {Kihara, Takayuki and Miyabe, Kenshi},
title = {Uniform {K}urtz randomness},
journal = {Journal of Logic and Computation},
volume = {24},
number = {4},
year = {2014},
pages = {863--882},
doi = {10.1093/logcom/ext054},
}
@article{KM15,
author = {Kihara, Takayuki and Miyabe, Kenshi},
title = {Unified characterizations of lowness properties via {K}olmogorov complexity},
journal = {Archive for Mathematical Logic},
volume = {54},
number = {3-4},
year = {2015},
pages = {329--358},
doi = {10.1007/s00153-014-0413-8},
}
@article{KM16,
author = {Kaushik, S.K. and Mantry, Poonam},
title = {Computable Frames in Computable {B}anach Spaces},
journal = {International Journal of Analysis and Applications},
volume = {11},
number = {2},
year = {2016},
pages = {93--100},
}
@article{KM19,
author = {Kihara, Takayuki and Montalb\'{a}n, Antonio},
title = {On the structure of the {W}adge degrees of bqo-valued {B}orel functions},
journal = {Transactions of the American Mathematical Society},
volume = {371},
number = {11},
year = {2019},
pages = {7885--7923},
doi = {10.1090/tran/7621},
}
@inproceedings{KM82,
author = {Kreisel, G. and Macintyre, A.},
title = {Constructive logic versus algebraization, {I}},
editor = {Troelstra, A.S. and van Dalen, D.},
booktitle = {The L. E. J. Brouwer Centenary Sympos.},
series = {Studies in Logic and the Foundations of Mathematics},
volume = {110},
publisher = {North-Holland},
address = {Amsterdam},
year = {1982},
pages = {217--260},
note = {(Noordwijkerhout, June 8--13, 1981)},
}
@article{KM99,
author = {Koiran, Pascal and Moore, Christopher},
title = {Closed-form analytic maps in one and two dimensions can simulate universal {T}uring machines},
journal = {Theoretical Computer Science},
volume = {219},
year = {1999},
pages = {217--223},
}
@article{KMMS20,
author = {Kumabe, Masahiro and Miyabe, Kenshi and Mizusawa, Yuki and Suzuki, Toshio},
title = {Solovay reducibility and continuity},
journal = {Journal of Logic and Analysis},
volume = {12},
year = {2020},
pages = {Paper No. 2, 22},
doi = {10.4115/jla.2020.12.2},
}
@article{KMP20,
author = {Kihara, Takayuki and Marcone, Alberto and Pauly, Arno},
title = {Searching for an analogue of {$ATR_0$} in the {W}eihrauch lattice},
journal = {Journal of Symbolic Logic},
volume = {85},
number = {3},
year = {2020},
pages = {1006--1043},
doi = {10.1017/jsl.2020.12},
}
@article{KMRZ15,
author = {Kawamura, Akitoshi and M{\"u}ller, Norbert and R{\"o}snick, Carsten and Ziegler, Martin},
title = {Computational benefit of smoothness: parameterized bit-complexity of numerical operators on analytic functions and {G}evrey's hierarchy},
journal = {Journal of Complexity},
volume = {31},
number = {5},
year = {2015},
pages = {689--714},
doi = {10.1016/j.jco.2015.05.001},
}
@inproceedings{KMT10,
author = {Kawamura, Akitoshi and Matou{\v{s}}ek, Ji{\v{r}}{\'{\i}} and Tokuyama, Takeshi},
title = {Zone diagrams in {E}uclidean spaces and in other normed spaces},
booktitle = {Computational geometry ({SCG}'10)},
publisher = {ACM},
address = {New York},
year = {2010},
pages = {216--221},
doi = {10.1145/1810959.1810997},
}
@article{KMT12,
author = {Kawamura, Akitoshi and Matou{\v{s}}ek, Ji{\v{r}}{\'{\i}} and Tokuyama, Takeshi},
title = {Zone diagrams in {E}uclidean spaces and in other normed spaces},
journal = {Math. Ann.},
volume = {354},
number = {4},
year = {2012},
pages = {1201--1221},
doi = {10.1007/s00208-011-0761-1},
}
@incollection{KN07,
author = {Kjos-Hanssen, Bj{\o}rn and Nerode, Anil},
title = {The law of the iterated logarithm for algorithmically random {B}rownian motion},
editor = {Artemov, Sergei N. and Nerode, Anil},
booktitle = {Logical Foundations of Computer Science},
series = {Lecture Notes in Computer Science},
volume = {4514},
publisher = {Springer},
address = {Berlin},
year = {2007},
pages = {310--317},
note = {{P}roceedings of the {I}nternational {S}ymposium ({LFCS} 2007) held at the {C}ity {U}niversity of {N}ew {Y}ork, {N}ew {Y}ork, {J}une 4--7, 2007},
doi = {10.1007/978-3-540-72734-7_22},
}
@article{KN09,
author = {Kjos-Hanssen, Bj{\o}rn and Nerode, Anil},
title = {Effective dimension of points visited by {B}rownian motion},
journal = {Theoretical Computer Science},
volume = {410},
number = {4-5},
year = {2009},
pages = {347--354},
doi = {10.1016/j.tcs.2008.09.045},
}
@article{KN21,
author = {Kone{\v{c}}n{\'{y}}, Michal and Neumann, Eike},
title = {Representations and evaluation strategies for feasibly approximable functions },
journal = {Computability},
volume = {10},
number = {1},
year = {2021},
pages = {63--89},
doi = {10.3233/COM-180234},
}
@article{KNP15,
author = {Ku\v{c}era, Anton{\'\i}n and Nies, Andr\'{e} and Porter, Christopher P.},
title = {{D}emuth's Path to Randomness},
journal = {The Bulletin of Symbolic Logic},
volume = {21},
number = {3},
year = {2015},
pages = {270--305},
doi = {10.1017/bsl.2015.24},
}
@article{KNR14,
author = {Kjos-Hanssen, Bj{\o}rn and Nguyen, Paul Kim Long V. and Rute, Jason},
title = {Algorithmic randomness for {D}oob's martingale convergence theorem in continuous time},
journal = {Logical Methods in Computer Science},
volume = {10},
number = {4:12},
year = {2014},
pages = {1--35},
doi = {10.2168/LMCS-10(4:12)2014},
}
@inproceedings{KNS03,
author = {Kjos-Hanssen, Bj{\o}rn and Nies, Andr\'{e} and Stephan, Frank},
title = {On a question of {A}mbos-{S}pies and {K}u\v{c}era},
editor = {Brattka, Vasco and Schr{\"{o}}der, Matthias and Weihrauch, Klaus and Zhong, Ning},
booktitle = {Computability and Complexity in Analysis},
series = {Informatik Berichte},
volume = {302},
publisher = {FernUniversit\"at in Hagen},
year = {2003},
month = aug,
pages = {275--278},
note = {International Conference, CCA 2003, Cincinnati, USA, August 28--30, 2003},
}
@proceedings{KNW02,
title = {Computability and Complexity in Analysis},
editor = {Ko, Ker-I and Nerode, Anil and Weihrauch, Klaus},
series = {Theoretical Computer Science},
volume = {284(2)},
publisher = {Elsevier},
address = {Amsterdam},
year = {2002},
}
@article{KO03,
author = {Kohlenbach, Ulrich and Oliva, Paulo},
title = {Proof mining in $L_1$-approximation},
journal = {Annals of Pure and Applied Logic},
volume = {121},
year = {2003},
pages = {1--38},
}
@inproceedings{Ko03a,
author = {Ko, Ker-I},
title = {Computational Complexity of Fractals},
editor = {Downey, Rod and Decheng, Ding and Ping, Tung Shih and Hui, Qiu Yu and Yasugi, Mariko},
booktitle = {Proceedings of the 7th and 8th Asian Logic Conferences},
publisher = {World Scientific},
address = {Singapore},
year = {2003},
pages = {252--269},
note = {7th Conference: Hsi-Tou, Taiwan, June 6--10, 1999; 8th Conference: Chongqing, China, August 29 -- September 2, 2002},
}
@article{Ko13,
author = {Ko, Ker-I},
title = {On the complexity of computing the {H}ausdorff distance},
journal = {J. Complexity},
volume = {29},
number = {3-4},
year = {2013},
pages = {248--262},
doi = {10.1016/j.jco.2013.03.002},
}
@inproceedings{KO14,
author = {Kawamura, Akitoshi and Ota, Hiroyuki},
title = {Small complexity classes for computable analysis},
booktitle = {Mathematical foundations of computer science 2014. {P}art {II}},
series = {Lecture Notes in Comput. Sci.},
volume = {8635},
publisher = {Springer, Heidelberg},
year = {2014},
pages = {432--444},
doi = {10.1007/978-3-662-44465-8_37},
}
@article{Ko82,
author = {Ko, Ker-I},
title = {The maximum value problem and {N}{P} real numbers},
journal = {Journal of Computer and Systems Sciences},
volume = {24},
year = {1982},
pages = {15--35},
}
@article{Ko82a,
author = {Ko, Ker-I},
title = {Some negative results on the computational complexity of total variation and differentiation},
journal = {Inform. Contr.},
volume = {53},
year = {1982},
pages = {21--31},
}
@article{Ko83,
author = {Ko, Ker-I},
title = {On the computational complexity of ordinary differential equations},
journal = {Inform. Contr.},
volume = {58},
year = {1983},
pages = {157--194},
}
@article{Ko83a,
author = {Ko, Ker-I},
title = {On the definitions of some complexity classes of real numbers},
journal = {Math. Systems Theory},
volume = {16},
year = {1983},
pages = {95--109},
}
@article{Ko84,
author = {Ko, Ker-I},
title = {Reducibilities on real numbers},
journal = {Theoretical Computer Science},
volume = {31},
year = {1984},
pages = {101--123},
}
@article{Ko85,
author = {Ko, Ker-I},
title = {Continuous optimization problems and a polynomial hierarchy of real functions},
editor = {Traub, J.F.},
journal = {Journal of Complexity},
volume = {1},
year = {1985},
pages = {210--231},
note = {(Special issue: Complexity of Approximating Solved Problems, Papers from Sympos. Columbia Univ., Morningside Heights, NY, Apr. 17--19, 1985)},
}
@article{Ko86,
author = {Ko, Ker-I},
title = {Approximation to measurable functions and its relation to probabilistic computation},
journal = {Annals of Pure and Applied Logic},
volume = {30},
year = {1986},
pages = {173--200},
}
@article{Ko86a,
author = {Ko, Ker-I},
title = {On the computational complexity of best {C}hebyshev approximations},
journal = {Journal of Complexity},
volume = {2},
year = {1986},
pages = {95--120},
}
@article{Ko86b,
author = {Ko, Ker-I},
title = {On the continued fraction representation of computable real numbers},
journal = {Theoretical Computer Science},
volume = {47},
year = {1986},
pages = {299--313},
note = {corr. ibid., Vol. 54 (1987), Pages 341--343},
}
@article{Ko87,
author = {Ko, Ker-I},
title = {Corrigenda: ``{O}n the continued fraction representation of computable real numbers''},
journal = {Theoretical Computer Science},
volume = {54},
number = {2-3},
year = {1987},
pages = {341--343},
doi = {10.1016/0304-3975(87)90139-3},
}
@inproceedings{Ko90,
author = {Ko, Ker-I},
title = {Inverting a one-to-one real function is inherently sequential},
editor = {Buss, S. and Scott, P.J.},
booktitle = {Feasible Mathematics},
journal = {Progr. Comput. Sci. Appl. Logic},
volume = {9},
year = {1990},
pages = {239--257},
note = {(Proc. Workshop, June 16--18, 1989, Cornell Univ. Ithaca, NY)},
}
@book{Ko91,
author = {Ko, Ker-I},
title = {Complexity Theory of Real Functions},
series = {Progress in Theoretical Computer Science},
publisher = {Birkh\"auser},
address = {Boston},
year = {1991},
}
@article{Ko92,
author = {Ko, Ker-I},
title = {On the computational complexity of integral equations},
journal = {Annals of Pure and Applied Logic},
volume = {58},
year = {1992},
pages = {201--228},
}
@inproceedings{Ko95,
author = {Ko, Ker-I},
title = {Recent progress on complexity theory of real functions},
editor = {Ko, Ker-I and Weihrauch, Klaus},
booktitle = {Computability and Complexity in Analysis},
series = {Informatik Berichte},
volume = {190},
publisher = {FernUniversit\"at Hagen},
year = {1995},
month = sep,
pages = {83--90},
note = {CCA Workshop, Hagen, August 19--20, 1995},
}
@article{Ko95a,
author = {Ko, Ker-I},
title = {A polynomial-time computable curve whose interior has a nonrecursive measure},
journal = {Theoretical Computer Science},
volume = {145},
year = {1995},
pages = {241--270},
}
@article{Ko95b,
author = {Ko, Ker-I},
title = {Computational complexity of fixed points and intersection points},
journal = {Journal of Complexity},
volume = {11},
year = {1995},
pages = {265--292},
}
@inproceedings{Ko96,
author = {Ko, Ker-I},
title = {Fractals and complexity},
editor = {Ko, Ker-I and M\"uller, Norbert and Weihrauch, Klaus},
booktitle = {Computability and Complexity in Analysis},
publisher = {Universit\"at Trier},
year = {1996},
pages = {43--48},
note = {Second CCA Workshop, Trier, August 22--23, 1996},
}
@article{Ko98,
author = {Ko, Ker-I},
title = {On the computability of fractal dimensions and {H}ausdorff measure},
journal = {Annals of Pure and Applied Logic},
volume = {93},
year = {1998},
pages = {195--216},
}
@inproceedings{Ko98a,
author = {Ko, Ker-I},
title = {Polynomial-Time Computability in Analysis},
editor = {Ershov, Yu. L. and Goncharov, S.S. and Nerode, A. and Remmel, J.B.},
booktitle = {Handbook of Recursive Mathematics},
series = {Studies in Logic and the Foundations of Mathematics},
volume = {139},
publisher = {Elsevier},
address = {Amsterdam},
year = {1998},
pages = {1271--1317},
note = {Volume 2, Recursive Algebra, Analysis and Combinatorics},
}
@article{Kob07,
author = {K{\o}ber, Petter K.},
title = {Uniform domain representations of $\ell_p$--spaces},
journal = {Mathematical Logic Quarterly},
volume = {180},
number = {2},
year = {2007},
pages = {180--205},
}
@article{Koh00a,
author = {Kohlenbach, Ulrich},
title = {Things that can and things that cannot be done in {PRA}},
journal = {Annals of Pure and Applied Logic},
volume = {102},
year = {2000},
pages = {223--245},
}
@inproceedings{Koh01,
author = {Kohlenbach, Ulrich},
title = {On the Computational Content of the {K}rasnoselski and {I}shikawa Fixed Point Theorems},
editor = {Blanck, Jens and Brattka, Vasco and Hertling, Peter},
booktitle = {Computability and Complexity in Analysis},
series = {Lecture Notes in Computer Science},
volume = {2064},
publisher = {Springer},
address = {Berlin},
year = {2001},
pages = {119--145},
note = {4th International Workshop, CCA 2000, Swansea, UK, September 2000},
}
@article{Koh01b,
author = {Kohlenbach, Ulrich},
title = {A quantitative version of a theorem due to {B}orwein-{R}eich-{S}hafrir},
journal = {Numerical Functional Analysis and Optimization},
volume = {22},
number = {5},
year = {2001},
pages = {641--656},
}
@article{Koh02,
author = {Kohlenbach, Ulrich},
title = {On uniform weak {K}{\"{o}}nig's lemma},
journal = {Annals of Pure and Applied Logic},
volume = {114},
year = {2002},
pages = {103--116},
}
@article{Koh02a,
author = {Kohlenbach, Ulrich},
title = {On Weak {M}arkov's Principle},
journal = {Mathematical Logic Quarterly},
volume = {48},
number = {Suppl. 1},
year = {2002},
pages = {59--65},
}
@article{Koh03,
author = {Kohlenbach, Ulrich},
title = {Uniform asymptotic regularity for {M}ann iterates},
journal = {Journal of Mathematical Analysis and Applications},
volume = {279},
year = {2003},
pages = {531--544},
}
@article{Koh05,
author = {Kohlenbach, Ulrich},
title = {Some logical metatheorems with applications in functional analysis},
journal = {Transactions of the American Mathematical Society},
volume = {357},
year = {2005},
pages = {89--128},
}
@article{Koh05a,
author = {Kohlenbach, Ulrich},
title = {Some computational aspects of metric fixed point theory},
journal = {Nonlinear Analysis},
volume = {61},
year = {2005},
pages = {823--837},
}
@inproceedings{Koh05b,
author = {Kohlenbach, Ulrich},
title = {Higher order reverse mathematics},
editor = {Simpson, Stephen G.},
booktitle = {Reverse Mathematics 2001},
series = {Lecture Notes in Logic},
volume = {21},
publisher = {A K Peters},
address = {Wellesley},
year = {2005},
pages = {281--295},
doi = {10.1017/9781316755846.018},
}
@inproceedings{Koh06,
author = {Kohlenbach, Ulrich},
title = {A Logical Uniform Boundedness Principle for Abstract Metric and Hyperbolic Spaces},
editor = {Mints, Grigori and de Queiroz, Ruy},
booktitle = {Logic, Language, Information and Computation},
series = {Electronic Notes in Theoretical Computer Science},
volume = {165},
publisher = {Elsevier},
address = {Amsterdam},
year = {2006},
pages = {81--93},
note = {{WoLLIC} 2006, 13th Workshop on Logic, Language, Information and Computation, Stanford University, CA, USA, 18-21 July 2006},
}
@article{Koh07,
author = {Kohlenbach, Ulrich},
title = {Proof interpretations and the computational content of proofs in mathematics},
journal = {Bulletin of the EATCS},
volume = {93},
year = {2007},
pages = {143--173},
}
@inproceedings{Koh08,
author = {Kohlenbach, Ulrich},
title = {Effective bounds from proofs in abstract functional analysis},
editor = {Cooper, S. Barry and L{\"o}we, Benedikt and Sorbi, Andrea},
booktitle = {New Computational Paradigms: Changing Conceptions of What Is Computable},
publisher = {Springer},
address = {New York},
year = {2008},
pages = {223--258},
}
@book{Koh08a,
author = {Kohlenbach, Ulrich},
title = {Applied Proof Theory: Proof Interpretations and Their Use in Mathematics},
publisher = {Springer},
address = {Berlin},
year = {2008},
}
@incollection{Koh10,
author = {Kohlenbach, Ulrich},
title = {On the logical analysis of proofs based on nonseparable {H}ilbert space theory},
booktitle = {Proofs, categories and computations},
series = {Tributes},
volume = {13},
publisher = {Coll. Publ., London},
year = {2010},
pages = {131--143},
}
@article{Koh11,
author = {Kohlenbach, Ulrich},
title = {On quantitative versions of theorems due to {F}. {E}. {B}rowder and {R}. {W}ittmann},
journal = {Adv. Math.},
volume = {226},
number = {3},
year = {2011},
pages = {2764--2795},
doi = {10.1016/j.aim.2010.10.002},
}
@article{Koh11a,
author = {Kohlenbach, Ulrich},
title = {On the asymptotic behavior of odd operators},
journal = {J. Math. Anal. Appl.},
volume = {382},
number = {2},
year = {2011},
pages = {615--620},
doi = {10.1016/j.jmaa.2011.04.065},
}
@article{Koh12,
author = {Kohlenbach, Ulrich},
title = {A uniform quantitative form of sequential weak compactness and {B}aillon's nonlinear ergodic theorem},
journal = {Commun. Contemp. Math.},
volume = {14},
number = {1},
year = {2012},
pages = {1250006, 20},
doi = {10.1142/S021919971250006X},
}
@article{Koh12a,
author = {Kohlenbach, Ulrich},
title = {G\"odel functional interpretation and weak compactness},
journal = {Ann. Pure Appl. Logic},
volume = {163},
number = {11},
year = {2012},
pages = {1560--1579},
doi = {10.1016/j.apal.2011.12.009},
}
@article{Koh15,
author = {Kohlenbach, Ulrich},
title = {On the Disjunctive {M}arkov Principle},
journal = {Studia Logica},
volume = {103},
number = {6},
year = {2015},
pages = {1313--1317},
}
@article{Koh19,
author = {Kohlenbach, Ulrich},
title = {On the reverse mathematics and {W}eihrauch complexity of moduli of regularity and uniqueness},
journal = {Computability},
volume = {8},
number = {3, 4},
year = {2019},
pages = {377--387},
doi = {10.3233/COM-180097},
}
@article{Koh21,
author = {Kohlenbach, Ulrich},
title = {Proof-theoretic uniform boundedness and bounded collection principles and countable {H}eine–{B}orel compactness},
journal = {Archive for Mathematical Logic},
volume = {60},
number = {7--8},
year = {2021},
pages = {995--1003},
doi = {10.1007/s00153-021-00771-w},
}
@article{Koh93,
author = {Kohlenbach, Ulrich},
title = {Effective moduli from ineffective uniqueness proofs. An unwinding of de {L}a {V}all\'{e} {P}oussin's proof for {C}hebycheff approximation},
journal = {Annals of Pure and Applied Logic},
volume = {64},
year = {1993},
pages = {27-94},
}
@article{Koh93a,
author = {Kohlenbach, Ulrich},
title = {New effective moduli of uniqueness and uniform a priori estimates for constants of strong unicity by logical analysis of known proofs in best approximation theory},
journal = {Numer. Funct. Anal. and Optimiz.},
volume = {14},
year = {1993},
pages = {581-606},
}
@inproceedings{Koh96,
author = {Kohlenbach, Ulrich},
title = {Analysing Proofs in Analysis},
editor = {Hodges, Wilfried and Hyland, Martin and Steinhorn, Charles and Truss, John},
booktitle = {Logic: from Foundations to Applications},
publisher = {Clarendon Press},
address = {Oxford},
year = {1996},
pages = {225--260},
note = {European Logic Colloquium},
}
@inproceedings{Koh97,
author = {Kohlenbach, Ulrich},
title = {Arithmetizing proofs in analysis},
editor = {Larrazabal, J.M. and Lascar, D. and Mints, G.},
booktitle = {Logic Colloquium '96},
series = {Lecture Notes in Logic},
volume = {12},
publisher = {Springer},
address = {Berlin},
year = {1997},
pages = {115--158},
note = {Proceedings of the Colloquium held in Sebasti\'{a}n, Spain, July 9--15, 1996},
}
@article{Koh98,
author = {Kohlenbach, Ulrich},
title = {Proof theory and computational analysis},
journal = {Electronic Notes in Theoretical Computer Science},
volume = {13},
year = {1998},
pages = {1--34},
}
@inproceedings{Koh99,
author = {Kohlenbach, Ulrich},
title = {The use of a logical principle of uniform boundedness in analysis},
editor = {Cantini, A. and Casari, E. and Minari, P.},
booktitle = {Logic and Foundations of Mathematics},
series = {Synthese Library},
volume = {280},
publisher = {Kluwer Academic Publishers},
year = {1999},
pages = {93--106},
}
@article{Kol25,
author = {Kolmogorov, Andrei N.},
title = {On the principle of tertium non datur ({R}ussian)},
journal = {Mat. Sb.},
volume = {32},
year = {1925},
pages = {646--667},
note = {[translated in: From Frege to G\"odel: A Source Book in Logic, 1879--1931, J. van Heijenroot, (ed.), (Harvard Univ. Press, Cambridge, Mass. and Oxford Univ. Press, London, 1967) 414--437]},
}
@phdthesis{Kon00,
author = {Kone{\v{c}}n{\'{y}}, Michal},
title = {Many-Valued Real Functions Computable by Finite Transducers using IFS-Representations},
school = {School of Computer Science, University of Birmingham},
address = {Birmingham},
year = {2000},
}
@article{Kon02,
author = {Kone{\v{c}}n{\'{y}}, Michal},
title = {Real functions computable by finite automata using affine representations},
journal = {Theoretical Computer Science},
volume = {284},
number = {2},
year = {2002},
pages = {373--396},
}
@article{Kon04,
author = {Kone{\v{c}}n{\'{y}}, Michal},
title = {Real functions incrementally computable by finite automata},
journal = {Theoretical Computer Science},
volume = {315},
year = {2004},
pages = {109--133},
}
@inproceedings{Kor02,
author = {Korovina, Margarita V.},
title = {Fixed Points on the Real Numbers without the Equality Test},
editor = {Brattka, Vasco and Schr{\"{o}}der, Matthias and Weihrauch, Klaus},
booktitle = {{CCA} 2002 Computability and Complexity in Analysis},
series = {Electronic Notes in Theoretical Computer Science},
volume = {66},
publisher = {Elsevier},
address = {Amsterdam},
year = {2002},
note = {5th International Workshop, {CCA} 2002, M{\'{a}}laga, Spain, July 12--13, 2002},
}
@article{Kor17,
author = {Kornev, R. A.},
title = {Reducibility of computable metrics on the real line},
journal = {Algebra Logic},
volume = {56},
number = {4},
year = {2017},
pages = {302--317},
doi = {0.1007/s10469-017-9451-8},
}
@article{Kor92,
author = {Korovina, M.V.},
title = {Generalized computability of real functions},
journal = {Siberian Advances in Mathematics},
volume = {2},
number = {4},
year = {1992},
pages = {85--103},
}
@inproceedings{KORZ12,
author = {Kawamura, Akitoshi and Ota, Hiroyuki and R{\"o}snick, Carsten and Ziegler, Martin},
title = {Computational complexity of smooth differential equations},
booktitle = {Mathematical foundations of computer science 2012},
series = {Lecture Notes in Comput. Sci.},
volume = {7464},
publisher = {Springer, Heidelberg},
year = {2012},
pages = {578--589},
doi = {10.1007/978-3-642-32589-2_51},
}
@article{KORZ14,
author = {Kawamura, Akitoshi and Ota, Hiroyuki and R{\"o}snick, Carsten and Ziegler, Martin},
title = {Computational Complexity of Smooth Differential Equations},
journal = {Logical Methods in Computer Science},
volume = {10},
year = {2014},
pages = {1:6,15},
doi = {10.2168/LMCS-10(1:6)2014},
}
@inproceedings{KP14a,
author = {Kawamura, Akitoshi and Pauly, Arno},
title = {Function spaces for second-order polynomial time},
booktitle = {Language, life, limits},
series = {Lecture Notes in Comput. Sci.},
volume = {8493},
publisher = {Springer, Cham},
year = {2014},
pages = {245--254},
doi = {10.1007/978-3-319-08019-2_25},
}
@inproceedings{KP16a,
author = {Kihara, Takayuki and Pauly, Arno},
title = {Dividing by Zero - How Bad Is It, Really?},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
volume = {58},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
year = {2016},
pages = {58:1--58:14},
doi = {10.4230/LIPIcs.MFCS.2016.58},
}
@incollection{KP16b,
author = {Kihara, Takayuki and Pauly, Arno},
title = {Dividing by zero---how bad is it, really?},
booktitle = {41st {I}nternational {S}ymposium on {M}athematical {F}oundations of {C}omputer {S}cience},
series = {LIPIcs. Leibniz Int. Proc. Inform.},
volume = {58},
publisher = {Schloss Dagstuhl. Leibniz-Zent. Inform., Wadern},
year = {2016},
pages = {Art. No. 58, 14},
doi = {10.4230/LIPIcs.MFCS.2016.58},
}
@incollection{KP19,
author = {Kihara, Takayuki and Pauly, Arno},
title = {Finite choice, convex choice and sorting},
editor = {Gopal, T.V. and Watada, Junzo},
booktitle = {Theory and applications of models of computation},
series = {Lecture Notes in Computer Science},
volume = {11436},
publisher = {Springer},
address = {Cham},
year = {2019},
pages = {378--393},
note = {15th Annual Conference, TAMC 2019, Kitakyushu, Japan, April 13--16, 2019},
doi = {10.1007/978-3-030-14812-6_23},
}
@article{KP22,
author = {Kihara, Takayuki and Pauly, Arno},
title = {Point degree spectra of represented spaces},
journal = {Forum of Mathematics. Sigma},
volume = {10},
year = {2022},
pages = {Paper No. e31, 27},
doi = {10.1017/fms.2022.7},
}
@article{KP57,
author = {Kreisel, G. and Putnam, H.},
title = {Eine {U}nableitbarkeitsbeweismethode f\"ur den intuitionistischen {A}ussagenkalk\"ul},
journal = {Arch. Math. Logic Grundlag},
volume = {3},
year = {1957},
pages = {74--78},
}
@article{KPSZ23,
author = {Koswara, Ivan and Pogudin, Gleb and Selivanova, Svetlana and Ziegler, Martin},
title = {Bit-complexity of classical solutions of linear evolutionary systems of partial differential equations},
journal = {Journal of Complexity},
year = {2023},
pages = {101727},
doi = {10.1016/j.jco.2022.101727},
}
@incollection{KPT21,
author = {Kone\v{c}n\'{y}, Michal and Park, Sewon and Thies, Holger},
title = {Axiomatic reals and certified efficient exact real computation},
booktitle = {Logic, language, information, and computation},
series = {Lecture Notes in Comput. Sci.},
volume = {13038},
publisher = {Springer, Cham},
year = {2021},
pages = {252--268},
}
@article{KR79,
author = {Kalantari, I. and Retzlaff, A.},
title = {Recursive constructions in topological spaces},
journal = {The Journal of Symbolic Logic},
volume = {44},
year = {1979},
pages = {609--625},
}
@article{KR83,
author = {Kalantari, I. and Remmel, J.B.},
title = {Degrees of recursively enumerable topological spaces},
journal = {The Journal of Symbolic Logic},
volume = {48},
year = {1983},
pages = {610--622},
}
@article{Kre11,
author = {Kreuzer, Alexander P.},
title = {The cohesive principle and the {B}olzano-{W}eierstra\ss{} Principle},
journal = {Mathematical Logic Quarterly},
volume = {57},
number = {3},
year = {2011},
pages = {292--298},
doi = {10.1002/malq.201010008},
}
@article{Kre12,
author = {Kreuzer, Alexander P.},
title = {On the Strength of Weak Compactness},
journal = {Computability},
volume = {1},
number = {2},
year = {2012},
pages = {171--179},
doi = {10.3233/COM-12010},
}
@inproceedings{Kre12a,
author = {Kreinovich, V.},
title = {Negative results of computable analysis disappear if we restrict ourselves to random (or, more generally, typical) inputs},
booktitle = {Mathematical structures and modeling. {N}umber 25 ({R}ussian)},
publisher = {Omsk. Gos. Univ.},
address = {Omsk},
year = {2012},
pages = {100--113, 131},
}
@article{Kre12b,
author = {Kreuzer, Alexander P.},
title = {Primitive recursion and the chain antichain principle},
journal = {Notre Dame Journal of Formal Logic},
volume = {53},
number = {2},
year = {2012},
pages = {245--265},
doi = {10.1215/00294527-1715716},
}
@article{Kre12c,
author = {Kreuzer, Alexander P.},
title = {Non-principal ultrafilters, program extraction and higher-order reverse mathematics},
journal = {Journal of Mathematical Logic},
volume = {12},
number = {1},
year = {2012},
pages = {1250002, 16},
doi = {10.1142/S021906131250002X},
}
@article{Kre12d,
author = {Kreuzer, Alexander P.},
title = {A logical analysis of the generalized {B}anach contractions principle},
journal = {Journal of Logic and Analysis},
volume = {4},
year = {2012},
pages = {Paper 17, 16},
}
@article{Kre13,
author = {Kreuzer, Alexander P.},
title = {Program extraction for 2-random reals},
journal = {Archive for Mathematical Logic},
volume = {52},
number = {5-6},
year = {2013},
pages = {659--666},
doi = {10.1007/s00153-013-0336-9},
}
@article{Kre14,
author = {Kreuzer, Alexander P.},
title = {From {B}olzano-{W}eierstra\ss\ to {A}rzel\`a-{A}scoli},
journal = {Mathematical Logic Quarterly},
volume = {60},
number = {3},
year = {2014},
pages = {177--183},
doi = {10.1002/malq.201200076},
}
@article{Kre14a,
author = {Kreuzer, Alexander P.},
title = {Bounded variation and the strength of {H}elly's selection theorem},
journal = {Logical Methods in Computer Science},
volume = {10},
number = {4:16},
year = {2014},
pages = {1--23},
doi = {10.2168/LMCS-10(4:16)2014},
}
@article{Kre15a,
author = {Kreuzer, Alexander P.},
title = {Measure theory and higher order arithmetic},
journal = {Proceedings of the American Mathematical Society},
volume = {143},
number = {12},
year = {2015},
pages = {5411--5425},
doi = {10.1090/proc/12671},
}
@article{Kre17,
author = {Kreinovich, Vladik},
title = {Why some physicists are excited about the undecidability of the spectral gap problem and why should we},
journal = {Bulletin of the EATCS},
volume = {122},
year = {2017},
pages = {100--113},
}
@article{Kre52,
author = {Kreisel, Georg},
title = {On the interpretation of non-finitist proofs. {II}. {I}nterpretation of number theory. {A}pplications},
journal = {The Journal of Symbolic Logic},
volume = {17},
year = {1952},
pages = {43--58},
}
@inproceedings{Kre59,
author = {Kreisel, G.},
title = {Interpretation of analysis by means of constructive functionals of finite types},
editor = {Heyting, A.},
booktitle = {Constructivity in Mathematics},
series = {Studies in Logic and the Foundations of Mathematics},
publisher = {North-Holland},
address = {Amsterdam},
year = {1959},
pages = {101--128},
note = {Proc. Colloq., Amsterdam, Aug. 26--31, 1957},
}
@inproceedings{Kre62,
author = {Kreisel, G.},
title = {Foundations of {I}ntuitionistic {L}ogic, {M}ethodology and {P}hilisophy of {S}cience},
booktitle = {Logic, Methodology, and Philosophy of Science},
year = {1962},
pages = {198--210},
note = {(Proc. Internatl. Congr., Stanford, CA, 1960)},
}
@inproceedings{Kre70,
author = {Kreisel, G.},
title = {Church's thesis: {A} kind of reducibility axiom for constructive mathematics},
editor = {Kino, A. and Myhill, J. and Vesley, R.E.},
booktitle = {Intuitionism and Proof Theory},
series = {Studies in Logic and the Foundations of Mathematics},
publisher = {North-Holland},
address = {Amsterdam},
year = {1970},
pages = {121--150},
note = {(Proc. Conf., Buffalo, N.Y., 1968)},
}
@inproceedings{Kre73,
author = {Kreisel, G.},
title = {Perspectives in the philosophy of pure mathematics},
editor = {Suppes, P. and Henkin, L. and Joja, A. and Moisil, Gr.C.},
booktitle = {Logic, Methodology, and Philosophy of Science {V}{I}},
series = {Studies in Logic and the Foundations of Mathematics},
publisher = {North-Holland},
address = {Amsterdam},
year = {1973},
pages = {255--277},
note = {(Proc. 4th. Internatl. Congr. Logic, Methodology and Philos. Sci., Bucharest, Aug. 29--Sept. 4,1971)},
}
@article{Kre82,
author = {Kreisel, G.},
title = {Reviews: {P}our-{E}l and {R}ichards '{A} computable differential equation which possesses no computable solution' (1979), and 'The wave equation, with computable initial data such that its unique solution' (1981)},
journal = {The Journal of Symbolic Logic},
volume = {47},
year = {1982},
pages = {900--902},
}
@phdthesis{Kre84,
author = {Kreitz, Christoph},
title = {Theorie der Darstellungen und ihre Anwendungen in der konstruktiven Analysis},
school = {Fachbereich Mathematik und Informatik},
address = {FernUniversit\"{a}t Hagen},
year = {1984},
}
@article{Kre85,
author = {Kreisel, G.},
title = {Mathematical logic: tool and object lesson for science. {T}he present state of the problem of foundations of mathematics, Florence, 1981},
journal = {Synthese Lib.},
volume = {62},
year = {1985},
pages = {139--151},
}
@article{Kri17,
author = {Kristiansen, Lars},
title = {On subrecursive representability of irrational numbers},
journal = {Computability},
volume = {6},
number = {3},
year = {2017},
pages = {249--276},
doi = {10.3233/COM-160063},
}
@inproceedings{Kri21,
author = {Kristiansen, Lars},
title = {On Subrecursive Representation of Irrational Numbers: Contractors and {B}aire Sequences},
editor = {De Mol, Liesbeth and Weiermann, Andreas and Manea, Florin and Fern{\'a}ndez-Duque, David},
booktitle = {Connecting with Computability},
publisher = {Springer},
address = {Cham},
year = {2021},
pages = {308--317},
doi = {10.1007/978-3-030-80049-9_28},
}
@article{Kru02,
author = {Krupski, Vladimir N.},
title = {Effective simultaneous approximability of reals},
journal = {Theoretical Computer Science},
volume = {284},
number = {2},
year = {2002},
pages = {397--417},
}
@inproceedings{Krz01,
author = {Krznari\'{c}, Marko},
title = {Computing a Required Absolute Precision from a Stream of Linear Fractional Transformations},
editor = {Blanck, Jens and Brattka, Vasco and Hertling, Peter},
booktitle = {Computability and Complexity in Analysis},
series = {Lecture Notes in Computer Science},
volume = {2064},
publisher = {Springer},
address = {Berlin},
year = {2001},
pages = {169--186},
note = {4th International Workshop, CCA 2000, Swansea, UK, September 2000},
}
@inproceedings{KS05,
author = {Kunkle, Daren and Schr{\"{o}}der, Matthias},
title = {Some Examples of Non-Metrizable Spaces Allowing a Simple Type-2 Complexity Theory},
editor = {Brattka, Vasco and Staiger, Ludwig and Weihrauch, Klaus},
booktitle = {Proceedings of the 6th Workshop on Computability and Complexity in Analysis},
series = {Electronic Notes in Theoretical Computer Science},
volume = {120},
publisher = {Elsevier},
address = {Amsterdam},
year = {2005},
pages = {111--123},
note = {6th International Workshop, {CCA} 2004, Wittenberg, Germany, August 16--20, 2004},
}
@article{KS14,
author = {Kohlenbach, Ulrich and Safarik, Pavol},
title = {Fluctuations, effective learnability and metastability in analysis},
journal = {Annals of Pure and Applied Logic},
volume = {165},
number = {1},
year = {2014},
pages = {266--304},
doi = {10.1016/j.apal.2013.07.014},
}
@inproceedings{KS16,
author = {Kudinov, Oleg V. and Selivanov, Victor L.},
title = {On the Lattices of Effectively Open Sets},
editor = {Beckmann, Arnold and Bienvenu, Laurent and Jonoska, Nata\v{s}a},
booktitle = {Pursuit of the Universal},
series = {Lecture Notes in Computer Science},
volume = {9709},
publisher = {Springer},
address = {Switzerland},
year = {2016},
pages = {302--311},
note = {12th Conference on Computability in Europe, CiE 2016, Paris, France, June 27 - July 1, 2016},
doi = {10.1007/978-3-319-40189-8_31},
}
@inproceedings{KS17,
author = {Kawamura, Akitoshi and Steinberg, Florian},
title = {Polynomial running times for polynomial-time oracle machines},
booktitle = {2nd {I}nternational {C}onference on {F}ormal {S}tructures for {C}omputation and {D}eduction},
series = {LIPIcs. Leibniz Int. Proc. Inform.},
volume = {84},
publisher = {Schloss Dagstuhl. Leibniz-Zent. Inform.},
address = {Wadern},
year = {2017},
pages = {Art. No. 23, 18},
}
@inproceedings{KS18,
author = {Kapron, Bruce M. and Steinberg, Florian},
title = {Type-two polynomial-time and restricted lookahead},
booktitle = {L{ICS} '18---33rd {A}nnual {ACM}/{IEEE} {S}ymposium on {L}ogic in {C}omputer {S}cience},
publisher = {ACM},
address = {New York},
year = {2018},
pages = {10},
doi = {10.1145/3209108.3209124},
}
@inproceedings{KS19,
author = {Kapron, Bruce M. and Steinberg, Florian},
title = {Type-two iteration with bounded query revision},
booktitle = {Proceedings {T}hird {J}oint {W}orkshop on {D}evelopments in {I}mplicit {C}omputational compl{E}xity and {F}oundational \& {P}ractical {A}spects of {R}esource {A}nalysis},
series = {Electronic Proceedings of Theoretical Computer Science},
volume = {298},
publisher = {EPTCS},
year = {2019},
pages = {61--73},
doi = {10.4204/EPTCS.298.5},
}
@article{KS20,
author = {Kapron, Bruce M. and Steinberg, Florian},
title = {Type-two polynomial-time and restricted lookahead},
journal = {Theoretical Computer Science},
volume = {813},
year = {2020},
pages = {1--19},
doi = {10.1016/j.tcs.2019.07.003},
}
@inproceedings{KS20a,
author = {Kristiansen, Lars and Simonsen, Jakob Grue},
title = {On the Complexity of Conversion Between Classic Real Number Representations},
editor = {Anselmo, Marcella and Della Vedova, Gianluca and Manea, Florin and Pauly, Arno},
booktitle = {Beyond the Horizon of Computability},
publisher = {Springer International Publishing},
address = {Cham},
year = {2020},
pages = {75--86},
doi = {10.1007/978-3-030-51466-2_7},
}
@article{KS22,
author = {Kihara, Takayuki and Selivanov, Victor},
title = {Wadge-like degrees of {B}orel bqo-valued functions},
journal = {Proceedings of the American Mathematical Society},
volume = {150},
number = {9},
year = {2022},
pages = {3989--4003},
doi = {10.1090/proc/15930},
}
@inproceedings{KS95,
author = {Kummer, Martin and Sch\"afer, Marcus},
title = {Computability of convex sets},
editor = {Mayr, Ernst W. and Puech, Claude},
booktitle = {STACS'95},
series = {Lecture Notes in Computer Science},
volume = {900},
publisher = {Springer},
address = {Berlin},
year = {1995},
pages = {550--561},
note = {12th Annual STACS, Munich},
}
@inproceedings{KST18,
author = {Kawamura, Akitoshi and Steinberg, Florian and Thies, Holger},
title = {Parameterized complexity for uniform operators on multidimensional analytic functions and {ODE} solving},
editor = {Moss, L.S. and de Queiroz, R. and Martinez, M.},
booktitle = {Logic, language, information, and computation},
series = {Lecture Notes in Computer Science},
volume = {10944},
publisher = {Springer},
address = {Berlin},
year = {2018},
pages = {223--236},
doi = {10.1007/978-3-662-57669-4_13},
}
@inproceedings{KST19,
author = {Kawamura, Akitoshi and Steinberg, Florian and Thies, Holger},
title = {Second-Order Linear-Time Computability with Applications to Computable Analysis},
editor = {Gopal, T.V. and Watada, Junzo},
booktitle = {Theory and Applications of Models of Computation},
series = {Lecture Notes in Computer Science},
volume = {11436},
publisher = {Springer},
address = {Cham},
year = {2019},
pages = {337--358},
note = {15th Annual Conference, TAMC 2019, Kitakyushu, Japan, April 13--16, 2019},
doi = {10.1007/978-3-030-14812-6_21},
}
@inproceedings{KST20,
author = {Kone{\v{c}}n{\'{y}}, Michal and Steinberg, Florian and Thies, Holger},
title = {Continuous and Monotone Machines},
editor = {Esparza, Javier and Kr{\'a}l', Daniel},
booktitle = {45th International Symposium on Mathematical Foundations of Computer Science ({MFCS} 2020)},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
volume = {170},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
year = {2020},
pages = {56:1--56:16},
doi = {10.4230/LIPIcs.MFCS.2020.56},
}
@incollection{KST20a,
author = {Kone\v{c}n\'{y}, Michal and Steinberg, Florian and Thies, Holger},
title = {Computable analysis for verified exact real computation},
booktitle = {40th {IARCS} {A}nnual {C}onference on {F}oundations of {S}oftware {T}echnology and {T}heoretical {C}omputer {S}cience},
series = {LIPIcs. Leibniz Int. Proc. Inform.},
volume = {182},
publisher = {Schloss Dagstuhl. Leibniz-Zent. Inform., Wadern},
year = {2020},
pages = {Art. No. 50, 18},
}
@inproceedings{KSZ10,
author = {Kudinov, Oleg V. and Selivanov, Victor L. and Zhukov, Anton V.},
title = {Undecidability in {W}eihrauch Degrees},
editor = {Ferreira, Fernando and L{\"o}we, Benedikt and Mayordomo, Elvira and Mendes Gomes, Lu{\'i}s},
booktitle = {Programs, Proofs, Processes},
series = {Lecture Notes in Computer Science},
volume = {6158},
publisher = {Springer},
address = {Berlin},
year = {2010},
pages = {256--265},
note = {6th Conference on Computability in Europe, CiE 2010, Ponta Delgada, Azores, Portugal, June/July 2010},
}
@inproceedings{KSZ16,
author = {Kawamura, Akitoshi and Steinberg, Florian and Ziegler, Martin},
title = {Towards Computational Complexity Theory on Advanced Function Spaces in Analysis},
editor = {Beckmann, Arnold and Bienvenu, Laurent and Jonoska, Nata\v{s}a},
booktitle = {Pursuit of the Universal},
series = {Lecture Notes in Computer Science},
volume = {9709},
publisher = {Springer},
address = {Switzerland},
year = {2016},
pages = {142--152},
note = {12th Conference on Computability in Europe, CiE 2016, Paris, France, June 27 - July 1, 2016},
doi = {10.1007/978-3-319-40189-8_15},
}
@inproceedings{KSZ16a,
author = {Kawamura, Akitoshi and Steinberg, Florian and Ziegler, Martin},
title = {Complexity theory of (functions on) compact metric spaces},
booktitle = {Proceedings of the 31st {A}nnual {ACM}-{IEEE} {S}ymposium on {L}ogic in {C}omputer {S}cience ({LICS} 2016)},
publisher = {ACM},
address = {New York},
year = {2016},
pages = {10},
doi = {10.1145/2933575.2935311},
}
@article{KSZ17,
author = {Kawamura, Akitoshi and Steinberg, Florian and Ziegler, Martin},
title = {On the computational complexity of the {D}irichlet Problem for {P}oisson's Equation},
journal = {Mathematical Structures in Computer Science},
volume = {27},
number = {8},
publisher = {Cambridge University Press},
year = {2017},
pages = {1437--1465},
doi = {10.1017/S096012951600013X},
}
@inproceedings{KSZ19,
author = {Koswara, Ivan and Selivanova, Svetlana and Ziegler, Martin},
title = {Computational complexity of real powering and improved solving linear differential equations},
booktitle = {Computer science---theory and applications},
series = {Lecture Notes in Computer Science},
volume = {11532},
publisher = {Springer, Cham},
year = {2019},
pages = {215--227},
doi = {10.1007/978-3-030-19955-5_19},
}
@article{KT14,
author = {Kuyper, Rutger and Terwijn, Sebastiaan A.},
title = {Effective genericity and differentiability},
journal = {Journal of Logic and Analysis},
volume = {6},
year = {2014},
pages = {Paper 4, 14},
}
@article{KT55,
author = {Kuzn{\'e}cov, A.V. and Traht{\'e}nbrot, B.A.},
title = {Investigation of partially recursive operators by means of the theory of {B}aire space ({R}ussian)},
journal = {Dokl. Akad. Nauk SSSR},
volume = {105},
year = {1955},
pages = {897--900},
}
@article{KT70,
author = {Kreisel, G. and Troelstra, A.S.},
title = {Formal systems for some branches of intuitionistic analysis},
journal = {Ann. Math. Logic},
volume = {1},
year = {1970},
pages = {229--387},
}
@inproceedings{KTZ18,
author = {Kawamura, Akitoshi and Thies, Holger and Ziegler, Martin},
title = {Average-case polynomial-time computability of {H}amiltonian dynamics},
booktitle = {43rd {I}nternational {S}ymposium on {M}athematical {F}oundations of {C}omputer {S}cience},
series = {LIPIcs. Leibniz Int. Proc. Inform.},
volume = {117},
publisher = {Schloss Dagstuhl. Leibniz-Zent. Inform.},
address = {Wadern},
year = {2018},
pages = {Art. No. 30, 17},
}
@inproceedings{Kun03,
author = {Kunkle, Daren},
title = {Computability on spaces of integrable functions},
editor = {Brattka, Vasco and Schr{\"{o}}der, Matthias and Weihrauch, Klaus and Zhong, Ning},
booktitle = {Computability and Complexity in Analysis},
series = {Informatik Berichte},
volume = {302},
publisher = {FernUniversit\"at in Hagen},
year = {2003},
month = aug,
pages = {279--301},
note = {International Conference, CCA 2003, Cincinnati, USA, August 28--30, 2003},
}
@article{Kun04a,
author = {Kunkle, Daren},
title = {Type-2 computability on spaces of integrable functions},
journal = {Mathematical Logic Quarterly},
volume = {50},
number = {4,5},
year = {2004},
pages = {417--430},
}
@inproceedings{Kus03,
author = {Kushner, Boris Abramovich},
title = {The centenary of {A}.{A}. {M}arkov, Jr.; {H}is personality, his constructive mathematics},
editor = {Brattka, Vasco and Schr{\"{o}}der, Matthias and Weihrauch, Klaus and Zhong, Ning},
booktitle = {Computability and Complexity in Analysis},
series = {Informatik Berichte},
volume = {302},
publisher = {FernUniversit\"at in Hagen},
year = {2003},
month = aug,
pages = {55--79},
note = {International Conference, CCA 2003, Cincinnati, USA, August 28--30, 2003},
}
@article{Kus64,
author = {Kushner, Boris Abramovich},
title = {Riemann integration in constructive analysis ({R}ussian)},
journal = {Dokl. Akad. Nauk SSSR},
volume = {156},
year = {1964},
pages = {255--257},
note = {[translated in: Soviet Math.-Dokl., 5 (1964) 628--630]},
}
@article{Kus65,
author = {Kushner, Boris Abramovich},
title = {Constructive theory of the {R}iemann integral ({R}ussian)},
journal = {Dokl. Akad. Nauk SSSR},
volume = {165},
year = {1965},
pages = {1238--1240},
note = {[translated in: Soviet Math.-Dokl. 6 (1965) 1584--1587]},
}
@article{Kus65a,
author = {Kushner, Boris Abramovich},
title = {The existence of unbounded constructive analytic functions ({R}ussian)},
journal = {Dokl. Akad. Nauk SSSR},
volume = {160},
year = {1965},
pages = {29--31},
note = {[translated in: Soviet Math.-Dokl., 6 (1965) 26--28]},
}
@article{Kus67,
author = {Kushner, Boris Abramovich},
title = {On constructive antiderivatives ({R}ussian)},
journal = {Mat. Zametki},
volume = {2},
year = {1967},
pages = {157--166},
note = {[translated as: Primitive constructive functions, Math. Notes, 2 (1967) 577--582]},
}
@article{Kus68,
author = {Kushner, Boris Abramovich},
title = {A remark on the domains of definition of constructive analytic functions ({R}ussian)},
journal = {Zap. Nau\v{c}n. Sem. Leningrad. Otdel. Inst. Steklov.},
volume = {8},
year = {1968},
pages = {103--106},
}
@article{Kus70,
author = {Kushner, Boris Abramovich},
title = {Some mass problems connected with the integration of constructive functions ({R}ussian)},
journal = {Trudy Mat. Inst. Steklov.},
volume = {113},
year = {1970},
pages = {39--72},
note = {[translated in: Proc. Stehlov Inst. Math., 113 (1970) 42--83]},
}
@article{Kus73,
author = {Kushner, Boris Abramovich},
title = {Computationally complex real numbers ({R}ussian)},
journal = {Zeitschrift f\"ur Mathematische Logik und Grundlagen der Mathematik},
volume = {19},
year = {1973},
pages = {447--452},
}
@article{Kus73a,
author = {Kushner, Boris Abramovich},
title = {Continuity theorems for some types of computable operators ({R}ussian)},
journal = {Dokl. Akad. Nauk SSSR},
volume = {208},
year = {1973},
pages = {1031--1034},
note = {[translated in: Soviet Math. - Dokl., 14 (1973) 221--225]},
}
@book{Kus73b,
author = {Kushner, Boris Abramovich},
title = {Lectures on Constructive Mathematical Analysis ({R}ussian)},
publisher = {Izdat. Nauka},
year = {1973},
note = {translated: by Mendelson, E., and edited by Leifman, L.J., Transl. Math. Monographs, 60 (1984)},
}
@article{Kus74,
author = {Kushner, Boris Abramovich},
title = {On a type of computable real function ({R}ussian)},
journal = {Dokl. Akad. Nauk SSSR},
volume = {215},
year = {1974},
pages = {259--262},
note = {[translated in: Soviet Math. - Dokl., 15 (1974) 466--470]},
}
@inproceedings{Kus74a,
author = {Kushner, Boris Abramovich},
title = {A constructive version of {K}\"onig's theorem; functions that are computable in the sense of {M}arkov, {G}rzegorczyk and {L}acombe ({R}ussian)},
booktitle = {Theory of algorithms and mathematical logic (dedicated to A.A. Markov on the occasion of his seventieth birthday)},
year = {1974},
pages = {87--111, 215},
note = {(Vy\v{c}isl. Centr Akad. Nauk SSSR)},
}
@article{Kus76,
author = {Kushner, Boris Abramovich},
title = {The computation of isolated roots of constructive functions ({R}ussian)},
journal = {Zeitschrift f\"ur Mathematische Logik und Grundlagen der Mathematik},
volume = {22},
year = {1976},
pages = {311--332},
}
@inproceedings{Kus76a,
author = {Kushner, Boris Abramovich},
title = {On {G}rzegorczyk's theorem on the computability of an isolated extremum ({R}ussian)},
editor = {Markov, A.A. and Ku\v{s}ner, B.A.},
booktitle = {Studies in the Theory of Algorithms and Mathematical Logic},
volume = {2},
year = {1976},
pages = {112--121, 158},
note = {(Vy\v{c}isl. Centr Akad. Nauk SSSR)},
}
@inproceedings{Kus79,
author = {Kushner, Boris Abramovich},
title = {Segmental coverings and uniform continuity of constructive functions ({R}ussian)},
editor = {Markov, A.A. and Homi\v{c}, V.I.},
booktitle = {Studies in the Theory of Algorithms and Mathematical Logic},
publisher = {Nauka},
year = {1979},
pages = {62--69, 133},
}
@inproceedings{Kus81,
author = {Kushner, Boris Abramovich},
title = {Behavior of the general term of a {S}pecker series ({R}ussian)},
editor = {Gladki\u{i}, M.},
booktitle = {Mathematical Logic and Mathematical Linguistics},
publisher = {Kalinin. Gos. Univ.},
year = {1981},
pages = {112--116},
}
@article{Kus81a,
author = {Kushner, Boris Abramovich},
title = {On some topological properties of constructive plane curves ({R}ussian)},
journal = {Dokl. Akad. Nauk SSSR},
volume = {260},
year = {1981},
pages = {281--283},
note = {[translated in: Soviet Math. - Dokl., 24 (1981) 258--261]},
}
@inproceedings{Kus82,
author = {Kushner, Boris Abramovich},
title = {Some extensions of {M}arkov's constructive continuum and their applications to the theory of constructive functions},
editor = {Troelstra, A.S. and van Dalen, D.},
booktitle = {The L.E.J. Brouwer Centenary Symposium (Noordwijkerhout, June 8-13,1981)},
series = {Studies in Logic and the Foundations of Mathematics},
volume = {110},
publisher = {North-Holland},
address = {Amsterdam},
year = {1982},
pages = {261--273},
}
@inproceedings{Kus83,
author = {Kushner, Boris Abramovich},
title = {A class of {S}pecker sequences ({R}ussian)},
editor = {Gladli\u{i}, M.},
booktitle = {Mathematical Logic, Mathematical Linguistics and Theory of Algorithms},
publisher = {Kalinin. Gos. Univ.},
year = {1983},
pages = {62--65},
}
@book{Kus84,
author = {Kushner, Boris Abramovich},
title = {Lectures on Constructive Mathematical Analysis},
series = {Translations of Mathematical Monographs},
volume = {60},
publisher = {American Mathematical Society},
address = {Providence},
year = {1984},
}
@article{Kus85,
author = {Kushner, Boris Abramovich},
title = {Differentiability and uniform continuity of constructive functions ({R}ussian)},
journal = {Doklady Akademii Nauk},
volume = {281},
year = {1985},
pages = {1314--1316},
note = {[translated in: Soviet Math. - Dokl., 31 (1985) 433--435]},
}
@inproceedings{Kus87,
author = {Kushner, Boris Abramovich},
title = {The principle of bar-induction in {B}rouwer's theory of the continuum ({R}ussian)},
editor = {Panov, M.I.},
booktitle = {Patterns in the Development of Modern Mathematics, Methodological Aspects},
publisher = {Nauka},
year = {1987},
pages = {230--250},
}
@inproceedings{Kus88,
author = {Kushner, Boris Abramovich},
title = {Effective meaning of a theorem on uniform limit transition ({R}ussian)},
editor = {Nagorny\u{i}, N.M.},
booktitle = {Problems in Mathematical Logic and in the Theory of Algorithms},
publisher = {Akad. Nauk SSSR, Vy\v{c}isl. Centr.},
year = {1988},
pages = {3--10},
}
@inproceedings{Kus90,
author = {Kushner, Boris Abramovich},
title = {Markov's constructive mathematical analysis: the expectations and the results},
editor = {Petkov, P.P.},
booktitle = {Mathematical Logic},
publisher = {Plenum},
year = {1990},
pages = {53--58},
note = {(Proc. Heyting '88 Summer School, Chaika, Sept. 13--23, 1988)},
}
@article{Kus93,
author = {Kushner, Boris Abramovich},
title = {The constructive mathematics of {A}.{A}. {M}arkov: some reflections ({R}ussian)},
journal = {Modern Logic},
volume = {3},
year = {1993},
pages = {119--144},
}
@inproceedings{Kus93a,
author = {Kushner, Boris Abramovich},
title = {Markov and {B}ishop: an essay in memory of {A}.{A}. {M}arkov (1903--1979) and {E}. {B}ishop (1928--1983)},
editor = {Zdrovkovska, S. and Duren, P.L.},
booktitle = {Golden Years of Moscow Mathematics},
series = {Hist. Math.},
volume = {6},
year = {1993},
pages = {179--197},
}
@inproceedings{Kus96,
author = {Kushner, Boris Abramovich},
title = {Kurt {G}\"odel and the constructive mathematics of {A}.{A}. {M}arkov},
editor = {H\'ajek, P.},
booktitle = {G\"odel '96},
series = {Lecture Notes in Logic},
volume = {6},
year = {1996},
pages = {50--63},
note = {Proc. Conf, Brno, August 1996},
}
@article{Kus99,
author = {Kushner, Boris Abramovich},
title = {Markov's constructive analysis; a participant's view},
journal = {Theoretical Computer Science},
volume = {219},
year = {1999},
pages = {267--285},
}
@article{Kuy17,
author = {Kuyper, Rutger},
title = {On {W}eihrauch reducibility and intuitionistic reverse mathematics},
journal = {Journal of Symbolic Logic},
volume = {82},
number = {4},
year = {2017},
pages = {1438--1458},
doi = {10.1017/jsl.2016.61},
}
@article{Kuy19,
author = {Kuyper, Rutger},
title = {Levels of uniformity},
journal = {Notre Dame Journal of Formal Logic},
volume = {60},
number = {1},
year = {2019},
pages = {119--138},
doi = {10.1215/00294527-2018-0024},
}
@book{KV65,
author = {Kleene, Stephen C. and Vesli, R.},
title = {The foundations of intuitionistic mathematics. Especially in relation to recursive functions.},
series = {Studies in Logic and the Foundations of Mathematics},
publisher = {North-Holland},
address = {Amsterdam},
year = {1965},
}
@inproceedings{KW02a,
author = {Kalantari, Iraj and Welch, Lawrence},
title = {Recursive Quantum Functions, Avoidable Points, \& Shadow Points in Recursive Analysis},
editor = {Brattka, Vasco and Schr{\"{o}}der, Matthias and Weihrauch, Klaus},
booktitle = {{CCA} 2002 Computability and Complexity in Analysis},
series = {Electronic Notes in Theoretical Computer Science},
volume = {66},
publisher = {Elsevier},
address = {Amsterdam},
year = {2002},
note = {5th International Workshop, {CCA} 2002, M{\'{a}}laga, Spain, July 12--13, 2002},
}
@article{KW03,
author = {Kalantari, Iraj and Welch, Larry},
title = {A blend of methods of recursion theory and topology},
journal = {Annals of Pure and Applied Logic},
volume = {124},
number = {1--3},
year = {2003},
pages = {141--178},
}
@article{KW04,
author = {Kalantari, Iraj and Welch, Larry},
title = {Density and {B}aire category in recursive topology},
journal = {Mathematical Logic Quarterly},
volume = {50},
number = {4,5},
year = {2004},
pages = {381--391},
}
@article{KW08,
author = {Kalantari, Iraj and Welch, Larry},
title = {On degree-preserving homeomorphisms between trees in computable topology},
journal = {Archive for Mathematical Logic},
volume = {46},
number = {7--8},
year = {2008},
pages = {679--693},
}
@article{KW08a,
author = {Kalantari, Iraj and Welch, Larry},
title = {On {T}uring degrees of points in computable topology},
journal = {Mathematical Logic Quarterly},
volume = {54},
number = {5},
year = {2008},
pages = {470--482},
}
@article{KW13,
author = {Kalantari, Iraj and Welch, Larry},
title = {When series of computable functions with varying domains are computable},
journal = {MLQ Math. Log. Q.},
volume = {59},
number = {6},
year = {2013},
pages = {471--493},
doi = {10.1002/malq.201200053},
}
@inproceedings{KW21,
author = {Kjos-Hanssen, Bj{\o}rn and Webb, David J.},
title = {{KL}-Randomness and Effective Dimension Under Strong Reducibility},
editor = {De Mol, Liesbeth and Weiermann, Andreas and Manea, Florin and Fern{\'a}ndez-Duque, David},
booktitle = {Connecting with Computability},
publisher = {Springer},
address = {Cham},
year = {2021},
pages = {457--468},
doi = {10.1007/978-3-030-80049-9_45},
}
@inproceedings{KW83a,
author = {Kreitz, Christoph and Weihrauch, Klaus},
title = {Complexity theory on real numbers and functions},
editor = {Cremers, A.B. and Kriegel, H.P.},
booktitle = {Theoretical Computer Science},
series = {Lecture Notes in Computer Science},
volume = {145},
publisher = {Springer},
year = {1983},
note = {6th GI-Conference, Dortmund, January 5--7, 1983},
}
@inproceedings{KW84,
author = {Kreitz, Christoph and Weihrauch, Klaus},
title = {A unified approach to constructive and recursive analysis},
editor = {Richter, M.M. and B\"orger, E. and Oberschelp, W. and Schinzel, B. and Thomas, W.},
booktitle = {Computation and Proof Theory},
series = {Lecture Notes in Mathematics},
volume = {1104},
publisher = {Springer},
address = {Berlin},
year = {1984},
pages = {259--278},
note = {Proceedings of the Logic Colloquium, Aachen, July 18--23, 1983, Part II},
}
@inproceedings{KW84a,
author = {Kreitz, Christoph and Weihrauch, Klaus},
title = {Towards a theory of representations},
editor = {Wechsung, G.},
booktitle = {Frege Conference 1984},
publisher = {Akademie-Verlag},
address = {Berlin},
year = {1984},
pages = {73--79},
note = {Proceedings of the International Conference held at Schwerin, September 10--14, 1984},
}
@article{KW85,
author = {Kreitz, Christoph and Weihrauch, Klaus},
title = {Theory of representations},
journal = {Theoretical Computer Science},
volume = {38},
year = {1985},
pages = {35--53},
}
@article{KW85a,
author = {Kalantari, I. and Weitkamp, G.},
title = {Effective topological spaces, {I}. {A} definability theory},
journal = {Annals of Pure and Applied Logic},
volume = {29},
year = {1985},
pages = {1--27},
}
@article{KW85b,
author = {Kalantari, I. and Weitkamp, G.},
title = {Effective topological spaces, {I}{I}. {A} hierarchy},
journal = {Annals of Pure and Applied Logic},
volume = {29},
year = {1985},
pages = {207--224},
}
@article{KW85c,
author = {Kalantari, I. and Weitkamp, G.},
title = {Effective topological spaces, {I}{I}{I}. Forcing and definability},
journal = {Annals of Pure and Applied Logic},
volume = {36},
year = {1985},
pages = {17--27},
}
@article{KW87,
author = {Kreitz, Christoph and Weihrauch, Klaus},
title = {Compactness in constructive analysis revisited},
journal = {Annals of Pure and Applied Logic},
volume = {36},
year = {1987},
pages = {29--38},
}
@inproceedings{KW96,
author = {Ko, Ker-I and Weihrauch, Klaus},
title = {On the measure of two-dimensional regions with polynomial-time computable boundaries},
editor = {Homer, Steve and Cai, Jin-Yi},
booktitle = {Eleventh Annual IEEE Conference on Computational Complexity},
publisher = {IEEE Computer Society Press},
address = {Los Alamitos},
year = {1996},
pages = {150--159},
}
@article{KW98,
author = {Kalantari, Iraj and Welch, Lawrence},
title = {Point-free topological spaces, functions and recursive points; filter foundation for recursive analysis. {I}},
journal = {Annals of Pure and Applied Logic},
volume = {93},
number = {1--3},
year = {1998},
pages = {125--151},
}
@article{KW99,
author = {Kalantari, Iraj and Welch, Lawrence},
title = {Recursive and nonextendible functions over the reals; filter foundation for recursive analysis, {I}{I}},
journal = {Annals of Pure and Applied Logic},
volume = {98},
number = {1--3},
year = {1999},
pages = {87--110},
}
@inproceedings{KY07,
author = {Ko, Ker-I and Yu, Fuxiang},
title = {{J}ordan Curves with Polynomial Inverse Moduli of Continuity},
editor = {Cenzer, Douglas and Dillhage, Ruth and Grubba, Tanja and Weihrauch, Klaus},
booktitle = {Proceedings of the Third International Conference on Computability and Complexity in Analysis},
series = {Electronic Notes in Theoretical Computer Science},
volume = {167},
publisher = {Elsevier},
address = {Amsterdam},
year = {2007},
pages = {425--447},
note = {{CCA} 2006, Gainesville, Florida, USA, November 1--5, 2006},
}
@article{KY07a,
author = {Ko, Ker-I and Yu, Fuxiang},
title = {On the complexity of computing the logarithm and square root functions on a complex domain},
journal = {Journal of Complexity},
volume = {23},
number = {1},
year = {2007},
pages = {2--24},
}
@article{KY07d,
author = {Ko, Ker-I and Yu, Fuxiang},
title = {Jordan curves with polynomial inverse moduli of continuity},
journal = {Theoretical Computer Science},
volume = {381},
number = {1--3},
year = {2007},
pages = {148--161},
}
@inproceedings{KY08,
author = {Ko, Ker-I and Yu, Fuxiang},
title = {On the Complexity of Convex Hulls of Subsets of the Two-Dimensional Plane},
editor = {Dillhage, Ruth and Grubba, Tanja and Sorbi, Andrea and Weihrauch, Klaus and Zhong, Ning},
booktitle = {Proceedings of the Fourth International Conference on Computability and Complexity in Analysis ({CCA} 2007)},
series = {Electronic Notes in Theoretical Computer Science},
volume = {202},
publisher = {Elsevier},
year = {2008},
pages = {121--135},
note = {{CCA} 2007, Siena, Italy, June 16--18, 2007},
}
@phdthesis{Lab86,
author = {Labhalla, Salah-Eddine},
title = {Complexit{\'e} du Calcul du D{\'e}veloppement d'un Nombre R{\'e}el en Fractions Continu{\'e}s},
school = {Universit{\'e} de Caen Normandie},
year = {1986},
}
@article{Lab91,
author = {Labhalla, Salah},
title = {Complexit\'e du calcul du d\'eveloppement d'un nombre r\'eel en fractions continues},
journal = {Theoretical Computer Science},
volume = {83},
year = {1991},
pages = {219--235},
}
@article{Lac03,
author = {Laczkovich, M.},
title = {The removal of {$\pi$} from some undecidable problems involving elementary functions},
journal = {Proceedings of the American Mathematical Society},
volume = {131},
number = {7},
year = {2003},
pages = {2235--2240},
doi = {10.1090/S0002-9939-02-06753-9},
}
@article{Lac55,
author = {Lacombe, Daniel},
title = {Classes r\'{e}cursivement ferm\'{e}s et fonctions majorantes},
journal = {Comptes Rendus Acad\'emie des Sciences Paris},
volume = {240},
year = {1955},
month = jun,
pages = {716--718},
}
@article{Lac55a,
author = {Lacombe, Daniel},
title = {Extension de la notion de fonction r\'{e}cursive aux fonctions d'une ou plusieurs variables r\'{e}elles {I}},
journal = {Comptes Rendus Acad\'emie des Sciences Paris},
volume = {240},
year = {1955},
month = jun,
pages = {2478--2480},
}
@article{Lac55b,
author = {Lacombe, Daniel},
title = {Extension de la notion de fonction r\'{e}cursive aux fonctions d'une ou plusieurs variables r\'{e}elles {II}},
journal = {Comptes Rendus Acad\'emie des Sciences Paris},
volume = {241},
year = {1955},
month = jul,
pages = {13--14},
}
@article{Lac55c,
author = {Lacombe, Daniel},
title = {Extension de la notion de fonction r\'{e}cursive aux fonctions d'une ou plusieurs variables r\'{e}elles {III}},
journal = {Comptes Rendus Acad\'emie des Sciences Paris},
volume = {241},
year = {1955},
month = jul,
pages = {151--153},
}
@article{Lac55d,
author = {Lacombe, Daniel},
title = {Remarques sur les op\'{e}rateurs r\'{e}cursifs et sur les fonctions r\'{e}cursives d'une variable r\'{e}elle},
journal = {Comptes Rendus Acad\'emie des Sciences Paris},
volume = {241},
year = {1955},
month = nov,
pages = {1250--1252},
}
@article{Lac57,
author = {Lacombe, Daniel},
title = {Les ensembles r\'{e}cursivement ouverts ou ferm\'{e}s, et leurs applications \`{a} l'{A}nalyse r\'{e}cursive},
journal = {Comptes Rendus Acad\'emie des Sciences Paris},
volume = {245},
year = {1957},
pages = {1040--1043},
}
@article{Lac57a,
author = {Lacombe, Daniel},
title = {Quelques propri\'et\'es d'analyse r\'ecursive},
journal = {Comptes Rendus Acad\'emie des Sciences Paris},
volume = {244},
year = {1957},
pages = {838--840,996--997},
}
@article{Lac58,
author = {Lacombe, Daniel},
title = {Les ensembles r\'{e}cursivement ouverts ou ferm\'{e}s, et leurs applications \`{a} l'{A}nalyse r\'{e}cursive},
journal = {Comptes Rendus Acad\'emie des Sciences Paris},
volume = {246},
year = {1958},
pages = {28--31},
}
@inproceedings{Lac58a,
author = {Lacombe, Daniel},
title = {Sur les possibilites d'extension de la notion de fonction r\'{e}cursive aux fonctions d'une ou plusieurs variables r\'{e}elles},
booktitle = {Le raisonnement en mathematiques et en sciences},
publisher = {Editions du Centre National de la Recherche Scientifique},
address = {Paris},
year = {1958},
pages = {67--75},
note = {Colloques Internationaux du Centre National de la Recherche Scientifique, LXX},
}
@inproceedings{Lac59,
author = {Lacombe, Daniel},
title = {Quelques proc\'{e}d\'{e}s de d\'{e}finition en topologie r\'{e}cursive},
editor = {Heyting, A.},
booktitle = {Constructivity in Mathematics},
publisher = {North-Holland},
address = {Amsterdam},
year = {1959},
pages = {129--158},
note = {Colloquium at Amsterdam, 1957},
}
@article{Lac63,
author = {Lachlan, A.H.},
title = {Recursive real numbers},
journal = {The Journal of Symbolic Logic},
volume = {28},
year = {1963},
pages = {1--16},
}
@inproceedings{Lam03,
author = {Lambov, Branimir},
title = {A two-layer approach to the computability and complexity of real functions},
editor = {Brattka, Vasco and Schr{\"{o}}der, Matthias and Weihrauch, Klaus and Zhong, Ning},
booktitle = {Computability and Complexity in Analysis},
series = {Informatik Berichte},
volume = {302},
publisher = {FernUniversit\"at in Hagen},
year = {2003},
month = aug,
pages = {303--324},
note = {International Conference, CCA 2003, Cincinnati, USA, August 28--30, 2003},
}
@inproceedings{Lam05,
author = {Lambov, Branimir},
title = {Rates of Convergence of Recursively Defined Sequences},
editor = {Brattka, Vasco and Staiger, Ludwig and Weihrauch, Klaus},
booktitle = {Proceedings of the 6th Workshop on Computability and Complexity in Analysis},
series = {Electronic Notes in Theoretical Computer Science},
volume = {120},
publisher = {Elsevier},
address = {Amsterdam},
year = {2005},
pages = {125--133},
note = {6th International Workshop, {CCA} 2004, Wittenberg, Germany, August 16--20, 2004},
}
@inproceedings{Lam05a,
author = {Lambov, Branimir},
title = {{RealLib}: an efficient implementation of Exact Real Arithmetic},
editor = {Grubba, Tanja and Hertling, Peter and Tsuiki, Hideki and Weihrauch, Klaus},
booktitle = {Computability and Complexity in Analysis},
series = {Informatik Berichte},
volume = {326},
publisher = {FernUniversit\"at in Hagen},
year = {2005},
month = jul,
pages = {169--175},
note = {Proccedings, Second International Conference, CCA 2005, Kyoto, Japan, August 25--29, 2005},
}
@phdthesis{Lam05b,
author = {Lambov, Branimir},
title = {Topics in the Theory and Practice of Computable Analysis},
school = {Department of Computer Science, University of Aarhus, Denmark},
address = {Aarhus},
year = {2005},
}
@article{Lam06,
author = {Lambov, Branimir},
title = {The basic feasible functionals in computable analysis},
journal = {Journal of Complexity},
volume = {22},
number = {6},
year = {2006},
pages = {909--917},
}
@article{Lam07,
author = {Lambov, Branimir},
title = {{RealLib}: {A}n efficient implementation of exact real arithmetic},
journal = {Mathematical Structures in Computer Science},
volume = {17},
year = {2007},
pages = {81--98},
}
@article{LB06,
author = {Lewis, Andrew E.M. and Barmpalias, George},
title = {Random reals and {L}ipschitz continuity},
journal = {Mathematical Structures in Computer Science},
volume = {16},
number = {5},
year = {2006},
pages = {737--749},
}
@article{LCL02,
author = {Lester, David and Chambers, Scott and Lu, Heoi Lee},
title = {A constructive algorithm for finding the exact roots of polynomials with computable real coefficients},
journal = {Theoretical Computer Science},
volume = {279},
year = {2002},
pages = {51--64},
}
@article{LCM07,
author = {Loff, Bruno and Costa, Jos{\'e} F{\'e}lix and Mycka, Jerzy},
title = {Computability on reals, infinite limits and differential equations},
journal = {Applied Mathematics and Computation},
volume = {191},
number = {2},
year = {2007},
pages = {353--391},
}
@incollection{LD13,
author = {Lubarsky, Robert S. and Diener, Hannes},
title = {Separating the {F}an {T}heorem and its weakenings},
booktitle = {Logical foundations of computer science},
series = {Lecture Notes in Comput. Sci.},
volume = {7734},
publisher = {Springer},
address = {Heidelberg},
year = {2013},
pages = {280--295},
doi = {10.1007/978-3-642-35722-0_20},
}
@article{LD13a,
author = {Lubarsky, Robert S. and Diener, Hannes},
title = {Principles weaker than {BD}-{N}},
journal = {The Journal of Symbolic Logic},
volume = {78},
number = {3},
year = {2013},
pages = {873--885},
}
@article{LD14,
author = {Lubarsky, Robert S. and Diener, Hannes},
title = {Separating the {F}an theorem and its weakenings},
journal = {The Journal of Symbolic Logic},
volume = {79},
number = {3},
year = {2014},
pages = {792--813},
doi = {10.1017/jsl.2014.9},
}
@article{Le09,
author = {Le{\v{s}}nik, Davorin},
title = {Constructive {U}rysohn universal metric space},
journal = {Journal of Universal Computer Science},
volume = {15},
number = {6},
year = {2009},
pages = {1236--1263},
doi = {10.3217/jucs-015-06-1236},
}
@phdthesis{Le10,
author = {Le{\v{s}}nik, Davorin},
title = {Synthetic Topology and Constructive Metric Spaces},
school = {University of Ljubljana, Faculty of Mathematics and Physics, Department of Mathematics},
address = {Ljubljana},
year = {2010},
}
@article{Leh61,
author = {Lehman, R.S.},
title = {On primitive recursive real numbers},
journal = {Fundamenta Mathematicae},
volume = {49},
year = {1961},
pages = {105--118},
}
@inproceedings{Les08,
author = {Le{\v{s}}nik, Davorin},
title = {Constructive {U}rysohn's Universal Metric Space},
editor = {Brattka, Vasco and Dillhage, Ruth and Grubba, Tanja and Klutsch, Angela},
booktitle = {{CCA} 2008, Fifth International Conference on Computability and Complexity in Analysis},
series = {Electronic Notes in Theoretical Computer Science},
volume = {221},
publisher = {Elsevier},
year = {2008},
pages = {171--179},
note = {{CCA} 2008, Fifth International Conference, Hagen, Germany, August 21--24, 2008},
}
@inproceedings{Leu06,
author = {Leu{\c{s}}tean, Lauren{\c{t}}iu},
title = {Proof Mining in {$R$}-trees and Hyperbolic Spaces},
editor = {Mints, Grigori and de Queiroz, Ruy},
booktitle = {Logic, Language, Information and Computation},
series = {Electronic Notes in Theoretical Computer Science},
volume = {165},
publisher = {Elsevier},
address = {Amsterdam},
year = {2006},
pages = {95--106},
note = {{WoLLIC} 2006, 13th Workshop on Logic, Language, Information and Computation, Stanford University, CA, USA, 18-21 July 2006},
}
@article{Leu07,
author = {Leu{\c{s}}tean, Lauren{\c{t}}iu},
title = {A quadratic rate of asymptotic regularity for {CAT(0)}-spaces},
journal = {J. Math. Anal. Appl.},
volume = {325},
year = {2007},
pages = {386--399},
}
@article{Lew92,
author = {Lewis, A.A.},
title = {Some aspects of effectively constructive mathematics that are relevant to the foundations of neoclassical mathematical economics and the theory of games},
journal = {Math. Social Sciences},
volume = {24},
year = {1992},
pages = {209--235},
}
@phdthesis{Lie04,
author = {Lietz, Peter},
title = {From Constructive Mathematics to Computable Analysis via the Realizability Interpretation},
school = {Fachbereich Mathematik, TU Darmstadt},
address = {Darmstadt},
year = {2004},
}
@inproceedings{Lie98,
author = {Lieutier, Andr{\`{e}}},
title = {Toward a data type for Solid Modeling based on Domain Theory},
editor = {Ko, Ker-I and Nerode, Anil and Pour-El, Marian B. and Weihrauch, Klaus and Wiedermann, Ji{\v{r}}{\'{\i}}},
booktitle = {Computability and Complexity in Analysis},
series = {Informatik Berichte},
volume = {235},
publisher = {FernUniversit\"at Hagen},
year = {1998},
month = aug,
pages = {51--60},
note = {CCA Workshop, Brno, Czech Republic, August, 1998},
}
@article{Lif82,
author = {Lifschitz, Vladimir},
title = {Constructive assertions in an extension of classical mathematics},
journal = {The Journal of Symbolic Logic},
volume = {47},
number = {2},
year = {1982},
pages = {359--387},
}
@article{LL03,
author = {Lawson, Jimmie D. and Lu, Bin},
title = {Riemann and {E}dalat integration on domains},
journal = {Theoretical Computer Science},
volume = {305},
year = {2003},
pages = {259--275},
}
@article{LL15,
author = {Lutz, Jack H. and Lutz, Neil},
title = {Lines missing every random point},
journal = {Computability},
volume = {4},
number = {2},
year = {2015},
pages = {85--102},
doi = {10.3233/COM-150038},
}
@inproceedings{LL17,
author = {Lutz, Jack H. and Lutz, Neil},
title = {Algorithmic Information, Plane {K}akeya Sets, and Conditional Dimension},
editor = {Vollmer, Heribert and Vall{\'e}e, Brigitte},
booktitle = {34th Symposium on Theoretical Aspects of Computer Science (STACS 2017)},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
volume = {66},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
year = {2017},
pages = {53:1--53:13},
doi = {10.4230/LIPIcs.STACS.2017.53},
}
@article{LL18,
author = {Lutz, Jack H. and Lutz, Neil},
title = {Algorithmic information, plane {K}akeya sets, and conditional dimension},
journal = {ACM Transactions on Computation Theory},
volume = {10},
number = {2},
year = {2018},
pages = {Art. 7, 22},
doi = {10.1145/3201783},
}
@incollection{LL20,
author = {Lutz, Jack H. and Lutz, Neil},
title = {Who Asked Us? {H}ow the Theory of Computing Answers Questions about Analysis},
editor = {Du, Ding-Zhu and Wang, Jie},
booktitle = {Complexity and Approximation: In Memory of {Ker-I Ko}},
publisher = {Springer},
address = {Cham},
year = {2020},
pages = {48--56},
doi = {10.1007/978-3-030-41672-0_4},
}
@article{LL90,
author = {Labhalla, Salah and Lombardi, Henri},
title = {Real numbers, continued fractions, and complexity classes},
journal = {Annals of Pure and Applied Logic},
volume = {50},
year = {1990},
pages = {1--28},
}
@article{LL90a,
author = {Labhalla, Salah and Lombardi, Henri},
title = {Comparaison des complexit\'es des nombres r\'eels dans diff\'erentes repr\'esentations (\`a la {C}auchy, \`a la {D}edekind, par fractions continues)},
journal = {Comptes Rendus Acad\'emie des Sciences Paris},
volume = {310},
year = {1990},
pages = {483--488},
}
@article{LL90b,
author = {Labhalla, Salah and Lombardi, Henri},
title = {Comparaison des diff\'erentes repr\'esentations des nombres r\'eels du point de vue des fonctionnelles r\'ecursives},
journal = {Comptes Rendus Acad\'emie des Sciences Paris},
volume = {311},
year = {1990},
pages = {229--234},
}
@article{LL91a,
author = {Labhalla, Salah and Lombardi, Henri},
title = {Repr\'esentations des nombres r\'eels par d\'eveloppements en base enti\`ere et complexit\'e},
journal = {Theoretical Computer Science},
volume = {88},
number = {1},
year = {1991},
pages = {171--182},
doi = {10.1016/0304-3975(91)90080-L},
}
@article{LL96,
author = {Labhalla, Salah and Lombardi, Henri},
title = {Analyse de complexit\'e pour un th\'eor\`eme de {H}all sur les fractions continues},
journal = {Mathematical Logic Quarterly},
volume = {42},
year = {1996},
pages = {134--144},
}
@article{LLM01,
author = {Labhalla, S. and Lombardi, H. and Moutai, E.},
title = {Espaces m\'etriques rationnellement pr\'esent\'es et complexit\'e, le cas de l'espace des fonctions r\'eelles uniform\'ement continues sur un intervalle compact},
journal = {Theoretical Computer Science},
volume = {250},
year = {2001},
pages = {265--332},
}
@inproceedings{LLP11,
author = {Lathrop, James I. and Lutz, Jack H. and Patterson, Brian},
title = {Multi-resolution cellular automata for real computation},
booktitle = {Models of computation in context},
series = {Lecture Notes in Comput. Sci.},
volume = {6735},
publisher = {Springer},
address = {Heidelberg},
year = {2011},
pages = {181--190},
doi = {10.1007/978-3-642-21875-0_19},
}
@article{LM08,
author = {Lutz, Jack H. and Mayordomo, Elvira},
title = {Dimensions of points in self-similar fractals},
journal = {SIAM Journal on Computing},
volume = {38},
number = {3},
year = {2008},
pages = {1080--1112},
doi = {10.1137/070684689},
}
@inproceedings{LM08a,
author = {Lutz, Jack H. and Mayordomo, Elvira},
title = {Dimensions of points in self-similar fractals},
booktitle = {Computing and combinatorics},
series = {Lecture Notes in Comput. Sci.},
volume = {5092},
publisher = {Springer},
address = {Berlin},
year = {2008},
pages = {215--224},
doi = {10.1007/978-3-540-69733-6_22},
}
@incollection{LM21,
author = {Lutz, Jack H. and Mayordomo, Elvira},
title = {Algorithmic Fractal Dimensions in Geometric Measure Theory},
editor = {Brattka, Vasco and Hertling, Peter},
booktitle = {Handbook of Computability and Complexity in Analysis},
series = {Theory and Applications of Computability},
publisher = {Springer},
address = {Cham},
year = {2021},
pages = {271--302},
doi = {10.1007/978-3-030-59234-9_8},
}
@book{LN15,
author = {Longley, John and Normann, Dag},
title = {Higher-Order Computability},
edition = {1st},
publisher = {Springer},
year = {2015},
}
@inproceedings{LNS09,
author = {Lewis, Andrew and Nies, Andr{\'e} and Sorbi, Andrea},
title = {The first order theories of the {M}edvedev and {M}uchnik lattices},
booktitle = {Mathematical theory and computational practice},
series = {Lecture Notes in Comput. Sci.},
volume = {5635},
publisher = {Springer},
address = {Berlin},
year = {2009},
pages = {324--331},
doi = {10.1007/978-3-642-03073-4_33},
}
@article{Loe05,
author = {Iris Loeb},
title = {Equivalents of the (Weak) Fan Theorem},
journal = {Annals of Pure and Applied Logic},
volume = {132},
number = {1},
year = {2005},
pages = {51--66},
}
@article{Loe09,
author = {Loeb, Iris},
title = {Indecomposability of negative dense subsets of {$\Bbb R$} in constructive reverse mathematics},
journal = {Logic Journal of the IGPL},
volume = {17},
number = {2},
year = {2009},
pages = {173--177},
doi = {10.1093/jigpal/jzp002},
}
@article{Loe13,
author = {Loeb, Iris},
title = {Lipschitz functions in constructive reverse mathematics},
journal = {Log. J. IGPL},
volume = {21},
number = {1},
year = {2013},
pages = {28--43},
doi = {10.1093/jigpal/jzs020},
}
@article{Lor51,
author = {Lorenzen, Paul},
title = {Mass und {I}ntegral in der konstruktiven {A}nalysis},
journal = {Mathematische Zeitschrift},
volume = {54},
year = {1951},
pages = {275--290},
}
@book{Lor65,
author = {Lorenzen, Paul},
title = {Differential und {I}ntegral. {E}ine konstruktive {E}inf\"uhrung in die klassische {A}nalysis.},
publisher = {Akademische Verlagsgesellschaft},
address = {Frankfurt},
year = {1965},
}
@article{Lor78,
author = {Lorenzen, Paul},
title = {Konstruktive {A}nalysis und das geometrische {K}ontinuum},
journal = {Dialectica},
volume = {32},
year = {1978},
pages = {221--227},
}
@inproceedings{LP13,
author = {Le Roux, St{\'e}phane and Pauly, Arno},
title = {Closed Choice for Finite and for Convex Sets},
editor = {Bonizzoni, Paola and Brattka, Vasco and L{\"o}we, Benedikt},
booktitle = {The Nature of Computation. Logic, Algorithms, Applications},
series = {Lecture Notes in Computer Science},
volume = {7921},
publisher = {Springer},
address = {Berlin},
year = {2013},
pages = {294--305},
note = {9th Conference on Computability in Europe, CiE 2013, Milan, Italy, July 1-5, 2013},
doi = {10.1007/978-3-642-39053-1_34},
}
@article{LPJ05,
author = {Li, C. and Pion, S. and Yap, C.K.},
title = {Recent progress in exact geometric computation},
journal = {The Journal of Logic and Algebraic Programming},
volume = {64},
year = {2005},
pages = {85--111},
}
@inproceedings{LR02,
author = {Langley, Simon and Richardson, Daniel},
title = {What can we do with a Solution?},
editor = {Brattka, Vasco and Schr{\"{o}}der, Matthias and Weihrauch, Klaus},
booktitle = {{CCA} 2002 Computability and Complexity in Analysis},
series = {Electronic Notes in Theoretical Computer Science},
volume = {66},
publisher = {Elsevier},
address = {Amsterdam},
year = {2002},
note = {5th International Workshop, {CCA} 2002, M{\'{a}}laga, Spain, July 12--13, 2002},
}
@article{LR09,
author = {Lubarsky, Robert S. and Richman, Fred},
title = {Signed-bit representations of real numbers},
journal = {Journal of Logic and Analysis},
volume = {1},
year = {2009},
pages = {Paper 10, 18},
doi = {10.4115/jla.2009.1.10},
}
@inproceedings{LRP15,
author = {Le Roux, St{\'e}phane and Pauly, Arno},
title = {Weihrauch Degrees of Finding Equilibria in Sequential Games (Extended Abstract)},
editor = {Beckmann, Arnold and Mitrana, Victor and Soskova, Mariya},
booktitle = {Evolving Computability},
series = {Lecture Notes in Computer Science},
volume = {9136},
publisher = {Springer},
address = {Cham},
year = {2015},
pages = {246--257},
note = {11th Conference on Computability in Europe, CiE 2015, Bucharest, Romania, June 29--July 3, 2015},
doi = {10.1007/978-3-319-20028-6_25},
}
@article{LRP15a,
author = {Le Roux, St{\'{e}}phane and Pauly, Arno},
title = {Finite choice, convex choice and finding roots},
journal = {Logical Methods in Computer Science},
volume = {11},
number = {4},
year = {2015},
pages = {4:6, 31},
doi = {10.2168/LMCS-11(4:6)2015},
}
@inproceedings{LRPR17,
author = {Le Roux, St{\'e}phane and Pauly, Arno and Raskin, Jean-Fran{\c{c}}ois},
title = {{M}inkowski Games},
editor = {Vollmer, Heribert and Vall{\'e}e, Brigitte},
booktitle = {34th Symposium on Theoretical Aspects of Computer Science (STACS 2017)},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
volume = {66},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
year = {2017},
pages = {50:1--50:13},
doi = {10.4230/LIPIcs.STACS.2017.50},
}
@inproceedings{LS00,
author = {Lisovik, Leonid and Shkaravska, Olha},
title = {On Fractal Dimension of Sets Defined by Transducers},
editor = {Blanck, Jens and Brattka, Vasco and Hertling, Peter and Weihrauch, Klaus},
booktitle = {Computability and Complexity in Analysis},
series = {Informatik Berichte},
volume = {272},
publisher = {FernUniversit\"at Hagen},
year = {2000},
month = sep,
pages = {261--270},
note = {CCA 2000 Workshop, Swansea, Wales, September 17--19, 2000},
}
@article{LS12,
author = {Lietz, Peter and Streicher, Thomas},
title = {Realizability models refuting {I}shihara's boundedness principle},
journal = {Annals of Pure and Applied Logic},
volume = {163},
number = {12},
year = {2012},
pages = {1803--1807},
doi = {10.1016/j.apal.2012.04.004},
}
@inproceedings{LS17,
author = {Lutz, Neil and Stull, D.M.},
title = {Dimension Spectra of Lines},
editor = {Kari, Jarkko and Manea, Florin and Petre, Ion},
booktitle = {Unveiling Dynamics and Complexity},
series = {Lecture Notes in Computer Science},
volume = {10307},
publisher = {Springer},
address = {Cham},
year = {2017},
pages = {304--314},
note = {13th Conference on Computability in Europe, CiE 2017, Turku, Finland, June 12-16, 2017},
doi = {10.1007/978-3-319-58741-7_29},
}
@inproceedings{LS17a,
author = {Lutz, Neil and Stull, D. M.},
title = {Bounding the dimension of points on a line},
editor = {Gopal, T. V. and J{\"a}ger, Gerhard and Steila, Silvia},
booktitle = {Theory and Applications of Models of Computation},
series = {Lecture Notes in Computer Science},
volume = {10185},
publisher = {Springer},
address = {Cham},
year = {2017},
pages = {425--439},
doi = {10.1007/978-3-319-55911-7},
}
@inproceedings{LS17b,
author = {Lutz, Neil and Stull, D. M.},
title = {Bounding the dimension of points on a line},
editor = {Gopal, T.V. and J{\"a}ger , Gerhard and Steila, Silvia},
booktitle = {Theory and applications of models of computation},
series = {Lecture Notes in Computer Science},
volume = {10185},
publisher = {Springer},
address = {Cham},
year = {2017},
pages = {425--439},
doi = {10.1007/978-3-319-55911-7},
}
@inproceedings{LS18,
author = {Lutz, Neil and Stull, Donald M.},
title = {Projection theorems using effective dimension},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
booktitle = {43rd {I}nternational {S}ymposium on {M}athematical {F}oundations of {C}omputer {S}cience},
series = {LIPIcs. Leibniz Int. Proc. Inform.},
volume = {117},
publisher = {Schloss Dagstuhl. Leibniz-Zent. Inform., Wadern},
year = {2018},
pages = {Art. No. 71, 15},
}
@article{LS20,
author = {Lutz, Neil and Stull, D. M.},
title = {Bounding the dimension of points on a line},
journal = {Information and Computation},
volume = {275},
year = {2020},
pages = {104601, 15},
doi = {10.1016/j.ic.2020.104601},
}
@article{LS22,
author = {Lutz, Neil and Stull, D. M.},
title = {Dimension spectra of lines},
journal = {Computability},
volume = {11},
number = {2},
year = {2022},
pages = {85--112},
doi = {10.3233/com-190292},
}
@inproceedings{Lub07,
author = {Lubarsky, Robert S.},
title = {On the {C}auchy completeness of the constructive {C}auchy reals},
editor = {Cenzer, Douglas and Dillhage, Ruth and Grubba, Tanja and Weihrauch, Klaus},
booktitle = {Proceedings of the Third International Conference on Computability and Complexity in Analysis},
series = {Electronic Notes in Theoretical Computer Science},
volume = {167},
publisher = {Elsevier},
address = {Amsterdam},
year = {2007},
pages = {225--254},
note = {{CCA} 2006, Gainesville, Florida, USA, November 1--5, 2006},
}
@article{Lub07a,
author = {Lubarsky, Robert S.},
title = {On the {C}auchy completeness of the constructive {C}auchy reals},
journal = {Mathematical Logic Quarterly},
volume = {53},
number = {4--5},
year = {2007},
pages = {396--414},
}
@article{Lub13,
author = {Lubarsky, Robert S.},
title = {On the failure of {BD}-{$\Bbb{N}$} and {BD}, and an application to the anti-{S}pecker property},
journal = {J. Symbolic Logic},
volume = {78},
number = {1},
year = {2013},
pages = {39--56},
doi = {10.2178/jsl.7801030},
}
@article{Lub19,
author = {Lubarsky, Robert S.},
title = {Separating the Fan Theore and its Weakenings {II}},
journal = {The Journal of Symbolic Logic},
volume = {84},
number = {4},
year = {2019},
pages = {1484--1509},
doi = {10.1017/jsl.2019.1},
}
@article{Luc22,
author = {Lucier, Bradley J.},
title = {The Nature of Numbers: Real Computing},
journal = {Journal of Humanistic Mathematics},
volume = {12},
number = {1},
year = {2022},
pages = {317--347},
doi = {10.5642/jhummath.202201.25},
}
@article{Luc77,
author = {Luckhardt, Horst},
title = {A fundamental effect in computations on real numbers},
journal = {Theoretical Computer Science},
volume = {5},
number = {3},
year = {1977},
pages = {321--324},
}
@article{Lut05,
author = {Lutz, Jack H.},
title = {Effective fractal dimensions},
journal = {Mathematical Logic Quarterly},
volume = {51},
number = {1},
year = {2005},
pages = {62--72},
}
@incollection{Lut09,
author = {Lutz, Jack H.},
title = {A divergence formula for randomness and dimension},
booktitle = {Mathematical theory and computational practice},
series = {Lecture Notes in Comput. Sci.},
volume = {5635},
publisher = {Springer},
address = {Berlin},
year = {2009},
pages = {342--351},
doi = {10.1007/978-3-642-03073-4_35},
}
@article{Lut11,
author = {Lutz, Jack H.},
title = {A divergence formula for randomness and dimension},
journal = {Theoret. Comput. Sci.},
volume = {412},
number = {1-2},
year = {2011},
pages = {166--177},
doi = {10.1016/j.tcs.2010.09.005},
}
@article{Lut17,
author = {Lutz, Neil},
title = {Open problems column: {S}ome open problems in algorithmic fractal geometry},
journal = {ACM SIGACT News},
volume = {48},
number = {4},
year = {2017},
pages = {35--41},
note = {Edited by William Gasarch},
doi = {10.1145/3173127.3173134},
}
@inproceedings{Lut17a,
author = {Lutz, Neil},
title = {Fractal intersections and products via algorithmic dimension},
editor = {Larsen, Kim G. and Bodlaender, Hans L. and Raskin, Jean-Fran\c{c}ois},
booktitle = {42nd {I}nternational {S}ymposium on {M}athematical {F}oundations of {C}omputer {S}cience},
series = {LIPIcs. Leibniz Int. Proc. Inform.},
volume = {83},
publisher = {Schloss Dagstuhl. Leibniz-Zent. Inform., Wadern},
year = {2017},
pages = {Art. No. 58, 12},
}
@phdthesis{Lut21,
author = {Lutz, Patrick},
title = {Results on {M}artin's Conjecture},
school = {University of California, Berkeley},
year = {2021},
}
@inproceedings{LW07,
author = {Lu, Hong and Weihrauch, Klaus},
title = {Computable {R}iesz representation for the dual of {$C[0;1]$}},
editor = {Cenzer, Douglas and Dillhage, Ruth and Grubba, Tanja and Weihrauch, Klaus},
booktitle = {Proceedings of the Third International Conference on Computability and Complexity in Analysis},
series = {Electronic Notes in Theoretical Computer Science},
volume = {167},
publisher = {Elsevier},
address = {Amsterdam},
year = {2007},
pages = {157--177},
note = {{CCA} 2006, Gainesville, Florida, USA, November 1--5, 2006},
}
@article{LW07a,
author = {Lu, Hong and Weihrauch, Klaus},
title = {Computable {R}iesz representation for the dual of {$C[0;1]$}},
journal = {Mathematical Logic Quarterly},
volume = {53},
number = {4--5},
year = {2007},
pages = {415--430},
}
@inproceedings{LW08,
author = {Lu, Dianchen and Wang, Qingyan},
title = {Computing the Solution of the m-{K}orteweg-de {V}ries Equation on {T}uring Machines},
editor = {Dillhage, Ruth and Grubba, Tanja and Sorbi, Andrea and Weihrauch, Klaus and Zhong, Ning},
booktitle = {Proceedings of the Fourth International Conference on Computability and Complexity in Analysis ({CCA} 2007)},
series = {Electronic Notes in Theoretical Computer Science},
volume = {202},
publisher = {Elsevier},
year = {2008},
pages = {219--236},
note = {{CCA} 2007, Siena, Italy, June 16--18, 2007},
}
@inproceedings{LW08a,
author = {Lu, Hong and Weihrauch, Klaus},
title = {Computable {R}iesz Representation for Locally Compact {H}ausdorff Spaces},
editor = {Dillhage, Ruth and Grubba, Tanja and Sorbi, Andrea and Weihrauch, Klaus and Zhong, Ning},
booktitle = {Proceedings of the Fourth International Conference on Computability and Complexity in Analysis ({CCA} 2007)},
series = {Electronic Notes in Theoretical Computer Science},
volume = {202},
publisher = {Elsevier},
year = {2008},
pages = {3--12},
note = {{CCA} 2007, Siena, Italy, June 16--18, 2007},
}
@inproceedings{LW08b,
author = {Lutz, Jack and Weihrauch, Klaus},
title = {Connectivity Properties of Dimension Level Sets},
editor = {Dillhage, Ruth and Grubba, Tanja and Sorbi, Andrea and Weihrauch, Klaus and Zhong, Ning},
booktitle = {Proceedings of the Fourth International Conference on Computability and Complexity in Analysis ({CCA} 2007)},
series = {Electronic Notes in Theoretical Computer Science},
volume = {202},
publisher = {Elsevier},
year = {2008},
pages = {295--304},
note = {{CCA} 2007, Siena, Italy, June 16--18, 2007},
}
@article{LW08c,
author = {Lu, Hong and Weihrauch, Klaus},
title = {Computable {R}iesz Representation for Locally Compact {H}ausdorff Spaces},
journal = {Journal of Universal Computer Science},
volume = {14},
number = {6},
year = {2008},
pages = {845--860},
}
@article{LW08d,
author = {Lutz, Jack H. and Weihrauch, Klaus},
title = {Connectivity properties of dimension level sets},
journal = {Mathematical Logic Quarterly},
volume = {54},
number = {5},
year = {2008},
pages = {483--491},
}
@inproceedings{LZ08,
author = {Le Roux, St\'ephane and Ziegler, Martin},
title = {Singular Coverings and Non-Uniform Notions of Closed Set Computability},
editor = {Dillhage, Ruth and Grubba, Tanja and Sorbi, Andrea and Weihrauch, Klaus and Zhong, Ning},
booktitle = {Proceedings of the Fourth International Conference on Computability and Complexity in Analysis ({CCA} 2007)},
series = {Electronic Notes in Theoretical Computer Science},
volume = {202},
publisher = {Elsevier},
year = {2008},
pages = {73--88},
note = {{CCA} 2007, Siena, Italy, June 16--18, 2007},
}
@article{LZ08a,
author = {Le Roux, St\'ephane and Ziegler, Martin},
title = {Singular coverings and non-uniform notions of closed set computability},
journal = {Mathematical Logic Quarterly},
volume = {54},
number = {5},
year = {2008},
pages = {545--560},
}
@inproceedings{LZ20,
author = {Lim, Donghyun and Ziegler, Martin},
title = {Quantitative Coding and Complexity Theory of Compact Metric Spaces},
editor = {Anselmo, Marcella and Della Vedova, Gianluca and Manea, Florin and Pauly, Arno},
booktitle = {Beyond the Horizon of Computability},
publisher = {Springer International Publishing},
address = {Cham},
year = {2020},
pages = {205--214},
doi = {10.1007/978-3-030-51466-2_18},
}
@article{Mac16,
author = {Macintyre, Angus},
title = {Turing meets {S}chanuel},
journal = {Annals of Pure and Applied Logic},
volume = {167},
number = {10},
year = {2016},
pages = {901--938},
doi = {10.1016/j.apal.2015.10.003},
}
@book{Mai18,
author = {Mainzer, Klaus},
title = {The Digital and the Real World},
publisher = {World Scientific Publishing},
address = {Singapore},
year = {2018},
doi = {10.1142/10583},
}
@phdthesis{Mal15,
author = {Maler, Adrian},
title = {Effective Theory of {L}{\'e}vy and {F}eller Processes},
school = {The Pennsylvania State University},
year = {2015},
}
@inproceedings{Man12,
author = {Manin, Yuri I.},
title = {A computability challenge: asymptotic bounds for error-correcting codes},
booktitle = {Computation, physics and beyond},
series = {Lecture Notes in Computer Science},
volume = {7160},
publisher = {Springer},
address = {Heidelberg},
year = {2012},
pages = {174--182},
}
@article{Man12a,
author = {Manin, Yuri I.},
title = {Renormalisation and computation {II}: time cut-off and the Halting Problem},
journal = {Mathematical Structures in Computer Science},
volume = {22},
number = {5},
publisher = {Cambridge University Press},
year = {2012},
pages = {729--751},
doi = {10.1017/S0960129511000508},
}
@incollection{Man13,
author = {Manin, Yuri I.},
title = {Renormalization and computation {I}: motivation and background},
booktitle = {O{PERADS} 2009},
series = {S\'{e}min. Congr.},
volume = {26},
publisher = {Soc. Math. France, Paris},
year = {2013},
pages = {181--222},
}
@article{Man71,
author = {Manukjan, S. N.},
title = {The interior points of non-degenerate constructive curves},
journal = {Doklady Akademii Nauk SSSR},
volume = {196},
year = {1971},
pages = {768--769},
}
@article{Man71a,
author = {Manukjan, S. N.},
title = {On interior points of nondegenerate constructive curves},
journal = {Soviet Mathematics. Doklady},
volume = {12},
publisher = {American Mathematical Society (AMS), Providence, RI},
year = {1971},
pages = {246--248},
}
@article{Man73,
author = {Manukjan, S. N.},
title = {Constructive everywhere dense simple arcs},
journal = {Izvestija Akademii Nauk Armjansko\u{\i} SSR. Serija Matematika},
volume = {8},
number = {4},
year = {1973},
pages = {291--305, 346},
}
@article{Man73a,
author = {S. N. {Manukjan}},
title = {{\"U}ber konstruktive {\"u}berall dichte einfache {B}{\"o}gen.},
journal = {Izvestiya Akademii Nauk Armyanskoi SSR. Matematika},
volume = {8},
publisher = {Academy of Sciences of the Armenian Soviet Socialist Republic - Armenian SSR (Akademiya Nauk Armyanskoi SSR), Yerevan},
year = {1973},
pages = {291--305},
}
@article{Man75,
author = {Manukjan, S. N.},
title = {The stability of constructive simple arcs with respect to algorithmic transformations},
journal = {Doklady Akademii Nauk SSSR},
volume = {220},
year = {1975},
pages = {1267--1270},
}
@article{Man75a,
author = {Manukjan, S. N.},
title = {Some properties of partitionings of the plane by nondegenerate constructive curves},
journal = {Trudy Vy\v{c}isl. Centra Akad. Nauk Armjan. SSR i Erevan. Gos. Univ. Mat. Voprosy Kibernet. i Vy\v{c}isl. Tehn.},
volume = {8},
year = {1975},
pages = {67--95},
}
@article{Man75b,
author = {Manukjan, S. N.},
title = {The stability of constructive simple arcs with respect to algorithmic transformations},
journal = {Soviet Mathematics. Doklady},
volume = {16},
publisher = {American Mathematical Society (AMS), Providence, RI},
year = {1975},
pages = {238--242},
}
@article{Man75c,
author = {Manukjan, S. N.},
title = {Some properties of partitioning of the plane by non-degenerate constructive curves},
journal = {Tr. Vychisl. Tsentra Akad. Nauk Arm. SSR Erevan. Gos. Univ.},
volume = {8},
publisher = {Izdatel'stvo Akademii Nauk Armyansko\u{\i} SSR, Erevan},
year = {1975},
pages = {67--95},
}
@article{Man76,
author = {Mandelkern, Mark},
title = {Connectivity of an interval},
journal = {Proceedings of the American Mathematical Society},
volume = {54},
year = {1976},
pages = {170--172},
}
@incollection{Man76a,
author = {Manukjan, S. N.},
title = {Some topological peculiarities of constructive simple arcs},
editor = {Markov, A.A. and Kushner, B. A.},
booktitle = {Studies in the theory of algorithms and mathematical logic, {V}ol. 2 ({R}ussian)},
publisher = {Vy\v{c}isl. Centr Akad. Nauk SSSR, Moscow},
year = {1976},
pages = {122--129, 158},
}
@article{Man77,
author = {Manukyan, S. N.},
title = {On a property of the notion of interior and exterior point with respect to constructive closed curve},
journal = {Izvestiya Akademii Nauk Armyanskoi SSR. Matematika},
volume = {12},
publisher = {Academy of Sciences of the Armenian Soviet Socialist Republic - Armenian SSR (Akademiya Nauk Armyanskoi SSR), Yerevan},
year = {1977},
pages = {303--309},
}
@article{Man82,
author = {Mandelkern, Mark},
title = {Continuity of monotone functions},
journal = {Pacific Journal of Mathematics},
volume = {99},
year = {1982},
pages = {413--418},
}
@article{Man82a,
author = {Manukyan, S. N.},
title = {Algorithms transforming constructive curves into points},
journal = {Matematicheskie Voprosy Kibernetiki i Vychislitel{\cprime} no\u{\i} Tekhniki. Trudy Vychislitel{\cprime} nogo Tsentra Akademii Nauk Armyansko\u{\i} SSR i Erevanskogo Gosudarstvennogo Universiteta},
number = {10},
year = {1982},
pages = {55--71},
}
@article{Man83,
author = {Mandelkern, Mark},
title = {Constructive continuity},
journal = {Memoirs of the American Mathematical Society},
volume = {42},
number = {277},
address = {Providence},
year = {1983},
pages = {v+117},
doi = {10.1090/memo/0277},
}
@article{Man84,
author = {Manukyan, S. N.},
title = {The {D}irichlet problem in constructive analysis},
journal = {Akademiya Nauk Armyansko\u{\i} SSR. Doklady},
volume = {79},
number = {2},
year = {1984},
pages = {58--62},
}
@article{Man86,
author = {Manukyan, S. N.},
title = {On uniqueness properties of constructive analytic functions},
journal = {Soviet Journal of Contemporary Mathematical Analysis. Armenian Academy of Sciences},
volume = {21},
number = {2},
publisher = {Allerton Press, Inc., New York},
year = {1986},
pages = {95--103},
}
@article{Man86a,
author = {Manukyan, S. N.},
title = {Uniqueness properties for constructive analytic functions},
journal = {Izvestiya Akademii Nauk Armyansko\u{\i} SSR. Seriya Matematika},
volume = {21},
number = {2},
year = {1986},
pages = {198--206, 208},
}
@article{Man88,
author = {Mandelkern, Mark},
title = {Constructively complete finite sets},
journal = {Zeitschrift f\"ur Mathematische Logik und Grundlagen der Mathematik},
volume = {34},
number = {2},
year = {1988},
pages = {97--103},
}
@article{Man88a,
author = {Mandelkern, Mark},
title = {Limited Omniscience and the {B}olzano-{W}eierstrass Principle},
journal = {Bulletin of the London Mathematical Society},
volume = {20},
year = {1988},
pages = {319--320},
}
@inproceedings{Mar00,
author = {Martin, Keye},
title = {Complexity and Verification of a Renee Equation},
editor = {Blanck, Jens and Brattka, Vasco and Hertling, Peter and Weihrauch, Klaus},
booktitle = {Computability and Complexity in Analysis},
series = {Informatik Berichte},
volume = {272},
publisher = {FernUniversit\"at Hagen},
year = {2000},
month = sep,
pages = {271--286},
note = {CCA 2000 Workshop, Swansea, Wales, September 17--19, 2000},
}
@phdthesis{Mar12,
author = {Marks, Andrew Scott},
title = {Recursion theory and countable {B}orel equivalence relations},
school = {University of California, Berkeley},
year = {2012},
}
@article{Mar54,
author = {Markov, A.A.},
title = {On the continuity of constructive functions ({R}ussian)},
journal = {Uspekhi Mat. Nauk (N.S.)},
volume = {9},
year = {1954},
pages = {226--230},
}
@article{Mar58,
author = {Markov, A.A.},
title = {On constructive functions ({R}ussian)},
journal = {Trudy Mat.\ Inst.\ Steklov},
volume = {52},
year = {1958},
pages = {315--348},
note = {(English trans. in AMS Trans. (2) 29, 1963)},
}
@book{Mar70,
author = {Martin-L\"{o}f, Per},
title = {Notes on constructive mathematics},
publisher = {Almqvist and Wiksell},
address = {Stockholm},
year = {1970},
}
@article{Mar78,
author = {Margenstern, Maurice},
title = {On a variant of constructivisation of the theory of almost periodic functions},
journal = {Zeitschrift f\"ur Mathematische Logik und Grundlagen der Mathematik},
volume = {24},
number = {6},
year = {1978},
pages = {495--507},
}
@article{Mar95,
author = {Margenstern, Maurice},
title = {L'{\'e}cole constructive de {M}arkov},
journal = {Revue d'histoire des math\'ematiques},
volume = {1},
number = {2},
publisher = {Soci{\'e}t{\'e} math{\'}ematique de France},
year = {1995},
pages = {271--305},
}
@article{May02,
author = {Mayordomo, Elvira},
title = {A {K}olmogorov complexity characterization of constructive {H}ausdorff dimension},
journal = {Information Processing Letters},
volume = {84},
number = {1},
year = {2002},
pages = {1--3},
doi = {10.1016/S0020-0190(02)00343-5},
}
@article{May18,
author = {Mayordomo, Elvira},
title = {Effective {H}ausdorff dimension in general metric spaces},
journal = {Theory of Computing Systems},
volume = {62},
number = {7},
year = {2018},
pages = {1620--1636},
doi = {10.1007/s00224-018-9848-3},
}
@book{Maz63,
author = {Mazur, Stanis{\l}aw},
title = {Computable Analysis},
series = {Razprawy Matematyczne},
volume = {33},
publisher = {P{\'a}nstwowe Wydawnictwo Naukowe},
address = {Warsaw},
year = {1963},
}
@inproceedings{MBV01,
author = {Meyssonnier, Charles and Boldi, Paolo and Vigna, Sebastiano},
title = {$\delta$-Approximable Functions},
editor = {Blanck, Jens and Brattka, Vasco and Hertling, Peter},
booktitle = {Computability and Complexity in Analysis},
series = {Lecture Notes in Computer Science},
volume = {2064},
publisher = {Springer},
address = {Berlin},
year = {2001},
pages = {187--199},
note = {4th International Workshop, CCA 2000, Swansea, UK, September 2000},
}
@article{MC04,
author = {Mycka, Jerzy and Costa, Jos\'{e} F\'{e}lix},
title = {Real recursive functions and their hierarchy},
journal = {Journal of Complexity},
volume = {20},
number = {6},
year = {2004},
pages = {835--857},
}
@incollection{MC04a,
author = {Mayordomo C{\'a}mara, Elvira},
title = {Effective {H}ausdorff dimension},
booktitle = {Classical and new paradigms of computation and their complexity hierarchies},
series = {Trends Log. Stud. Log. Libr.},
volume = {23},
publisher = {Kluwer Acad. Publ.},
address = {Dordrecht},
year = {2004},
pages = {171--186},
doi = {10.1007/978-1-4020-2776-5_10},
}
@inproceedings{MC05,
author = {Mycka, Jerzy and Costa, Jos\'{e} F\'{e}lix},
title = {The computational power of continuous dynamic systems},
editor = {Maurice Margenstern},
booktitle = {Machines, Computations, Universality},
series = {Lecture Notes in Computer Science},
volume = {3354},
publisher = {Springer},
address = {Berlin},
year = {2005},
pages = {163--174},
note = {Conference on Machines, Computations, Universality, MCU 2004, Saint-Petersburg, Russia, September 21--26, 2004},
}
@article{MC06,
author = {Mycka, Jerzy and Costa, Jos\'{e} F\'{e}lix},
title = {The {$P\not=NP$} conjecture in the context of real and complex analysis},
journal = {Journal of Complexity},
volume = {22},
number = {2},
year = {2006},
pages = {287--303},
}
@article{MC07,
author = {Mycka, Jerzy and Costa, Jos\'{e} F\'{e}lix},
title = {A new conceptual framework for analog computation},
journal = {Theoretical Computer Science},
volume = {374},
year = {2007},
pages = {277--290},
}
@article{McC21,
author = {McCarthy, Ethan},
title = {Pointwise complexity of the derivative of a computable function},
journal = {Archive for Mathematical Logic},
volume = {60},
number = {7--8},
year = {2021},
pages = {981--994},
doi = {10.1007/s00153-021-00769-4},
}
@inproceedings{McN07,
author = {McNicholl, Timothy H.},
title = {Computability and the implicit function theorem},
editor = {Cenzer, Douglas and Dillhage, Ruth and Grubba, Tanja and Weihrauch, Klaus},
booktitle = {Proceedings of the Third International Conference on Computability and Complexity in Analysis},
series = {Electronic Notes in Theoretical Computer Science},
volume = {167},
publisher = {Elsevier},
address = {Amsterdam},
year = {2007},
pages = {3--15},
note = {{CCA} 2006, Gainesville, Florida, USA, November 1--5, 2006},
}
@inproceedings{McN08,
author = {McNicholl, Timothy H.},
title = {Uniformly computable aspects of inner functions},
editor = {Dillhage, Ruth and Grubba, Tanja and Sorbi, Andrea and Weihrauch, Klaus and Zhong, Ning},
booktitle = {Proceedings of the Fourth International Conference on Computability and Complexity in Analysis ({CCA} 2007)},
series = {Electronic Notes in Theoretical Computer Science},
volume = {202},
publisher = {Elsevier},
year = {2008},
pages = {27--36},
note = {{CCA} 2007, Siena, Italy, June 16--18, 2007},
}
@article{McN08a,
author = {McNicholl, Timothy H.},
title = {A uniformly computable Implicit Function Theorem},
journal = {Mathematical Logic Quarterly},
volume = {54},
number = {3},
year = {2008},
pages = {272--279},
}
@article{McN08b,
author = {McNicholl, Timothy H.},
title = {Uniformly computable aspects of inner functions: estimation and factorization},
journal = {Mathematical Logic Quarterly},
volume = {54},
number = {5},
year = {2008},
pages = {508--518},
}
@article{McN08c,
author = {McNulty, George F.},
title = {The equational compatibility problem for the real line},
journal = {Algebra Universalis},
volume = {59},
number = {3-4},
year = {2008},
pages = {259--275},
}
@article{McN12,
author = {McNicholl, Timothy H.},
title = {An effective {C}arath\'eodory theorem},
journal = {Theory of Computing Systems},
volume = {50},
number = {4},
year = {2012},
pages = {579--588},
doi = {10.1007/s00224-011-9356-1},
}
@article{McN13,
author = {McNicholl, Timothy H.},
title = {The power of backtracking and the confinement of length},
journal = {Proceedings of the American Mathematical Society},
volume = {141},
number = {3},
year = {2013},
pages = {1041--1053},
doi = {10.1090/S0002-9939-2012-11385-1},
}
@article{McN13a,
author = {McNicholl, Timothy H.},
title = {Computing links and accessing arcs},
journal = {Mathematical Logic Quarterly},
volume = {59},
number = {1-2},
year = {2013},
pages = {101--107},
doi = {10.1002/malq.201200026},
}
@inproceedings{McN13b,
author = {McNicholl, Timothy H.},
title = {On the computable theory of bounded analytic functions},
booktitle = {Blaschke Products and Their Applications},
series = {Fields Inst. Commun.},
volume = {65},
publisher = {Springer},
address = {New York},
year = {2013},
pages = {223--248},
doi = {10.1007/978-1-4614-5341-3_13},
}
@article{McN14,
author = {McNicholl, Timothy H.},
title = {Computing boundary extensions of conformal maps},
journal = {LMS Journal of Computation and Mathematics},
volume = {17},
number = {1},
year = {2014},
pages = {360--378},
doi = {10.1112/S1461157014000096},
}
@inproceedings{McN15,
author = {McNicholl, Timothy H.},
title = {A Note on the Computable Categoricity of $\ell^p$ Spaces},
editor = {Beckmann, Arnold and Mitrana, Victor and Soskova, Mariya},
booktitle = {Evolving Computability},
series = {Lecture Notes in Computer Science},
volume = {9136},
publisher = {Springer},
address = {Cham},
year = {2015},
pages = {268--275},
note = {11th Conference on Computability in Europe, CiE 2015, Bucharest, Romania, June 29--July 3, 2015},
doi = {10.1007/978-3-319-20028-6_27},
}
@article{McN17,
author = {McNicholl, Timothy H.},
title = {Computable copies of $l_p$},
journal = {Computability},
volume = {6},
number = {4},
year = {2017},
pages = {391--408},
doi = {10.3233/COM-160065},
}
@article{McN20,
author = {McNicholl, Timothy H.},
title = {Computing the exponent of a {L}ebesgue space},
journal = {Journal of Logic and Analysis},
volume = {12},
year = {2020},
pages = {Paper No. 7, 28},
doi = {10.4115/jla.2020.12.7},
}
@article{McN21,
author = {McNicholl, Timothy H.},
title = {Continuous logic and embeddings of {L}ebesgue spaces},
journal = {Archive for Mathematical Logic},
volume = {60},
number = {1},
year = {2021},
pages = {105--119},
doi = {10.1007/s00153-020-00734-7},
}
@article{ME07,
author = {Escard\'{o}, Mart\'{\i}n H. and Marcial-Romero, J. Raymundo},
title = {Semantics of a sequential language for exact real-number computation},
journal = {Theoretical Computer Science},
volume = {379},
year = {2007},
pages = {120--141},
}
@article{Mel13,
author = {Melnikov, Alexander G.},
title = {Computably isometric spaces},
journal = {The Journal of Symbolic Logic},
volume = {78},
number = {4},
year = {2013},
month = {December},
pages = {1055--1085},
doi = {doi:10.2178/jsl.7804030},
}
@article{Mel21,
author = {Melnikov, A. G.},
title = {New degree spectra of {P}olish spaces},
journal = {Siberian Mathematical Journal},
volume = {62},
number = {5},
year = {2021},
pages = {882--894},
doi = {10.1134/s0037446621050116},
}
@article{Men05,
author = {M{\'e}nissier-Morain, Val{\'e}rie},
title = {Arbitrary precision real arithmetic: design and algorithms},
journal = {The Journal of Logic and Algebraic Programming},
volume = {64},
year = {2005},
pages = {13--39},
}
@article{Mes56a,
author = {Meschkowski, Herbert},
title = {Rekursive reelle {Z}ahlen},
journal = {Math. Z.},
volume = {66},
year = {1956},
pages = {189--202},
}
@inproceedings{MH05,
author = {McLaughlin, Sean and Harrison, John},
title = {A proof-producing decision procedure for real arithmetic},
booktitle = {Automated deduction---{CADE}-20},
series = {Lecture Notes in Comput. Sci.},
volume = {3632},
publisher = {Springer},
address = {Berlin},
year = {2005},
pages = {295--314},
doi = {10.1007/11532231_22},
}
@inproceedings{Mie08,
author = {Mielke, J\"oran},
title = {Refined Bounds on {K}olmogorov Complexity for $\omega$-Languages},
editor = {Brattka, Vasco and Dillhage, Ruth and Grubba, Tanja and Klutsch, Angela},
booktitle = {{CCA} 2008, Fifth International Conference on Computability and Complexity in Analysis},
series = {Electronic Notes in Theoretical Computer Science},
volume = {221},
publisher = {Elsevier},
year = {2008},
pages = {181--189},
note = {{CCA} 2008, Fifth International Conference, Hagen, Germany, August 21--24, 2008},
}
@inproceedings{Mil02,
author = {Miller, Joseph S.},
title = {Effectiveness for Embedded Spheres and Balls},
editor = {Brattka, Vasco and Schr{\"{o}}der, Matthias and Weihrauch, Klaus},
booktitle = {{CCA} 2002 Computability and Complexity in Analysis},
series = {Electronic Notes in Theoretical Computer Science},
volume = {66},
publisher = {Elsevier},
address = {Amsterdam},
year = {2002},
note = {5th International Workshop, {CCA} 2002, M{\'{a}}laga, Spain, July 12--13, 2002},
}
@phdthesis{Mil02a,
author = {Miller, Joseph Stephen},
title = {Pi-0-1 Classes in Computable Analysis and Topology},
school = {Cornell University},
address = {Ithaca, USA},
year = {2002},
}
@article{Mil04,
author = {Miller, Joseph S.},
title = {Degrees of unsolvability of continuous functions},
journal = {The Journal of Symbolic Logic},
volume = {69},
number = {2},
year = {2004},
pages = {555--584},
}
@incollection{Mil17,
author = {Miller, Joseph S.},
title = {On Work of {B}armpalias and {L}ewis-{P}ye: A Derivation on the D.C.E. Reals},
editor = {Day, Adam and Fellows, Michael and Greenberg, Noam and Khoussainov, Bakhadyr and Melnikov, Alexander and Rosamond, Frances},
booktitle = {Computability and Complexity: Essays Dedicated to Rodney G. Downey on the Occasion of His 60th Birthday},
series = {Lecture Notes in Computer Science},
volume = {10010},
publisher = {Springer},
address = {Cham},
year = {2017},
pages = {644--659},
doi = {10.1007/978-3-319-50062-1_39},
}
@article{Mil70,
author = {Miller, Webb},
title = {Recursive function theory and numerical analysis},
journal = {Journal of Computer and Systems Sciences},
volume = {4},
year = {1970},
pages = {465--472},
}
@article{Miy13,
author = {Miyabe, Kenshi},
title = {{$L^1$}-Computability, Layerwise Computability and {S}olovay Reducibility},
journal = {Computability},
volume = {2},
number = {1},
year = {2013},
pages = {15--29},
doi = {10.3233/COM-13015},
}
@article{Miy13a,
author = {Miyabe, Kenshi},
title = {Characterization of {K}urtz randomness by a differentiation theorem},
journal = {Theory Comput. Syst.},
volume = {52},
number = {1},
year = {2013},
pages = {113--132},
doi = {10.1007/s00224-012-9422-3},
}
@article{Miy14,
author = {Miyabe, Kenshi},
title = {Algorithmic randomness over general spaces},
journal = {Mathematical Logic Quarterly},
volume = {60},
number = {3},
year = {2014},
pages = {184--204},
doi = {10.1002/malq.201200051},
}
@article{Miy16,
author = {Miyabe, Kenshi},
title = {Reducibilities relating to {S}chnorr randomness},
journal = {Theory of Computing Systems},
volume = {58},
number = {3},
year = {2016},
pages = {441--462},
doi = {10.1007/s00224-014-9583-3},
}
@article{Miy18,
author = {Miyabe, Kenshi},
title = {Coherence of reducibilities with randomness notions},
journal = {Theory of Computing Systems},
volume = {62},
number = {7},
year = {2018},
pages = {1599--1619},
doi = {10.1007/s00224-017-9752-2},
}
@inproceedings{Miy19,
author = {Miyabe, Kenshi},
title = {Uniform Relativization},
editor = {Manea, Florin and Martin, Barnaby and Paulusma, Dani{\"e}l and Primiero, Giuseppe},
booktitle = {Computing with Foresight and Industry},
series = {Lecture Notes in Computer Science},
volume = {11558},
publisher = {Springer},
address = {Cham},
year = {2019},
pages = {50--61},
note = {15th Conference on Computability in Europe, CiE 2019, Durham, UK, July 15-19, 2019},
doi = {10.1007/978-3-030-22996-2_5},
}
@inproceedings{Miy19a,
author = {Miyabe, Kenshi},
title = {Muchnik degrees and {M}edvedev degrees of randomness notions},
booktitle = {Proceedings of the 14th and 15th {A}sian {L}ogic {C}onferences},
publisher = {World Sci. Publ.},
address = {Hackensack, NJ},
year = {2019},
pages = {108--128},
}
@inproceedings{MK08,
author = {Morozov, Andrei and Korovina, Margarita},
title = {Remarks on $\Sigma$-definability without the equality test over the reals},
editor = {Dillhage, Ruth and Grubba, Tanja and Sorbi, Andrea and Weihrauch, Klaus and Zhong, Ning},
booktitle = {Proceedings of the Fourth International Conference on Computability and Complexity in Analysis ({CCA} 2007)},
series = {Electronic Notes in Theoretical Computer Science},
volume = {202},
publisher = {Elsevier},
year = {2008},
pages = {315--322},
note = {{CCA} 2007, Siena, Italy, June 16--18, 2007},
}
@article{MK08a,
author = {Morozov, Andrei S. and Korovina, Margarita V.},
title = {On {$\Sigma$}-definability without equality over the real numbers},
journal = {Mathematical Logic Quarterly},
volume = {54},
number = {5},
year = {2008},
pages = {535--544},
}
@article{MK19,
author = {Mantry, Poonam and Kaushik, S. K.},
title = {Computability of frames in computable {H}ilbert spaces},
journal = {International Journal of Computer Mathematics: Computer Systems Theory},
volume = {4},
number = {1},
year = {2019},
pages = {16--29},
doi = {10.1080/23799927.2018.1553894},
}
@article{MKO04,
author = {Mulupuru, Bharat C. and Kreinovich, Vladik and Osegueda, Roberto},
title = {Interval Approach to Phase Measurements Can Lead to Arbitrarily Complex Sets - A Theorem and Ways Around It},
journal = {Numerical Algorithms},
volume = {37},
year = {2004},
pages = {285--299},
}
@inproceedings{MM08,
author = {Marcial-Romero, J. Raymundo and Moshier, M. Andrew},
title = {Sequential Real Number Computation and Recursive Relations},
editor = {Dillhage, Ruth and Grubba, Tanja and Sorbi, Andrea and Weihrauch, Klaus and Zhong, Ning},
booktitle = {Proceedings of the Fourth International Conference on Computability and Complexity in Analysis ({CCA} 2007)},
series = {Electronic Notes in Theoretical Computer Science},
volume = {202},
publisher = {Elsevier},
year = {2008},
pages = {171--189},
note = {{CCA} 2007, Siena, Italy, June 16--18, 2007},
}
@article{MM08a,
author = {Marcial-Romero, J. Raymundo and Moshier, M. Andrew},
title = {Sequential real number computation and recursive relations},
journal = {Mathematical Logic Quarterly},
volume = {54},
number = {5},
year = {2008},
pages = {492--507},
}
@article{MM08b,
author = {Matheson, Alec and McNicholl, Timothy H.},
title = {Computable analysis and {B}laschke products},
journal = {Proceedings of the American Mathematical Society},
volume = {136},
number = {1},
year = {2008},
pages = {321--332},
doi = {10.1090/S0002-9939-07-09102-2},
}
@article{MM14,
author = {Manin, Yuri and Marcolli, Matilde},
title = {Kolmogorov complexity and the asymptotic bound for error-correcting codes},
journal = {Journal of Differential Geometry},
volume = {97},
number = {1},
year = {2014},
pages = {91--108},
}
@inproceedings{MM93,
author = {M{\"u}ller, Norbert Th. and Moiske, B.},
title = {Solving Initial Value Problems in Polynomial Time},
booktitle = {Proceedings of the 22th JAIIO - Panel'93, Part 2},
year = {1993},
pages = {283--293},
note = {{B}uenos Aires, 1993},
}
@article{MMOS90,
author = {Matijasevi\v{c}, Yu.V. and Mints, G.E. and Orevkov, V.P. and Slisenko, A.O.},
title = {Nikola\u{i} {A}leksandrovich {S}hanin (on his seventieth birthday), ({R}ussian)},
journal = {Uspekhi Mat. Nauk},
volume = {45},
year = {1990},
pages = {205--206},
note = {[translated in: Russian Math. Surveys, 45:1 (1990) 239--240]},
}
@article{MN13,
author = {Melnikov, Alexander and Nies, Andr{\'e}},
title = {{$K$}-triviality in computable metric spaces},
journal = {Proc. Amer. Math. Soc.},
volume = {141},
number = {8},
year = {2013},
pages = {2885--2899},
doi = {10.1090/S0002-9939-2013-11528-5},
}
@article{MN16,
author = {Melnikov, Alexander G. and Ng, Keng Meng},
title = {Computable structures and operations on the space of continuous functions},
journal = {Fundamenta Mathematicae},
volume = {233},
number = {2},
year = {2016},
pages = {101-141},
doi = {10.4064/fm36-12-2015},
}
@inproceedings{MN82,
author = {Metakides, George and Nerode, Anil},
title = {The introduction of non-recursive methods into mathematics},
editor = {Troelstra, A.S. and van Dalen, D.},
booktitle = {The L.E.J. Brouwer Centenary Symposium},
series = {Studies in Logic and the foundations of mathematics},
volume = {110},
publisher = {North-Holland},
address = {Amsterdam},
year = {1982},
pages = {319--335},
note = {Proceedings of the conference held in Noordwijkerhout, June 8--13, 1981},
}
@article{MNS18,
author = {Miyabe, Kenshi and Nies, Andr{\'e} and Stephan, Frank},
title = {Randomness and {S}olovay degrees},
journal = {Journal of Logic and Analysis},
volume = {10},
year = {2018},
pages = {Paper No. 3, 13},
}
@inproceedings{MNS85,
author = {Metakides, George and Nerode, Anil and Shore, Richard A.},
title = {Recursive limits on the {H}ahn-{B}anach theorem},
editor = {Rosenblatt, Murray},
booktitle = {Errett Bishop: Reflections on Him and His Research},
series = {Contemporary Mathematics},
volume = {39},
publisher = {American Mathematical Society},
address = {Providence},
year = {1985},
pages = {85--91},
note = {Proceedings of the memorial meeting for Errett Bishop, University of California, San Diego, September 24, 1983},
}
@article{MNZ16,
author = {Miyabe, Kenshi and Nies, Andr\'e and Zhang, Jing},
title = {Using almost-everywhere theorems from analysis to study randomness},
journal = {The Bulletin of Symbolic Logic},
volume = {22},
number = {3},
year = {2016},
pages = {305--331},
doi = {10.1017/bsl.2016.10},
}
@incollection{Mon20,
author = {Monin, Benoit},
title = {Higher randomness},
editor = {Franklin, Johanna N.Y. and Porter, Christopher P.},
booktitle = {Algorithmic Randomness: Progress and Prospects},
series = {Lecture Notes in Logic},
volume = {50},
publisher = {Cambridge University Press},
year = {2020},
pages = {232--300},
doi = {10.1017/9781108781718.009},
}
@article{Moo96,
author = {Moore, Cristopher},
title = {Recursion theory on the reals and continuous-time computation},
journal = {Theoretical Computer Science},
volume = {162},
number = {1},
year = {1996},
pages = {23--44},
}
@inproceedings{Mor01a,
author = {Mori, Takakazu},
title = {Computabilities of Fine-Continuous Functions},
editor = {Blanck, Jens and Brattka, Vasco and Hertling, Peter},
booktitle = {Computability and Complexity in Analysis},
series = {Lecture Notes in Computer Science},
volume = {2064},
publisher = {Springer},
address = {Berlin},
year = {2001},
pages = {200--221},
note = {4th International Workshop, CCA 2000, Swansea, UK, September 2000},
}
@article{Mor02,
author = {Mori, Takakazu},
title = {On the computability of {W}alsh functions},
journal = {Theoretical Computer Science},
volume = {284},
number = {2},
year = {2002},
pages = {419--436},
}
@incollection{Mor17,
author = {Morozov, Andrey S.},
title = {Computable Model Theory over the Reals},
editor = {Day, Adam and Fellows, Michael and Greenberg, Noam and Khoussainov, Bakhadyr and Melnikov, Alexander and Rosamond, Frances},
booktitle = {Computability and Complexity: Essays Dedicated to Rodney G. Downey on the Occasion of His 60th Birthday},
series = {Lecture Notes in Computer Science},
volume = {10010},
publisher = {Springer},
address = {Cham},
year = {2017},
pages = {354--365},
doi = {10.1007/978-3-319-50062-1_22},
}
@article{Mor18,
author = {Moriakov, Nikita},
title = {On Effective {B}irkhoff's Ergodic Theorem for Computable Actions of Amenable Groups},
journal = {Theory of Computing Systems},
volume = {62},
number = {5},
year = {2018},
month = {Jul},
pages = {1269--1287},
doi = {10.1007/s00224-017-9822-5},
}
@inproceedings{Mos08,
author = {Moser, Philippe},
title = {On the Convergence of {F}ourier Series of Computable {L}ebesgue Integrable Functions},
editor = {Dillhage, Ruth and Grubba, Tanja and Sorbi, Andrea and Weihrauch, Klaus and Zhong, Ning},
booktitle = {Proceedings of the Fourth International Conference on Computability and Complexity in Analysis ({CCA} 2007)},
series = {Electronic Notes in Theoretical Computer Science},
volume = {202},
publisher = {Elsevier},
year = {2008},
pages = {13--18},
note = {{CCA} 2007, Siena, Italy, June 16--18, 2007},
}
@article{Mos10,
author = {Moschovakis, Joan Rand},
title = {Unavoidable sequences in constructive analysis},
journal = {MLQ Math. Log. Q.},
volume = {56},
number = {2},
year = {2010},
pages = {205--215},
doi = {10.1002/malq.200810046},
}
@article{Mos10a,
author = {Moschovakis, Yiannis N.},
title = {Classical descriptive set theory as a refinement of effective descriptive set theory},
journal = {Annals of Pure and Applied Logic},
volume = {162},
number = {3},
year = {2010},
pages = {243--255},
doi = {10.1016/j.apal.2010.09.010},
}
@article{Mos53,
author = {Mostowski, Andrzej},
title = {A lemma concerning recursive functions and its applications},
journal = {Bull. Acad. Polon. Sci. Cl. III},
volume = {1},
year = {1953},
pages = {277--280},
}
@book{Mos55,
author = {Mostowski, Andrzej},
title = {The present state of investigations on the foundations of mathematics},
series = {Rozprawy Matematyczne},
volume = {9},
publisher = {Polska Akademia Nauk},
address = {Warsaw},
year = {1955},
}
@article{Mos57,
author = {Mostowski, Andrzej},
title = {On computable sequences},
journal = {Fundamenta Mathematicae},
volume = {44},
year = {1957},
pages = {37--51},
}
@inproceedings{Mos59,
author = {Mostowski, Andrzej},
title = {On various degrees of constructivism},
editor = {Heyting, A.},
booktitle = {Constructivity in Mathematics},
series = {Studies in Logic and the Foundations of Mathematics},
publisher = {North-Holland},
address = {Amsterdam},
year = {1959},
pages = {178--194},
note = {Proc. Colloq., Amsterdam, Aug. 26--31, 1957},
}
@article{Mos64,
author = {Moschovakis, Yiannis Nicholas},
title = {Notation systems and recursive ordered fields},
journal = {Compositio Math.},
volume = {17},
year = {1964},
pages = {40--71},
}
@article{Mos64a,
author = {Moschovakis, Yiannis Nicholas},
title = {Recursive metric spaces},
journal = {Fundamenta Mathematicae},
volume = {55},
year = {1964},
pages = {215--238},
}
@article{Mos96,
author = {Moschovakis, J.R.},
title = {A classical view of the intuitionistic continuum},
journal = {Annals of Pure and Applied Logic},
volume = {81},
year = {1996},
pages = {9--24},
}
@article{MP19,
author = {Monin, Benoit and Patey, Ludovic},
title = {{$\Pi^0_1$}-encodability and omniscient reductions},
journal = {Notre Dame Journal of Formal Logic},
volume = {60},
number = {1},
year = {2019},
pages = {1--12},
doi = {10.1215/00294527-2018-0020},
}
@inproceedings{MR13,
author = {Miyabe, Kenshi and Rute, Jason},
title = {Van {L}ambalgen's theorem for uniformly relative {S}chnorr and computable randomness},
editor = {Downey, Rod and Brendle, J\"{o}rg and Goldblatt, Robert and Kim, Byunghan},
booktitle = {Proceedings of the 12th {A}sian {L}ogic {C}onference},
publisher = {World Scientifc Publishing},
address = {Hackensack, NJ},
year = {2013},
pages = {251--270},
note = {Held in Wellington, December 15--20, 2011},
doi = {10.1142/9789814449274_0014},
}
@article{MR18,
author = {Miller, Joseph S. and Rute, Jason},
title = {Energy randomness},
journal = {Israel Journal of Mathematics},
volume = {227},
number = {1},
year = {2018},
pages = {1--26},
doi = {10.1007/s11856-018-1731-z},
}
@article{MRSS15,
author = {Motto Ros, Luca and Schlicht, Philipp and Selivanov, Victor},
title = {{W}adge-like reducibilities on arbitrary quasi-{P}olish spaces},
journal = {Mathematical Structures in Computer Science},
volume = {25},
year = {2015},
month = {12},
pages = {1705--1754},
doi = {10.1017/S0960129513000339},
}
@article{MS02,
author = {Menni, Mat{\'{\i}}as and Simpson, Alex},
title = {Topological and limit-space subcategories of countably-based equilogical spaces},
journal = {Mathematical Structures in Computer Science},
volume = {12},
number = {6},
year = {2002},
pages = {739--770},
doi = {10.1017/S0960129502003699},
}
@article{MS15,
author = {Miyamoto, Kenji and Schwichtenberg, Helmut},
title = {Program extraction in exact real arithmetic},
journal = {Mathematical Structures in Computer Science},
volume = {25},
year = {2015},
month = {12},
pages = {1692--1704},
doi = {10.1017/S0960129513000327},
}
@article{MS19,
author = {McNicholl, Timothy H. and Stull, Donald M.},
title = {The isometry degree of a computable copy of {$\ell^{p1}$}},
journal = {Computability},
volume = {8},
number = {2},
year = {2019},
pages = {179--189},
}
@article{MS55,
author = {Myhill, J. and Shepherdson, J.},
title = {Effective operations on partial recursive functions},
journal = {Zeitschrift f\"ur Mathematische Logik und Grundlagen der Mathematik},
volume = {1},
year = {1955},
pages = {310--317},
}
@book{MSS18,
title = {Proof and Computation},
editor = {Mainzer, Klaus and Schuster, Peter and Schwichtenberg, Helmut},
publisher = {World Scientific Publishing},
address = {Singapore},
year = {2018},
doi = {10.1142/11005},
}
@inproceedings{MT20,
author = {Merkle, Wolfgang and Titov, Ivan},
title = {Speedable Left-c.e. Numbers},
editor = {Henning Fernau},
booktitle = {Computer Science - Theory and Applications - 15th International Computer Science Symposium in Russia, {CSR} 2020, Yekaterinburg, Russia, June 29 - July 3, 2020, Proceedings},
series = {Lecture Notes in Computer Science},
volume = {12159},
publisher = {Springer},
year = {2020},
pages = {303--313},
doi = {10.1007/978-3-030-50026-9_22},
}
@inproceedings{MTY05,
author = {Mori, Takakazu and Tsujii, Yoshiki and Yasugi, Mariko},
title = {Fine computable functions and effective {F}ine convergence},
editor = {Grubba, Tanja and Hertling, Peter and Tsuiki, Hideki and Weihrauch, Klaus},
booktitle = {Computability and Complexity in Analysis},
series = {Informatik Berichte},
volume = {326},
publisher = {FernUniversit\"at in Hagen},
year = {2005},
month = jul,
pages = {177--197},
note = {Proccedings, Second International Conference, CCA 2005, Kyoto, Japan, August 25--29, 2005},
}
@inproceedings{MTY10,
author = {Mori, Takakazu and Tsujii, Yoshiki and Yasugi, Mariko},
title = {Fine convergence of functions and its effectivization},
booktitle = {Automata, formal languages and algebraic systems},
publisher = {World Sci. Publ., Hackensack, NJ},
year = {2010},
pages = {139--162},
doi = {10.1142/9789814317610_0011},
}
@article{MTY13,
author = {Mori, Takakazu and Tsujii, Yoshiki and Yasugi, Mariko},
title = {Computability of Probability Distributions and Characteristic Functions},
journal = {Logical Methods in Computer Science},
volume = {9},
year = {2013},
pages = {3:9, 11},
doi = {10.2168/LMCS-9(3:9)2013},
}
@inproceedings{MTY97,
author = {Mori, Takakazu and Tsujii, Yoshiki and Yasugi, Mariko},
title = {Computability Structures on Metric Spaces},
editor = {Bridges, Douglas S. and Calude, Cristian S. and Gibbons, Jeremy and Reeves, Steve and Witten, Ian H.},
booktitle = {Combinatorics, Complexity, and Logic},
series = {Discrete Mathematics and Theoretical Computer Science},
publisher = {Springer},
address = {Singapore},
year = {1997},
pages = {351--362},
note = {Proceedings of DMTCS'96},
}
@inproceedings{Mue01,
author = {M{\"u}ller, Norbert Th.},
title = {The {iRRAM}: Exact Arithmetic in {C}++},
editor = {Blanck, Jens and Brattka, Vasco and Hertling, Peter},
booktitle = {Computability and Complexity in Analysis},
series = {Lecture Notes in Computer Science},
volume = {2064},
publisher = {Springer},
address = {Berlin},
year = {2001},
pages = {222--252},
note = {4th International Workshop, CCA 2000, Swansea, UK, September 2000},
}
@inproceedings{Mue02,
author = {M{\"u}ller, Norbert Th.},
title = {Real Numbers and {BDD}s},
editor = {Brattka, Vasco and Schr{\"{o}}der, Matthias and Weihrauch, Klaus},
booktitle = {{CCA} 2002 Computability and Complexity in Analysis},
series = {Electronic Notes in Theoretical Computer Science},
volume = {66},
publisher = {Elsevier},
address = {Amsterdam},
year = {2002},
note = {5th International Workshop, {CCA} 2002, M{\'{a}}laga, Spain, July 12--13, 2002},
}
@inproceedings{Mue86a,
author = {M{\"u}ller, Norbert Th.},
title = {Subpolynomial complexity classes of real functions and real numbers},
editor = {Kott, Laurent},
booktitle = {Proceedings of the 13th International Colloquium on Automata, Languages, and Programming},
series = {Lecture Notes in Computer Science},
volume = {226},
publisher = {Springer},
address = {Berlin},
year = {1986},
pages = {284--293},
}
@inproceedings{Mue87,
author = {M{\"u}ller, Norbert Th.},
title = {Uniform Computational Complexity of {T}aylor series},
editor = {Ottmann, Thomas},
booktitle = {Proceedings of the 14th International Colloquium on Automata, Languages, and Programming},
series = {Lecture Notes in Computer Science},
volume = {267},
publisher = {Springer},
address = {Berlin},
year = {1987},
pages = {435--444},
}
@phdthesis{Mue88,
author = {M{\"u}ller, Norbert Th.},
title = {Untersuchungen zur Komplexit\"at reeller Funktionen},
school = {Fachbereich Mathematik und Informatik},
address = {FernUniversit\"{a}t Hagen},
year = {1988},
}
@inproceedings{Mue93,
author = {M{\"u}ller, Norbert Th.},
title = {Polynomial Time Computation of {T}aylor series},
booktitle = {Proceedings of the 22th JAIIO - Panel'93, Part 2},
year = {1993},
pages = {259--281},
note = {Buenos Aires, 1993},
}
@inproceedings{Mue95,
author = {M{\"u}ller, Norbert Th.},
title = {Constructive aspects of analytic functions},
editor = {Ko, Ker-I and Weihrauch, Klaus},
booktitle = {Computability and Complexity in Analysis},
series = {Informatik Berichte},
volume = {190},
publisher = {FernUniversit\"at Hagen},
year = {1995},
month = sep,
pages = {105--114},
note = {CCA Workshop, Hagen, August 19--20, 1995},
}
@inproceedings{Mue96,
author = {M{\"u}ller, Norbert Th.},
title = {Towards a real {R}eal {RAM}: a prototype using {C$++$}},
editor = {Ko, Ker-I and M\"uller, Norbert and Weihrauch, Klaus},
booktitle = {Computability and Complexity in Analysis},
publisher = {Universit\"at Trier},
year = {1996},
pages = {59--66},
note = {Second CCA Workshop, Trier, August 22--23, 1996},
}
@inproceedings{Mue98,
author = {M{\"u}ller, Norbert Th.},
title = {Implementing limits in an interactive {RealRAM}},
editor = {Chesneaux, J.-M. and J\'{e}z\'{e}quel, F. and Lamotte, J.-L. and Vignes, J.},
booktitle = {Third Real Numbers and Computers Conference},
publisher = {Universit\'{e} Pierre et Marie Curie, Paris},
year = {1998},
pages = {59--66},
note = {Paris, France, April 27-29, 1998},
}
@article{Mue99,
author = {M{\"u}ller, Norbert Th.},
title = {Computability on random variables},
journal = {Theoretical Computer Science},
volume = {219},
number = {1-2},
year = {1999},
pages = {287--299},
}
@article{Muk15,
author = {Mukeru, Safari},
title = {The descriptive complexity of stochastic integration},
journal = {Journal of Complexity},
volume = {31},
number = {1},
year = {2015},
pages = {57--74},
doi = {10.1016/j.jco.2014.07.004},
}
@article{MV21,
author = {Marcone, Alberto and Valenti, Manlio},
title = {The open and clopen {R}amsey theorems in the {W}eihrauch lattice},
journal = {The Journal of Symbolic Logic},
volume = {86},
number = {1},
year = {2021},
pages = {316--351},
doi = {10.1017/jsl.2021.10},
}
@article{MV22,
author = {Marcone, Alberto and Valenti, Manlio},
title = {Effective aspects of {H}ausdorff and {F}ourier dimension },
journal = {Computability},
volume = {11},
number = {3-4},
year = {2022},
pages = {299--333},
doi = {10.3233/COM-210372},
}
@article{MW19,
author = {McKubre-Jordens, Maarten and Wilson, Phillip L.},
title = {Infinity in Computable Probability},
journal = {Journal of Applied Logics - {IfCoLog} Journal of Logics and their Applications},
volume = {6},
number = {7},
year = {2019},
pages = {1253--1261},
}
@article{MY04,
author = {Miyamoto, Shoki and Yoshikawa, Atsushi},
title = {Computable sequences in the {S}obolev spaces},
journal = {Proc. Japan Acad. Ser. A},
volume = {80},
number = {3},
year = {2004},
pages = {15--17},
}
@article{Myc07,
author = {Mycielski, Jan},
title = {Pure mathematics and physical reality (continuity and computability)},
journal = {Journal of Mathematical Sciences},
volume = {146},
number = {1},
year = {2007},
month = {Oct},
pages = {5552--5563},
doi = {10.1007/s10958-007-0368-y},
}
@article{Myh53,
author = {Myhill, John},
title = {Criteria of constructibility for real numbers},
journal = {The Journal of Symbolic Logic},
volume = {18},
number = {1},
year = {1953},
pages = {7--10},
}
@article{Myh71,
author = {Myhill, John},
title = {A recursive function defined on a compact interval and having a continuous derivative that is not recursive},
journal = {Michigan Math.\ J.},
volume = {18},
year = {1971},
pages = {97--98},
}
@article{Myh72,
author = {Myhill, John},
title = {What is a real number?},
journal = {The American Mathematical Monthly},
volume = {79},
year = {1972},
pages = {748--754},
}
@article{Myh75,
author = {John Myhill},
title = {Constructive Set Theory},
journal = {The Journal of Symbolic Logic},
volume = {40},
number = {3},
year = {1975},
pages = {347--382},
}
@article{Myk03,
author = {Mycka, Jerzy},
title = {$mu$--Recursion and infinite limits},
journal = {Theoretical Computer Science},
volume = {302},
year = {2003},
pages = {123--133},
}
@article{Myk03a,
author = {Mycka, Jerzy},
title = {Infinite limits and {R}-recursive functions},
journal = {Acta Cybernetica},
volume = {16},
number = {1},
year = {2003},
pages = {83--91},
}
@article{Myk03b,
author = {Mycka, Jerzy},
title = {Two hierarchies of {$R$}--recursive functions},
journal = {Annales UMCS Informatica Lublin-Polonia AI},
volume = {1},
year = {2003},
pages = {49--59},
}
@article{Myk05,
author = {Mycka, Jerzy},
title = {Real recursive functions and {B}aire classes},
journal = {Fundamenta Informaticae},
volume = {65},
number = {3},
year = {2005},
pages = {263--278},
}
@phdthesis{Myl06,
author = {Mylatz, Uwe},
title = {Vergleich unstetiger {F}unktionen: ``{P}rinciple of {O}mniscience'' und {V}ollst{\"a}ndigkeit in der {$C$}--Hierarchie},
school = {Faculty for Mathematics and Computer Science, University Hagen},
address = {Hagen, Germany},
year = {2006},
note = {{Ph.D.} thesis},
}
@inproceedings{Myr95,
author = {Myrvold, Wayne C.},
title = {Computability in Quantum Mechanics},
editor = {DePauli-Schimanovich, Werner and K\"ohler, Eckehart and Stadler, Friedrich},
booktitle = {The foundational debate},
series = {Vienna Circle Institute Yearbook},
volume = {3},
publisher = {Kluwer},
address = {Dordrecht},
year = {1995},
pages = {33--46},
note = {Conference on the Foundational Debate: Constructivity and Complexity in Logic, Mathematics and Physics held at the University of Vienna, Vienna, September 1994},
}
@inproceedings{Myr97,
author = {Myrvold, Wayne C.},
title = {The decision problem for entanglement},
editor = {Cohen, Robert S. and Horne, Michael and Stachel, John},
booktitle = {Potentiality, Entanglement and Passion-at-a-Distance},
series = {Boston Studies in the Philosophy of Science},
volume = {194},
publisher = {Kluwer},
address = {Dordrecht},
year = {1997},
pages = {177--190},
note = {Symposium on Foundations of Quantum Mechanics held at Boston University, Boston, MA, September 19, 1994},
}
@inproceedings{MYT08,
author = {Mori, Takakazu and Yasugi, Mariko and Tsujii, Yoshiki},
title = {Integral of {F}ine Computable functions and {W}alsh {F}ourier series},
editor = {Dillhage, Ruth and Grubba, Tanja and Sorbi, Andrea and Weihrauch, Klaus and Zhong, Ning},
booktitle = {Proceedings of the Fourth International Conference on Computability and Complexity in Analysis ({CCA} 2007)},
series = {Electronic Notes in Theoretical Computer Science},
volume = {202},
publisher = {Elsevier},
year = {2008},
pages = {279--293},
note = {{CCA} 2007, Siena, Italy, June 16--18, 2007},
}
@article{MYT08a,
author = {Mori, Takakazu and Yasugi, Mariko and Tsujii, Yoshiki},
title = {Effective {F}ine-convergence of {W}alsh-{F}ourier series},
journal = {Mathematical Logic Quarterly},
volume = {54},
number = {5},
year = {2008},
pages = {519--534},
}
@inproceedings{MYT08b,
author = {Mori, Takakazu and Yasugi, Mariko and Tsujii, Yoshiki},
title = {Integral of Two-dimensional {F}ine-computable Functions},
editor = {Brattka, Vasco and Dillhage, Ruth and Grubba, Tanja and Klutsch, Angela},
booktitle = {{CCA} 2008, Fifth International Conference on Computability and Complexity in Analysis},
series = {Electronic Notes in Theoretical Computer Science},
volume = {221},
publisher = {Elsevier},
year = {2008},
pages = {141--152},
note = {{CCA} 2008, Fifth International Conference, Hagen, Germany, August 21--24, 2008},
}
@article{MYT09,
author = {Mori, Takakazu and Yasugi, Mariko and Tsujii, Yoshiki},
title = {Fine-computable functions on the unit square and their integral},
journal = {Journal of Universal Computer Science},
volume = {15},
number = {6},
year = {2009},
pages = {1264--1279},
doi = {http://dx.doi.org/10.3217/jucs-015-06-1264},
}
@inproceedings{MZ08,
author = {M\"uller, Norbert Th. and Zhao, Xishun},
title = {Jordan Areas and Grids},
editor = {Brattka, Vasco and Dillhage, Ruth and Grubba, Tanja and Klutsch, Angela},
booktitle = {{CCA} 2008, Fifth International Conference on Computability and Complexity in Analysis},
series = {Electronic Notes in Theoretical Computer Science},
volume = {221},
publisher = {Elsevier},
year = {2008},
pages = {191--206},
note = {{CCA} 2008, Fifth International Conference, Hagen, Germany, August 21--24, 2008},
}
@article{MZ08a,
author = {Meer, Klaus and Ziegler, Martin},
title = {An explicit solution of {P}ost's problem over the reals},
journal = {Journal of Complexity},
volume = {24},
year = {2008},
pages = {3--15},
doi = {10.1016/j.jco.2006.09.004},
}
@article{MZ68,
author = {Manukjan, S.N. and Zaslavski\u{i}, Igor D.},
title = {Partitionings of the plane by constructive curves ({R}ussian)},
journal = {Trudy Vy\v{c}isl. Centr. Akad. Nauk Armjan. SSR i Erevan. Gos. Univ.},
volume = {5},
year = {1968},
pages = {26--138},
}
@inproceedings{Nak05,
author = {Nakamura, Masahiro},
title = {Ergodic theorems for algorithmically random sequences},
editor = {Dinneen, Michael J. and Speidel, Ulrich and Taylor, Desmond P.},
booktitle = {Proceedings of the {IEEE} {ITSOC} Information Theory Workshop 2005 on Coding and Complexity {ITW} 2005},
year = {2005},
pages = {147--150},
doi = {10.1109/ITW.2005.1531876},
}
@inproceedings{Nan08,
author = {Nandakumar, Satyadev},
title = {Characterization of Constructive Dimension},
editor = {Dillhage, Ruth and Grubba, Tanja and Sorbi, Andrea and Weihrauch, Klaus and Zhong, Ning},
booktitle = {Proceedings of the Fourth International Conference on Computability and Complexity in Analysis ({CCA} 2007)},
series = {Electronic Notes in Theoretical Computer Science},
volume = {202},
publisher = {Elsevier},
year = {2008},
pages = {323--337},
note = {{CCA} 2007, Siena, Italy, June 16--18, 2007},
}
@inproceedings{Nan08a,
author = {Nandakumar, Satyadev},
title = {An effective ergodic theorem and some applications},
booktitle = {{STOC}'08: Proceedings of the 40th Annual ACM Symposium on Theory of Computing},
publisher = {ACM},
address = {New York},
year = {2008},
pages = {39--44},
doi = {10.1145/1374376.1374383},
}
@article{ND06,
author = {N{\'e}meti, Istv{\'a}n and Gyula, D{\'a}vid},
title = {Relativistic computers and the {T}uring barrier},
journal = {Applied Mathematics and Computation},
volume = {178},
number = {1},
year = {2006},
pages = {118--142},
}
@inproceedings{Nem08,
author = {Nemoto, Takako},
title = {Weak weak {K}\"{o}nig's lemma in constructive reverse mathematics},
booktitle = {Proceedings of the 10th Asian Logic Conference (ALC 10)},
year = {2008},
pages = {263---270},
note = {{K}obe University in Kobe, Hyogo, Japan, September 1--6, 2008},
}
@article{Nem20,
author = {Nemoto, Takako},
title = {A constructive proof of the dense existence of nowhere-differentiable functions in {$C[0, 1]$}},
journal = {Computability},
volume = {9},
number = {3-4},
year = {2020},
pages = {315--326},
doi = {10.3233/COM-190247},
}
@inproceedings{Ner57,
author = {Nerode, Anil},
title = {General topology and partial recursive functionals},
booktitle = {Summaries of Talks at the {AMS} Summer Institute in Symbolic Logic},
publisher = {Cornell University Mathematics Department},
year = {1957},
}
@article{Neu15,
author = {Neumann, Eike},
title = {Computational Problems in Metric Fixed Point Theory and their {W}eihrauch Degrees},
journal = {Logical Methods in Computer Science},
volume = {11},
year = {2015},
pages = {4:20,44},
doi = {10.2168/LMCS-11(4:20)2015},
}
@article{Neu21,
author = {Neumann, Eike},
title = {Decision problems for linear recurrences involving arbitrary real numbers},
journal = {Logical Methods in Computer Science},
volume = {17},
number = {3},
year = {2021},
pages = {Paper No. 16, 26},
doi = {10.46298/LMCS-17(3:16)2021},
}
@article{Neu22,
author = {Neumann, Eike},
title = {On the computability of the set of automorphisms of the unit square},
journal = {Theoretical Computer Science},
volume = {903},
year = {2022},
pages = {74--83},
doi = {10.1016/j.tcs.2021.12.019},
}
@article{Neu22a,
author = {Neumann, Eike},
title = {Uniform Envelopes},
journal = {Logical Methods in Computer Science},
volume = {18},
number = {3},
year = {2022},
month = Jul,
pages = {8:1--8:34},
doi = {10.46298/lmcs-18(3:8)2022},
}
@article{NH02,
author = {Nakata, Masahiro and Hayashi, Susumu},
title = {A limiting first order realizability interpretation},
journal = {Sci. Math. Jpn.},
volume = {55},
number = {3},
year = {2002},
pages = {567--580},
}
@article{NH85,
author = {Nerode, Anil and Huang, Wen-Qi},
title = {Application of pure recursion theory in recursive analysis},
journal = {Acta Mathematica Sinica},
volume = {28},
year = {1985},
pages = {625--636},
note = {(in Chinese)},
}
@inproceedings{Nie14,
author = {Nies, Andr{\'e}},
title = {Differentiability of polynomial time computable functions},
editor = {Ernst W. Mayr and Natacha Portier},
booktitle = {31st International Symposium on Theoretical Aspects of Computer Science (STACS 2014)},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
volume = {25},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
year = {2014},
pages = {602--613},
}
@incollection{Nie17,
author = {Nies, Andr{\'e}},
title = {Lowness, Randomness, and Computable Analysis},
editor = {Day, Adam and Fellows, Michael and Greenberg, Noam and Khoussainov, Bakhadyr and Melnikov, Alexander and Rosamond, Frances},
booktitle = {Computability and Complexity: Essays Dedicated to Rodney G. Downey on the Occasion of His 60th Birthday},
series = {Lecture Notes in Computer Science},
volume = {10010},
publisher = {Springer},
address = {Cham},
year = {2017},
pages = {738--754},
doi = {10.1007/978-3-319-50062-1_42},
}
@phdthesis{Niq04,
author = {Niqui, Milad},
title = {Formalizing Exact Arithmetic -- Representations, Algorithms and Proofs},
school = {Institute for Programming Research and Algorithmics, University of Nijmegen},
address = {Nijmegen},
year = {2004},
}
@inproceedings{Niq05,
author = {Niqui, Milad},
title = {Formalising Exact Arithmetic in Type Theory},
editor = {Cooper, Barry S. and L{\"o}we, Benedikt and Torenvliet, Leen},
booktitle = {New Computational Paradigms},
series = {Lecture Notes in Computer Science},
volume = {3526},
publisher = {Springer},
address = {Berlin},
year = {2005},
pages = {368--377},
note = {First Conference on Computability in Europe, CiE 2005, Amsterdam, The Netherlands, June 2005},
}
@inproceedings{Niq06,
author = {Niqui, Milad},
title = {Coinductive field of exact real numbers and general corecursion},
booktitle = {Proceedings of the {E}ighth {W}orkshop on {C}oalgebraic {M}ethods in {C}omputer {S}cience ({CMCS} 2006)},
series = {Electron. Notes Theor. Comput. Sci.},
volume = {164},
publisher = {Elsevier},
address = {Amsterdam},
year = {2006},
pages = {121--139 (electronic)},
}
@article{Niq07,
author = {Niqui, Milad},
title = {Exact arithmetic on the {S}tern-{B}rocot tree},
journal = {Journal of Discrete Algorithms},
volume = {5},
number = {2},
year = {2007},
pages = {356--379},
doi = {10.1016/j.jda.2005.03.007},
}
@article{Niq07a,
author = {Niqui, Milad},
title = {Productivity of {E}dalat-{P}otts Exact Arithmetic in Constructive Type Theory},
journal = {Theory of Computing Systems},
volume = {41},
number = {1},
year = {2007},
pages = {127--154},
}
@article{NKS04,
author = {Nedialkov, Nedialko S. and Kreinovich, Vladik and Starks, Scott A.},
title = {Interval Arithmetic, Affine Arithmetic, Taylor Series Methods: Why, What Next?},
journal = {Numerical Algorithms},
volume = {37},
year = {2004},
pages = {325--336},
}
@proceedings{NKW99,
title = {Computability and Complexity in Analysis},
editor = {Nerode, Anil and Ko, Ker-I and Weihrauch, Klaus},
volume = {219},
publisher = {Elsevier},
address = {Amsterdam},
year = {1999},
note = {Special issue of Theoretical Computer Science},
}
@phdthesis{Nob18,
author = {Nobrega, Hugo},
title = {Games for functions - {B}aire classes, {W}eihrauch degrees, Transfinite Computations, and Ranks},
school = {Institute for Logic, Language and Computation, Universiteit van Amsterdam},
year = {2018},
}
@article{Nog66,
author = {Nogina, Elena Ju.},
title = {Effectively topological spaces},
journal = {Dokl. Akad. Nauk SSSR},
volume = {169},
year = {1966},
pages = {28--31},
}
@article{Nog69,
author = {Nogina, Elena Ju.},
title = {Correlations between certain classes of effectively topological spaces},
journal = {Mat. Zametki},
volume = {5},
year = {1969},
pages = {483--495},
}
@article{Nog78,
author = {Nogina, Elena Ju.},
title = {Enumerable topological spaces ({R}ussian)},
journal = {Zeitschrift f\"ur Mathematische Logik und Grundlagen der Mathematik},
volume = {24},
number = {2},
year = {1978},
pages = {141--176},
}
@incollection{Nog81,
author = {Nogina, Elena Ju.},
title = {The relation between separability and traceability of sets ({R}ussian)},
booktitle = {Mathematical logic and mathematical linguistics},
publisher = {Kalinin. Gos. Univ.},
address = {Klinin},
year = {1981},
pages = {135--144},
}
@article{Nor02,
author = {Normann, Dag},
title = {Exact real number computations relative to hereditarily total functionals},
journal = {Theoretical Computer Science},
volume = {284},
number = {2},
year = {2002},
pages = {437--453},
}
@article{Nor04,
author = {Normann, Dag},
title = {Hierarchies of total functionals over the reals},
journal = {Theoretical Computer Science},
volume = {316},
year = {2004},
pages = {137--151},
}
@article{Nor11,
author = {Normann, Dag},
title = {{B}anach Spaces as Data Types},
journal = {Logical Methods in Computer Science},
volume = {7},
year = {2011},
pages = {2:11, 20},
doi = {10.2168/LMCS-7(2:11)2011},
}
@inproceedings{Nor18,
author = {Normann, Dag},
title = {Functionals of Type 3 as Realisers of Classical Theorems in Analysis},
editor = {Manea, Florin and Miller, Russell G. and Nowotka, Dirk},
booktitle = {Sailing Routes in the World of Computation},
publisher = {Springer},
address = {Cham},
year = {2018},
pages = {318--327},
doi = {10.1007/978-3-319-94418-0_32},
}
@article{Nor21,
author = {Normann, Dag},
title = {Measure-theoretic uniformity and the {S}uslin functional},
journal = {Computability},
volume = {10},
number = {2},
year = {2021},
pages = {91--105},
doi = {10.3233/COM-190248},
}
@inproceedings{NP17,
author = {Nobrega, Hugo and Pauly, Arno},
title = {Game Characterizations and Lower Cones in the {W}eihrauch Degrees},
editor = {Kari, Jarkko and Manea, Florin and Petre, Ion},
booktitle = {Unveiling Dynamics and Complexity},
series = {Lecture Notes in Computer Science},
volume = {10307},
publisher = {Springer},
address = {Cham},
year = {2017},
pages = {327--337},
note = {13th Conference on Computability in Europe, CiE 2017, Turku, Finland, June 12-16, 2017},
doi = {10.1007/978-3-319-58741-7_31},
}
@article{NP18,
author = {Eike Neumann and Arno Pauly},
title = {A topological view on algebraic computation models},
journal = {Journal of Complexity},
volume = {44},
number = {Supplement C},
year = {2018},
pages = {1--22},
doi = {10.1016/j.jco.2017.08.003},
}
@article{NP19,
author = {Nobrega, Hugo and Pauly, Arno},
title = {Game characterizations and lower cones in the {W}eihrauch degrees},
journal = {Logical Methods in Computer Science},
volume = {15},
number = {3},
year = {2019},
pages = {Paper No. 11, 29},
doi = {10.23638/LMCS-15(3:11)2019},
}
@article{NPS18,
author = {Neumann, Eike and Pape, Martin and Streicher, Thomas},
title = {Computability in Basic Quantum Mechanics},
journal = {Logical Methods in Computer Science},
volume = {14},
number = {2},
year = {2018},
month = Jun,
doi = {10.23638/LMCS-14(2:14)2018},
}
@inproceedings{NS15,
author = {Nies, Andr{\'e} and Solecki, Slawomir},
title = {Local Compactness for Computable Polish Metric Spaces is $\Pi_1^1$--complete},
editor = {Beckmann, Arnold and Mitrana, Victor and Soskova, Mariya},
booktitle = {Evolving Computability},
series = {Lecture Notes in Computer Science},
volume = {9136},
publisher = {Springer},
address = {Cham},
year = {2015},
pages = {286--290},
note = {11th Conference on Computability in Europe, CiE 2015, Bucharest, Romania, June 29--July 3, 2015},
doi = {10.1007/978-3-319-20028-6_29},
}
@article{NS19,
author = {Normann, Dag and Sanders, Sam},
title = {Computability theory, nonstandard analysis, and their connections},
journal = {The Journal of Symbolic Logic},
volume = {84},
number = {4},
year = {2019},
pages = {1422--1465},
doi = {10.1017/jsl.2019.69},
}
@article{NS19a,
author = {Normann, Dag and Sanders, Sam},
title = {The strength of compactness in Computability Theory and Nonstandard Analysis},
journal = {Annals of Pure and Applied Logic},
volume = {170},
number = {11},
year = {2019},
pages = {102710},
doi = {10.1016/j.apal.2019.05.007},
}
@article{NS20,
author = {Neumann, Eike and Steinberg, Florian},
title = {Parametrised second-order complexity theory with applications to the study of interval computation},
journal = {Theoretical Computer Science},
volume = {806},
year = {2020},
pages = {281--304},
doi = {10.1016/j.tcs.2019.05.009},
}
@article{NS20a,
author = {Normann, Dag and Sanders, Sam},
title = {Pincherle's theorem in reverse mathematics and computability theory},
journal = {Annals of Pure and Applied Logic},
volume = {171},
number = {5},
year = {2020},
pages = {102788},
doi = {10.1016/j.apal.2020.102788},
}
@inproceedings{NS20b,
author = {Nies, Andr{\'e} and Stephan, Frank},
title = {Randomness and Initial Segment Complexity for Probability Measures},
editor = {Paul, Christophe and Bl{\"a}ser, Markus},
booktitle = {37th International Symposium on Theoretical Aspects of Computer Science ({STACS} 2020)},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
volume = {154},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
year = {2020},
pages = {55:1--55:14},
doi = {10.4230/LIPIcs.STACS.2020.55},
}
@inproceedings{NSW06,
author = {Ng, Keng Meng and Stephan, Frank and Wu, Guohua},
title = {Degrees of Weakly Computable Reals},
editor = {Beckmann, A. and Berger, U. and L{\"o}we, B. and Tucker, J.V.},
booktitle = {Logical Approaches to Computational Barriers},
series = {Lecture Notes in Computer Science},
volume = {3988},
publisher = {Springer},
address = {Berlin},
year = {2006},
pages = {413--422},
note = {Second Conference on Computability in Europe, CiE 2006, Swansea, UK, June 30-July 5, 2006},
}
@article{NTY21,
author = {Nies, Andr{\'e} and Triplett, Marcus A. and Yokoyama, Keita},
title = {The reverse mathematics of theorems of {J}ordan and {L}ebesgue},
journal = {The Journal of Symbolic Logic},
volume = {86},
number = {4},
year = {2021},
pages = {1657--1675},
doi = {10.1017/jsl.2021.16},
}
@article{NTY21a,
author = {Ng, Keng Meng and Tavana, Nazanin R. and Yang, Yue},
title = {A recursion theoretic foundation of computation over real numbers},
journal = {Journal of Logic and Computation},
volume = {31},
number = {7},
year = {2021},
pages = {1660--1689},
doi = {10.1093/logcom/exab042},
}
@article{Nub72,
author = {Nuber, J.A.},
title = {A constructive ergodic theorem},
journal = {Transactions of the American Mathematical Society},
volume = {164},
year = {1972},
pages = {115--137},
}
@article{Nub76,
author = {Nuber, J.A.},
title = {Erratum to: ``{A} constructive ergodic theorem''},
journal = {Transactions of the American Mathematical Society},
volume = {216},
year = {1976},
pages = {393},
}
@inproceedings{NV20,
author = {Nandakumar, Satyadev and Vishnoi, Prateek},
title = {Randomness and Effective Dimension of Continued Fractions},
editor = {Esparza, Javier and Kr{\'a}l', Daniel},
booktitle = {45th International Symposium on Mathematical Foundations of Computer Science ({MFCS} 2020)},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
volume = {170},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
year = {2020},
pages = {73:1--73:13},
doi = {10.4230/LIPIcs.MFCS.2020.73},
}
@article{Oco07,
author = {O'Connor, Russel},
title = {A monadic, functional implementation of real numbers},
journal = {Mathematical Structures in Computer Science},
volume = {17},
year = {2007},
pages = {129--159},
}
@article{OK03,
author = {Ord, Toby and Kieu, Tien D.},
title = {On the existence of a new family of {D}iophantine equations for {$\Omega$}},
journal = {Fundamenta Informaticae},
volume = {56},
number = {3},
year = {2003},
pages = {273--284},
}
@incollection{OK07,
author = {Ord, Toby and Kieu, Tien D.},
title = {{$\Omega$} in number theory},
editor = {Calude, Cristian S.},
booktitle = {Randomness and Complexity},
publisher = {World Scientific},
address = {Hackensack, NJ},
year = {2007},
pages = {161--173},
note = {{F}rom {L}eibniz to {C}haitin, {O}n the occasion of {G}regory {J}. {C}haitin's 60th birthday},
doi = {10.1142/9789812770837_0010},
}
@article{Oli02,
author = {Oliva, Paulo},
title = {On the Computational Complexity of Best $L_1$-approximation},
journal = {Mathematical Logic Quarterly},
volume = {48},
number = {Suppl. 1},
year = {2002},
pages = {66--77},
}
@phdthesis{Oli03,
author = {Oliva, Paulo},
title = {Proof Mining in Subsystems of Analysis},
school = {Department of Computer Science, University of Aarhus, Denmark},
address = {Aarhus},
year = {2003},
}
@article{OP15,
author = {Oliva, Paulo and Powell, Thomas},
title = {A constructive interpretation of {R}amsey's theorem via the product of selection functions},
journal = {Mathematical Structures in Computer Science},
volume = {25},
year = {2015},
month = {12},
pages = {1755--1778},
doi = {10.1017/S0960129513000340},
}
@article{Ord06,
author = {Ord, Toby},
title = {The many forms of hypercomputation},
journal = {Applied Mathematics and Computation},
volume = {178},
number = {1},
year = {2006},
pages = {143--153},
doi = {10.1016/j.amc.2005.09.076},
}
@article{Ore63,
author = {Orevkov, Vladimir P.},
title = {A constructive mapping of the square onto itself displacing every constructive point ({R}ussian)},
journal = {Doklady Akademii Nauk},
volume = {152},
year = {1963},
pages = {55--58},
note = {translated in: Soviet Math. - Dokl., 4 (1963) 1253--1256},
}
@article{Ore63a,
author = {Orevkov, Vladimir P.},
title = {Constructive mappings of polyhedra ({R}ussian)},
journal = {Doklady Akademii Nauk},
volume = {152},
year = {1963},
pages = {278--281},
}
@article{Ore64,
author = {Orevkov, Vladimir P.},
title = {Certain questions of the theory of polynomials with constructive real coefficients ({R}ussian)},
journal = {Trudy Mat. Inst. Steklov.},
volume = {72},
year = {1964},
pages = {462--487},
}
@article{Ore64a,
author = {Orevkov, Vladimir P.},
title = {On constructive mappings of a circle into itself ({R}ussian)},
journal = {Trudy Mat. Inst. Steklov.},
volume = {72},
year = {1964},
pages = {437--461},
}
@article{Ore67,
author = {Orevkov, Vladimir P.},
title = {Certain types of continuity of constructive operators ({R}ussian)},
journal = {Trudy Mat. Inst. Steklov.},
volume = {93},
year = {1967},
pages = {164--186},
}
@article{Ore67a,
author = {Orevkov, Vladimir P.},
title = {Constructive mappings of finite polyhedra ({R}ussian)},
journal = {Trudy Mat. Inst. Steklov.},
volume = {93},
year = {1967},
pages = {142--163},
}
@article{Ore69,
author = {Orevkov, Vladimir P.},
title = {Certain properties of homeomorphisms of constructive metric spaces ({R}ussian)},
journal = {Zap. Nau\v{c}n. Sem. Leningrad. Otdel. Inst. Steklov.},
volume = {16},
year = {1969},
pages = {157--164},
}
@article{Ore71,
author = {Orevkov, Vladimir P.},
title = {The continuity of constructive functionals ({R}ussian)},
journal = {Zap. Nau\v{c}n. Sem. Leningrad. Otdel. Inst. Steklov.},
volume = {20},
year = {1971},
pages = {160--169,287},
}
@article{Ore73,
author = {Orevkov, Vladimir P.},
title = {The complexity of the expansion of algebraic irrationalities in continued fractions ({R}ussian)},
journal = {Trudy Mat. Inst. Steklov.},
volume = {129},
year = {1973},
pages = {24--29,267},
}
@article{Ore74,
author = {Orevkov, Vladimir P.},
title = {A new proof of the uniqueness theorem for constructive differentiable functions of a complex variable ({R}ussian)},
journal = {Zap. Nau\v{c}n. Sem. Leningrad. Otdel. Inst. Steklov.},
volume = {40},
year = {1974},
pages = {119--126,159},
}
@article{OS10,
author = {O'Connor, Russell and Spitters, Bas},
title = {A computer-verified monadic functional implementation of the integral},
journal = {Theoret. Comput. Sci.},
volume = {411},
number = {37},
year = {2010},
pages = {3386--3402},
doi = {10.1016/j.tcs.2010.05.031},
}
@book{OS75,
title = {Problems in the constructive trend in mathematics {VI}},
editor = {Orevkov, V.P. and \v{{S}}anin, N.A.},
publisher = {American Mathematical Society},
address = {Providence, R.I.},
year = {1975},
note = {Proc. Steklov Inst. Math., 129 (1973)},
}
@inproceedings{OS94,
author = {Oliveira, W.R. de and Smyth, M.B.},
title = {Quasimetric {$\Sigma$}-algebras},
booktitle = {SEMISH'94},
publisher = {Sociedade Brasileira de Computa\c{c}\~{a}o},
year = {1994},
pages = {547--561},
note = {XXI Seminario Integrado de Software e Hardware, Minas Gerais, Brazil},
}
@book{Ous66,
author = {Ouspensky, V.A.},
title = {Le{\c{c}}ons sur les fonctions calculables},
series = {Mathematical Logic and the Foundations of Mathematics},
publisher = {Hermann},
address = {Paris},
year = {1966},
note = {(a translation of \cite{Usp60a})},
}
@article{Par03,
author = {Parker, Matthew W.},
title = {Undecidability in {$R^n$}: Riddled Basins, the {KAM} Tori, and the Stability of the Solar System},
journal = {Philosophy of Science},
volume = {70},
year = {2003},
pages = {359--382},
}
@article{Par06,
author = {Parker, Matthew W.},
title = {Three concepts of decidability for general subsets of uncountable spaces},
journal = {Theoretical Computer Science},
volume = {351},
number = {1},
year = {2006},
pages = {2--13},
}
@inproceedings{Pat05,
author = {Pattinson, Dirk},
title = {Domain-Theoretic Formulation of Linear Boundary Value Problems},
editor = {Cooper, Barry S. and L{\"o}we, Benedikt and Torenvliet, Leen},
booktitle = {New Computational Paradigms},
series = {Lecture Notes in Computer Science},
volume = {3526},
publisher = {Springer},
address = {Berlin},
year = {2005},
pages = {385--395},
note = {First Conference on Computability in Europe, CiE 2005, Amsterdam, The Netherlands, June 2005},
}
@article{Pat09,
author = {Pathak, Noopur},
title = {A computational aspect of the {L}ebesgue differentiation theorem},
journal = {Journal of Logic and Analysis},
volume = {1},
year = {2009},
pages = {Paper 9, 15},
doi = {10.4115/jla.2009.1.9},
}
@phdthesis{Pat16,
author = {Patey, Ludovic},
title = {The reverse mathematics of {R}amsey-type theorems},
school = {Universit{\'e} Paris Diderot},
address = {Paris, France},
year = {2016},
}
@article{Pat16a,
author = {Patey, Ludovic},
title = {The weakness of being cohesive, thin or free in reverse mathematics},
journal = {Israel Journal of Mathematics},
volume = {216},
year = {2016},
pages = {905--955},
doi = {10.1007/s11856-016-1433-3},
}
@inproceedings{Pau09,
author = {Pauly, Arno},
title = {How Discontinuous is Computing {N}ash Equilibria? ({E}xtended Abstract)},
editor = {Bauer, Andrej and Hertling, Peter and Ko, Ker-I},
booktitle = {6th International Conference on Computability and Complexity in Analysis (CCA'09)},
series = {OpenAccess Series in Informatics (OASIcs)},
volume = {11},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
year = {2009},
doi = {10.4230/OASIcs.CCA.2009.2271},
}
@article{Pau09b,
author = {Pauly, Arno},
title = {Representing measurement results},
journal = {Journal of Universal Computer Science},
volume = {15},
number = {6},
year = {2009},
pages = {1280--1300},
doi = {10.3217/jucs-015-06-1280},
}
@article{Pau10,
author = {Pauly, Arno},
title = {How Incomputable is Finding {N}ash Equilibria?},
journal = {Journal of Universal Computer Science},
volume = {16},
number = {18},
year = {2010},
pages = {2686--2710},
doi = {10.3217/jucs-016-18-2686},
}
@article{Pau10a,
author = {Pauly, Arno},
title = {On the (semi)lattices induced by continuous reducibilities},
journal = {Mathematical Logic Quarterly},
volume = {56},
number = {5},
year = {2010},
pages = {488--502},
doi = {10.1002/malq.200910104},
}
@phdthesis{Pau11,
author = {Pauly, Arno},
title = {Computable Metamathematics and its Application to Game Theory},
school = {University of Cambridge, Computer Laboratory, Clare College},
address = {Cambridge},
year = {2011},
note = {{Ph.D.} thesis},
}
@inproceedings{Pau12,
author = {Pauly, Arno},
title = {Multi-valued functions in computability theory},
editor = {Cooper, S. Barry and Dawar, Anuj and L{\"o}we, Benedikt},
booktitle = {How the World Computes},
series = {Lecture Notes in Computer Science},
volume = {7318},
publisher = {Springer},
address = {Heidelberg},
year = {2012},
pages = {571--580},
}
@article{Pau16,
author = {Pauly, Arno},
title = {On the topological aspects of the theory of represented spaces},
journal = {Computability},
volume = {5},
number = {2},
year = {2016},
pages = {159--180},
doi = {10.3233/COM-150049},
}
@article{Pau17,
author = {Pauly, Arno},
title = {Many-one reductions and the category of multivalued functions},
journal = {Mathematical Structures in Computer Science},
volume = {27},
number = {3},
year = {2017},
pages = {376--404},
doi = {10.1017/S0960129515000262},
}
@inproceedings{Pau18,
author = {Pauly, Arno},
title = {Enumeration Degrees and Topology},
editor = {Manea, Florin and Miller, Russell G. and Nowotka, Dirk},
booktitle = {Sailing Routes in the World of Computation},
publisher = {Springer},
address = {Cham},
year = {2018},
pages = {328--337},
doi = {10.1007/978-3-319-94418-0_33},
}
@article{PC75,
author = {Pour-El, Marian B. and Caldwell, J.},
title = {On a simple definition of computable functions of a real variable - with applications to functions of a complex variable},
journal = {Zeitschrift f\"ur Mathematische Logik und Grundlagen der Mathematik},
volume = {21},
year = {1975},
pages = {1--19},
}
@inproceedings{PdB14,
author = {Pauly, Arno and de Brecht, Matthew},
title = {Non-deterministic computation and the {J}ayne-{R}ogers Theorem},
editor = {L{\"{o}}we, Benedikt and Winskel, Glynn},
booktitle = {Proceedings 8th International Workshop on Developments in Computational Models, {DCM} 2012, Cambridge, United Kingdom, 17 June 2012.},
series = {Electronic Proceedings in Theoretical Computer Science},
volume = {143},
year = {2014},
pages = {87--96},
doi = {10.4204/EPTCS.143.8},
}
@inproceedings{PdB15,
author = {Pauly, Arno and de Brecht, Matthew},
title = {Descriptive Set Theory in the Category of Represented Spaces},
booktitle = {30th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)},
year = {2015},
pages = {438-449},
doi = {10.1109/LICS.2015.48},
}
@article{PDD17,
author = {Porter, Michelle and Day, Adam and Downey, Rodney},
title = {Notes on computable analysis},
journal = {Theory of Computing Systems},
volume = {60},
number = {1},
year = {2017},
pages = {53--111},
doi = {10.1007/s00224-016-9732-y},
}
@phdthesis{Peg13,
author = {P{\'e}gny, Ma{\"e}l},
title = {Sur les limites empiriques du calcul -- Calculabilit{\'e}, complexit{\'e} et physique},
school = {Universit{\'e} Paris 1 Panth{\'e}on-Sorbonne},
address = {Paris, France},
year = {2013},
}
@article{Peg16,
author = {P{\'e}gny, Ma{\"e}l},
title = {How to Make a Meaningful Comparison of Models: The {C}hurch--{T}uring Thesis Over the Reals},
journal = {Minds and Machines},
volume = {26},
number = {4},
year = {2016},
pages = {359--388},
doi = {10.1007/s11023-016-9407-0},
}
@article{Peq15,
author = {Pequignot, Yann},
title = {A {W}adge hierarchy for second countable spaces},
journal = {Archive for Mathematical Logic},
volume = {54},
year = {2015},
pages = {659--683},
doi = {10.1007/s00153-015-0434-y},
}
@phdthesis{Peq15a,
author = {Pequignot, Yann},
title = {Better-quasi-order: ideals and spaces},
school = {University of Lausanne and University Paris 7},
year = {2015},
}
@inproceedings{Pet15,
author = {Petrakis, Iosif},
title = {Completely Regular {B}ishop Spaces},
editor = {Beckmann, Arnold and Mitrana, Victor and Soskova, Mariya},
booktitle = {Evolving Computability},
series = {Lecture Notes in Computer Science},
volume = {9136},
publisher = {Springer},
address = {Cham},
year = {2015},
pages = {302--312},
note = {11th Conference on Computability in Europe, CiE 2015, Bucharest, Romania, June 29--July 3, 2015},
doi = {10.1007/978-3-319-20028-6_31},
}
@inproceedings{Pet16,
author = {Petrakis, Iosif},
title = {A Direct Constructive Proof of a {S}tone-{W}eierstrass Theorem for Metric Spaces},
editor = {Beckmann, Arnold and Bienvenu, Laurent and Jonoska, Nata\v{s}a},
booktitle = {Pursuit of the Universal},
series = {Lecture Notes in Computer Science},
volume = {9709},
publisher = {Springer},
address = {Switzerland},
year = {2016},
pages = {364--374},
note = {12th Conference on Computability in Europe, CiE 2016, Paris, France, June 27 - July 1, 2016},
doi = {10.1007/978-3-319-40189-8_37},
}
@inproceedings{Pet16a,
author = {Petrakis, Iosif},
title = {A constructive function-theoretic approach to topological compactness},
booktitle = {Proceedings of the 31st {A}nnual {ACM}-{IEEE} {S}ymposium on {L}ogic in {C}omputer {S}cience ({LICS} 2016)},
publisher = {ACM},
address = {New York},
year = {2016},
pages = {10},
}
@incollection{Pet16b,
author = {Petrakis, Iosif},
title = {The {U}rysohn extension theorem for {B}ishop spaces},
booktitle = {Logical foundations of computer science},
series = {Lecture Notes in Comput. Sci.},
volume = {9537},
publisher = {Springer},
address = {Cham},
year = {2016},
pages = {299--316},
doi = {10.1007/978-3-319-27683-0_21},
}
@article{Pet16c,
author = {Petrakis, Iosif},
title = {Limit spaces with approximations},
journal = {Annals of Pure and Applied Logic},
volume = {167},
number = {9},
year = {2016},
pages = {737--752},
doi = {10.1016/j.apal.2016.04.013},
}
@inproceedings{Pet17,
author = {Petrakis, Iosif},
title = {{McShane}-{W}hitney Pairs},
editor = {Kari, Jarkko and Manea, Florin and Petre, Ion},
booktitle = {Unveiling Dynamics and Complexity},
series = {Lecture Notes in Computer Science},
volume = {10307},
publisher = {Springer},
address = {Cham},
year = {2017},
pages = {351--363},
note = {13th Conference on Computability in Europe, CiE 2017, Turku, Finland, June 12-16, 2017},
doi = {10.1007/978-3-319-58741-7_33},
}
@incollection{Pet17a,
author = {Petrakis, Iosif},
title = {A density theorem for hierarchies of limit spaces over separable metric spaces},
booktitle = {Theory and applications of models of computation},
series = {Lecture Notes in Comput. Sci.},
volume = {10185},
publisher = {Springer},
address = {Cham},
year = {2017},
pages = {484--498},
}
@inproceedings{Pet19,
author = {Petrakis, Iosif},
title = {Borel and {B}aire Sets in {B}ishop Spaces},
editor = {Manea, Florin and Martin, Barnaby and Paulusma, Dani{\"e}l and Primiero, Giuseppe},
booktitle = {Computing with Foresight and Industry},
series = {Lecture Notes in Computer Science},
volume = {11558},
publisher = {Springer},
address = {Cham},
year = {2019},
pages = {240--252},
note = {15th Conference on Computability in Europe, CiE 2019, Durham, UK, July 15-19, 2019},
doi = {10.1007/978-3-030-22996-2_21},
}
@article{Pet19a,
author = {Petrakis, Iosif},
title = {Constructive uniformities of pseudometrics and {B}ishop topologies},
journal = {Journal of Logic and Analysis},
volume = {11},
year = {2019},
pages = {Paper No. FT2, 44},
}
@inproceedings{Pet20,
author = {Petrakis, Iosif},
title = {Functions of {B}aire Class One over a {B}ishop Topology},
editor = {Anselmo, Marcella and Della Vedova, Gianluca and Manea, Florin and Pauly, Arno},
booktitle = {Beyond the Horizon of Computability},
publisher = {Springer International Publishing},
address = {Cham},
year = {2020},
pages = {215--227},
doi = {10.1007/978-3-030-51466-2_19},
}
@book{Pet67,
author = {P{\'{e}}ter, R\'{o}zsa},
title = {Recursive Functions},
edition = {3rd},
publisher = {Academic Press},
address = {New York},
year = {1967},
}
@article{PF17,
author = {Pauly, Arno and Fouch{\'e}, Willem L.},
title = {How constructive is constructing measures?},
journal = {Journal of Logic \& Analysis},
volume = {9},
number = {c3},
year = {2017},
pages = {1--44},
doi = {10.4115/jla.2017.9.c3},
}
@article{PFD18,
author = {Pauly, Arno and Fouch{\'{e}}, Willem and Davie, George},
title = {{W}eihrauch-completeness for layerwise computability},
journal = {Logical Methods in Computer Science},
volume = {14},
number = {2},
year = {2018},
month = May,
doi = {10.23638/LMCS-14(2:11)2018},
}
@article{PG16,
author = {Pouly, Amaury and Gra\c{c}a, Daniel S.},
title = {Computational complexity of solving polynomial differential equations over unbounded domains},
journal = {Theoretical Computer Science},
volume = {626},
year = {2016},
pages = {67--82},
doi = {10.1016/j.tcs.2016.02.002},
}
@inproceedings{PHYT12,
author = {Peng, NingNing and Higuchi, Kojiro and Yamazaki, Takeshi and Tanaka, Kazuyuki},
title = {Relative randomness for {M}artin-{L}\"of random sets},
editor = {Cooper, S. Barry and Dawar, Anuj and L{\"o}we, Benedikt},
booktitle = {How the World Computes},
series = {Lecture Notes in Computer Science},
volume = {7318},
publisher = {Springer},
address = {Heidelberg},
year = {2012},
pages = {581--588},
}
@article{Pla99,
author = {Plato, Jan von},
title = {Order in open intervals of computable reals},
journal = {Mathematical Structures in Computer Science},
volume = {9},
year = {1999},
pages = {103--108},
}
@phdthesis{Pop03,
author = {Popa, Gabriela},
title = {A theoretical constructivisation of mathematical economics},
school = {Department of Mathematics \& Statistics, University of Canterbury},
address = {Christchurch},
year = {2003},
}
@article{Por16a,
author = {Porter, Christopher P.},
title = {On analogues of the {C}hurch-{T}uring thesis in algorithmic randomness},
journal = {The Review of Symbolic Logic},
volume = {9},
number = {3},
year = {2016},
pages = {456--479},
doi = {10.1017/S1755020316000113},
}
@incollection{Por20,
author = {Porter, Christopher P.},
title = {Biased algorithmic randomness},
editor = {Franklin, Johanna N.Y. and Porter, Christopher P.},
booktitle = {Algorithmic Randomness: Progress and Prospects},
series = {Lecture Notes in Logic},
volume = {50},
publisher = {Cambridge University Press},
year = {2020},
pages = {206--231},
doi = {10.1017/9781108781718.008},
}
@article{Pot06,
author = {Potgieter, Petrus H.},
title = {Zeno machines and hypercomputation},
journal = {Theoretical Computer Science},
volume = {358},
number = {1},
year = {2006},
pages = {23--33},
}
@article{Pot12,
author = {Potgieter, Paul},
title = {The rapid points of a complex oscillation},
journal = {Logical Methods in Computer Science},
volume = {8},
year = {2012},
pages = {1:23, 11},
doi = {10.2168/LMCS-8(1:23)2012},
}
@article{Pot18,
author = {Paul Potgieter},
title = {Algorithmically random series and {B}rownian motion},
journal = {Annals of Pure and Applied Logic},
volume = {169},
number = {11},
year = {2018},
pages = {1210--1226},
doi = {https://doi.org/10.1016/j.apal.2018.07.001},
}
@article{Pot22,
author = {Potgieter, Petrus H.},
title = {Computability of sets in {E}uclidean space},
journal = {Pure Mathematics and Applications},
volume = {30},
number = {3},
year = {2022},
pages = {65--77},
doi = {10.2478/puma-2022-0025},
}
@article{Pou74,
author = {Pour-El, Marian B.},
title = {Abstract computability and its relation to the general purpose analog computer (some connections between logic, differential equations and analog computers)},
journal = {Trans.\ Amer.\ Math.\ Soc.},
volume = {199},
year = {1974},
pages = {1--28},
}
@inproceedings{Pou95,
author = {Pour-El, Marian B.},
title = {Church's thesis and recursive analysis},
editor = {Ko, Ker-I and Weihrauch, Klaus},
booktitle = {Computability and Complexity in Analysis},
series = {Informatik Berichte},
volume = {190},
publisher = {FernUniversit\"at Hagen},
year = {1995},
month = sep,
pages = {115--118},
note = {CCA Workshop, Hagen, August 19--20, 1995},
}
@inproceedings{Pou98,
author = {Pour-El, Marian B.},
title = {Some Open Problems in Computable Analysis},
editor = {Ko, Ker-I and Nerode, Anil and Pour-El, Marian B. and Weihrauch, Klaus and Wiedermann, Ji{\v{r}}{\'{\i}}},
booktitle = {Computability and Complexity in Analysis},
series = {Informatik Berichte},
volume = {235},
publisher = {FernUniversit\"at Hagen},
year = {1998},
month = aug,
pages = {61},
note = {CCA Workshop, Brno, Czech Republic, August, 1998},
}
@article{Pou99,
author = {Pour-El, Marian B.},
title = {From axiomatics to intrinsic characterization: some open problems in computable analysis},
journal = {Theoretical Computer Science},
volume = {219},
year = {1999},
pages = {319--329},
}
@inproceedings{Pou99a,
author = {Pour-El, Marian B.},
title = {The structure of computability in analysis and physical theory: An extension of {C}hurch's thesis},
editor = {Griffor, Edward R.},
booktitle = {Handbook of Computability Theory},
series = {Studies in Logic and the Foundations of Mathematics},
volume = {140},
publisher = {Elsevier},
address = {Amsterdam},
year = {1999},
pages = {449--471},
}
@article{PR78,
author = {Pour-El, Marian B. and Richards, J. Ian},
title = {Differentiability properties of computable functions - a summary},
journal = {Acta Cybernetica},
volume = {4},
year = {1978},
pages = {123--125},
}
@article{PR79,
author = {Pour-El, Marian B. and Richards, J. Ian},
title = {A computable ordinary differential equation which possesses no computable solution},
journal = {Annals Math.\ Logic},
volume = {17},
year = {1979},
pages = {61--90},
}
@article{PR81,
author = {Pour-El, Marian B. and Richards, J. Ian},
title = {The wave equation with computable initial data such that its unique solution is not computable},
journal = {Advances in Math.},
volume = {39},
year = {1981},
pages = {215--239},
}
@article{PR83,
author = {Pour-El, Marian B. and Richards, J. Ian},
title = {Computability and noncomputability in classical analysis},
journal = {Trans.\ Amer.\ Math.\ Soc.},
volume = {275},
year = {1983},
pages = {539--560},
}
@article{PR83a,
author = {Pour-El, Marian B. and Richards, J. Ian},
title = {Noncomputability in analysis and physics: a complete determination of the class of noncomputable linear operators},
journal = {Advances in Math.},
volume = {48},
year = {1983},
pages = {44--74},
}
@article{PR84,
author = {Pour-El, Marian B. and Richards, J. Ian},
title = {{$L^p$}-computability in recursive analysis},
journal = {Proceedings of the American Mathematical Society},
volume = {92},
year = {1984},
pages = {93--97},
}
@article{PR86,
author = {Pour-El, Marian B. and Richards, J. Ian},
title = {Three theorems on the computability of linear operators, their eigenvalues and eigenvectors},
journal = {S\={u}rikaisekikenky\={u}sho K\={o}ky\={u}roku},
volume = {588},
year = {1986},
pages = {149--161},
}
@article{PR87,
author = {Pour-El, Marian B. and Richards, J. Ian},
title = {The eigenvalues of an effectively determined self-adjoint operator are computable, but the sequence of eigenvalues is not},
journal = {Advances in Math.},
volume = {63},
year = {1987},
pages = {1--41},
}
@book{PR89,
author = {Pour-El, Marian B. and Richards, J. Ian},
title = {Computability in Analysis and Physics},
series = {Perspectives in Mathematical Logic},
publisher = {Springer},
address = {Berlin},
year = {1989},
}
@article{PRS14,
author = {Pathak, Noopur and Rojas, Crist{\'o}bal and Simpson, Stephen G.},
title = {Schnorr randomness and the {L}ebesgue differentiation theorem},
journal = {Proceedings of the American Mathematical Society},
volume = {142},
number = {1},
year = {2014},
pages = {335--349},
doi = {10.1090/S0002-9939-2013-11710-7},
}
@inproceedings{PS06,
author = {Peshev, Peter and Skordev, Dimiter},
title = {A Subrecursive Refinement of the Fundamental Theorem of Algebra},
editor = {Beckmann, A. and Berger, U. and L{\"o}we, B. and Tucker, J.V.},
booktitle = {Logical Approaches to Computational Barriers},
series = {Lecture Notes in Computer Science},
volume = {3988},
publisher = {Springer},
address = {Berlin},
year = {2006},
pages = {435--444},
note = {Second Conference on Computability in Europe, CiE 2006, Swansea, UK, June 30-July 5, 2006},
}
@inproceedings{PS16,
author = {Pauly, Arno and Steinberg, Florian},
title = {Representations of analytic functions and {W}eihrauch degrees},
booktitle = {Computer science---theory and applications},
series = {Lecture Notes in Computer Science},
volume = {9691},
publisher = {Springer},
address = {Cham},
year = {2016},
pages = {367--381},
doi = {10.1007/978-3-319-34171-2_26},
}
@article{PS18,
author = {Pauly, Arno and Steinberg, Florian},
title = {Comparing Representations for Function Spaces in Computable Analysis},
journal = {Theory of Computing Systems},
volume = {62},
year = {2018},
pages = {557--582},
doi = {10.1007/s00224-016-9745-6},
}
@incollection{PSZ20,
author = {Pauly, Arno and Seon, Dongseong and Ziegler, Martin},
title = {Computing {H}aar measures},
editor = {Fern{\'a}ndez, Maribel and Muscholl, Anca},
booktitle = {28th {EACSL} {A}nnual {C}onference on {C}omputer {S}cience {L}ogic},
series = {LIPIcs. Leibniz Int. Proc. Inform.},
volume = {152},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl},
year = {2020},
pages = {34:1--34:17},
doi = {10.4230/LIPIcs.CSL.2020.34},
}
@article{PTD15,
author = {Pourmahdian, Masoud and Tavana, Nazanin R. and Didehvar, Farzad},
title = {Effective metric model theory},
journal = {Mathematical Structures in Computer Science},
volume = {25},
year = {2015},
month = {12},
pages = {1779--1798},
doi = {10.1017/S0960129513000352},
}
@article{Put65,
author = {Putnam, Hilary},
title = {Trial and error predicates and the solution to a problem of {M}ostowski},
journal = {The Journal of Symbolic Logic},
volume = {30},
year = {1965},
pages = {49--57},
}
@article{PWY20,
author = {Pauly, Arno and Westrick, Linda and Yu, Liang},
title = {Lusin's {(N)} and randomness reflection},
journal = {The Journal of Symbolic Logic},
number = {to appear},
year = {2020},
doi = {10.1017/jsl.2020.73},
}
@inproceedings{PZ03,
author = {Pour-El, Marian B. and Zhong, Ning},
title = {Boundary regularity and computability},
editor = {Brattka, Vasco and Schr{\"{o}}der, Matthias and Weihrauch, Klaus and Zhong, Ning},
booktitle = {Computability and Complexity in Analysis},
series = {Informatik Berichte},
volume = {302},
publisher = {FernUniversit\"at in Hagen},
year = {2003},
month = aug,
pages = {325--343},
note = {International Conference, CCA 2003, Cincinnati, USA, August 28--30, 2003},
}
@article{PZ13,
author = {Pauly, Arno and Ziegler, Martin},
title = {Relative computability and uniform continuity of relations},
journal = {Journal of Logic and Analysis},
volume = {5},
number = {7},
year = {2013},
pages = {1--39},
}
@article{PZ15,
author = {Pour-El, I. and Zhong, Ning},
title = {A {T}ribute to {M}arian {B}oykan {P}our-{E}l (1928--2009)},
journal = {Journal of Logic and Computation},
volume = {25},
number = {4},
year = {2015},
pages = {1133--1140},
doi = {10.1093/logcom/exs073},
}
@incollection{PZ16,
author = {Po\c{c}as, Diogo and Zucker, Jeffery},
title = {Fixed point techniques in analog systems},
editor = {B\'{e}lair, Jacques and Frigaard, Ian A. and Kunze, Herb and Makarov, Roman and Melnik, Roderick and Spiteri, Raymond J.},
booktitle = {Mathematical and Computational Approaches in Advancing Modern Science and Engineering},
publisher = {Springer},
address = {Cham},
year = {2016},
pages = {701--711},
}
@article{PZ18,
author = {Po\c{c}as, Diogo and Zucker, Jeffery},
title = {Analog networks on function data streams},
journal = {Computability},
volume = {7},
number = {4},
year = {2018},
pages = {301--322},
doi = {10.3233/com-170077},
}
@article{PZ19,
author = {Po\c{c}as, Diogo and Zucker, Jeffery},
title = {Approximability in the {GPAC}},
journal = {Logical Methods in Computer Science},
volume = {15},
number = {3},
year = {2019},
pages = {Paper No. 24, 24},
doi = {10.23638/LMCS-15(3:24)2019},
}
@article{PZ97,
author = {Pour-El, Marian B. and Zhong, Ning},
title = {The Wave Equation with Computable Initial Data Whose Unique Solution Is Nowhere Computable},
journal = {Mathematical Logic Quarterly},
volume = {43},
number = {4},
year = {1997},
pages = {499--509},
}
@inproceedings{Rai05,
author = {Raichev, Alexander},
title = {Relative Randomness and Real Closed Fields},
editor = {Brattka, Vasco and Staiger, Ludwig and Weihrauch, Klaus},
booktitle = {Proceedings of the 6th Workshop on Computability and Complexity in Analysis},
series = {Electronic Notes in Theoretical Computer Science},
volume = {120},
publisher = {Elsevier},
address = {Amsterdam},
year = {2005},
pages = {135--143},
note = {6th International Workshop, {CCA} 2004, Wittenberg, Germany, August 16--20, 2004},
}
@phdthesis{Rak15,
author = {Rakotoniaina, Tahina},
title = {On the Computational Strength of {R}amsey's Theorem},
school = {Department of Mathematics and Applied Mathematics, University of Cape Town},
address = {Rondebosch, South Africa},
year = {2015},
note = {{Ph.D.} thesis},
}
@article{RB99,
author = {Richman, Fred and Bridges, Douglas S.},
title = {A constructive proof of {G}leason's theorem},
journal = {Journal of Functional Analysis},
volume = {162},
number = {2},
year = {1999},
pages = {287--312},
}
@article{RBCJM81,
author = {Richman, Fred and Bridges, Douglas S. and Calder, Allan and Julian, William and Mines, Ray},
title = {Compactly generated {B}anach spaces},
journal = {Archiv der Mathematik. Archives of Mathematics. Archives Math\'ematiques},
volume = {36},
number = {3},
year = {1981},
pages = {239--243},
}
@article{RBS02,
author = {Richman, Fred and Bridges, Douglas S. and Schuster, Peter},
title = {Trace-class operators},
journal = {Houston Journal of Mathematics},
volume = {28},
number = {3},
year = {2002},
pages = {565--583},
}
@inproceedings{Ret05,
author = {Rettinger, Robert},
title = {A fast algorithm for {J}ulia sets of hyperbolic rational functions},
editor = {Brattka, Vasco and Staiger, Ludwig and Weihrauch, Klaus},
booktitle = {Proceedings of the 6th Workshop on Computability and Complexity in Analysis},
series = {Electronic Notes in Theoretical Computer Science},
volume = {120},
publisher = {Elsevier},
address = {Amsterdam},
year = {2005},
pages = {145--157},
note = {6th International Workshop, {CCA} 2004, Wittenberg, Germany, August 16--20, 2004},
}
@inproceedings{Ret07,
author = {Rettinger, Robert},
title = {Computable {R}iemann Surfaces},
editor = {Cooper, S. Barry and L{\"o}we, Benedikt and Sorbi, Andrea},
booktitle = {Computation and Logic in the Real World},
series = {Lecture Notes in Computer Science},
volume = {4497},
publisher = {Springer},
address = {Berlin},
year = {2007},
pages = {638--647},
note = {Third Conference on Computability in Europe, CiE 2007, Siena, Italy, June 18-23, 2007},
}
@inproceedings{Ret08,
author = {Rettinger, Robert},
title = {On the Computability of {B}lochs Constant},
editor = {Dillhage, Ruth and Grubba, Tanja and Sorbi, Andrea and Weihrauch, Klaus and Zhong, Ning},
booktitle = {Proceedings of the Fourth International Conference on Computability and Complexity in Analysis ({CCA} 2007)},
series = {Electronic Notes in Theoretical Computer Science},
volume = {202},
publisher = {Elsevier},
year = {2008},
pages = {315--322},
note = {{CCA} 2007, Siena, Italy, June 16--18, 2007},
}
@article{Ret08a,
author = {Rettinger, Robert},
title = {{B}loch's Constant is Computable},
journal = {Journal of Universal Computer Science},
volume = {14},
number = {6},
year = {2008},
pages = {896--907},
}
@inproceedings{Ret08b,
author = {Rettinger, Robert},
title = {Lower Bounds on the Continuation of Holomorphic Functions},
editor = {Brattka, Vasco and Dillhage, Ruth and Grubba, Tanja and Klutsch, Angela},
booktitle = {{CCA} 2008, Fifth International Conference on Computability and Complexity in Analysis},
series = {Electronic Notes in Theoretical Computer Science},
volume = {221},
publisher = {Elsevier},
year = {2008},
pages = {207--217},
note = {{CCA} 2008, Fifth International Conference, Hagen, Germany, August 21--24, 2008},
}
@article{Ret12,
author = {Rettinger, Robert},
title = {On computable approximations of {L}andau's constant},
journal = {Log. Methods Comput. Sci.},
volume = {8},
number = {4},
year = {2012},
pages = {4:15, 11},
}
@inproceedings{Ret12a,
author = {Rettinger, Robert},
title = {Compactness and the effectivity of uniformization},
editor = {Cooper, S. Barry and Dawar, Anuj and L{\"o}we, Benedikt},
booktitle = {How the World Computes},
series = {Lecture Notes in Computer Science},
volume = {7318},
publisher = {Springer},
address = {Heidelberg},
year = {2012},
pages = {626--625},
}
@article{Ret17,
author = {Rettinger, Robert},
title = {Effective {R}iemann mappings of multiply connected domains and {R}iemann surfaces},
journal = {Mathematical Structures in Computer Science},
volume = {27},
number = {8},
publisher = {Cambridge University Press},
year = {2017},
pages = {1495--1520},
doi = {10.1017/S0960129516000153},
}
@inproceedings{Ric01,
author = {Richardson, Daniel},
title = {The Uniformity Conjecture},
editor = {Blanck, Jens and Brattka, Vasco and Hertling, Peter},
booktitle = {Computability and Complexity in Analysis},
series = {Lecture Notes in Computer Science},
volume = {2064},
publisher = {Springer},
address = {Berlin},
year = {2001},
pages = {253--272},
note = {4th International Workshop, CCA 2000, Swansea, UK, September 2000},
}
@inproceedings{Ric01b,
author = {Richman, Fred},
title = {Constructive Mathematics without Choice},
editor = {Peter Schuster and Ulrich Berger and Horst Osswald},
booktitle = {Reuniting the Antipodes: Constructive and Nonstandard Views of the Continuum},
series = {Synthese Library},
volume = {306},
publisher = {Kluwer A. P.},
year = {2001},
}
@article{Ric02,
author = {Richman, Fred},
title = {Omniscience Principles and Functions of Bounded Variation},
journal = {Mathematical Logic Quarterly},
volume = {48},
number = {1},
year = {2002},
pages = {111--116},
}
@article{Ric08,
author = {Richman, Fred},
title = {Real numbers and other completions},
journal = {Mathematical Logic Quarterly},
volume = {54},
number = {1},
year = {2008},
pages = {98--108},
doi = {10.1002/malq.200710024},
}
@article{Ric09a,
author = {Richman, Fred},
title = {Intuitionistic notions of boundedness in $\mathbb{N}$},
journal = {Mathematical Logic Quarterly},
volume = {55},
number = {1},
year = {2009},
pages = {31--36},
}
@article{Ric54,
author = {Rice, H. Gordon},
title = {Recursive real numbers},
journal = {Proc.\ Amer.\ Math.\ Soc.},
volume = {5},
year = {1954},
pages = {784--791},
}
@article{Ric68,
author = {Richardson, D.B.},
title = {Some undecidable problems involving elementary functions of a real variable},
journal = {The Journal of Symbolic Logic},
volume = {33},
year = {1968},
pages = {514--520},
}
@article{Ric90,
author = {Richman, Fred},
title = {Polynomials and linear transformations},
journal = {Linear Algebra and its Applications},
volume = {131},
number = {1},
year = {1990},
pages = {131--137},
}
@article{Ric90a,
author = {Fred Richman},
title = {Intuitionism As Generalization},
journal = {Philosophia Mathematica},
volume = {1},
year = {1990},
pages = {124--128},
}
@article{Rob51,
author = {Robinson, R.M.},
title = {Review of ``{P}eter, {R}., {R}ekursive {F}unktionen''},
journal = {The Journal of Symbolic Logic},
volume = {16},
year = {1951},
pages = {280-282},
}
@article{Roe18,
author = {R{\"o}snick-Neugebauer, Carsten},
title = {Closed Sets and Operators thereon: Representations, Computability and Complexity},
journal = {Logical Methods in Computer Science},
volume = {14},
number = {2},
year = {2018},
pages = {2:1, 41},
doi = {10.23638/LMCS-14(2:1)2018},
}
@article{Roj08,
author = {Rojas, Cristobal},
title = {Computability and information in models of randomness and chaos},
journal = {Mathematical Structures in Computer Science},
volume = {18},
number = {2},
year = {2008},
pages = {291--307},
doi = {10.1017/S0960129508006646},
}
@phdthesis{Roj22,
author = {Rojas, Diego Antonio},
title = {Effective convergence in computable measure theory},
school = {Iowa State University},
address = {Ames, Iowa, USA},
year = {2022},
note = {{Ph.D.} thesis},
}
@article{Ros06,
author = {Ross, David A.},
title = {A nonstandard proof of a lemma from constructive measure theory},
journal = {Mathematical Logic Quarterly},
volume = {52},
number = {5},
year = {2006},
pages = {494--497},
}
@article{Ros45,
author = {Rosenbloom, Paul C.},
title = {An elementary constructive proof of the fundamental theorem of algebra},
journal = {American Mathematical Monthly},
volume = {52},
number = {10},
year = {1945},
pages = {562--570},
}
@proceedings{Ros85,
title = {{E}rrett {B}ishop: {R}eflections on him and his research},
editor = {Rosenblatt, M.},
series = {Contemp. Math.},
volume = {39},
publisher = {Amer. Math. Soc.},
address = {Providence},
year = {1985},
}
@phdthesis{Roy11,
author = {Roy, Daniel},
title = {Computability, inference and modeling in probabilistic programming},
school = {Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology},
address = {Cambridge, Boston, USA},
year = {2011},
month = {April},
}
@article{RS15,
author = {Reimann, Jan and Slaman, Theodore A.},
title = {Measures and their random reals},
journal = {Transactions American Mathematical Society},
volume = {367},
number = {7},
year = {2015},
pages = {5081--5097},
doi = {10.1090/S0002-9947-2015-06184-4},
}
@article{RT11,
author = {Rojas, Cristobal and Troubetzkoy, Serge},
title = {Coding discretizations of continuous functions},
journal = {Discrete Math.},
volume = {311},
number = {8-9},
year = {2011},
pages = {620--627},
doi = {10.1016/j.disc.2011.01.011},
}
@article{Ruo04,
author = {Ruohonen, Keijo},
title = {Chomskian hierarchies of families of sets of piecewise continuous functions},
journal = {Theory of Computing Systems},
volume = {37},
number = {5},
year = {2004},
pages = {609--638},
doi = {10.1007/s00224-004-1176-0},
}
@incollection{Ruo94,
author = {Ruohonen, Keijo},
title = {Event detection for {ODE}s and nonrecursive hierarchies},
editor = {Karhum\"{a}ki, J. and Maurer, H. and Rozenberg, G.},
booktitle = {Results and trends in theoretical computer science ({G}raz, 1994)},
series = {Lecture Notes in Computer Science},
volume = {812},
publisher = {Springer},
address = {Berlin},
year = {1994},
pages = {358--371},
doi = {10.1007/3-540-58131-6_59},
}
@article{Ruo97,
author = {Ruohonen, Keijo},
title = {Undecidable event detection problems for {ODE}s of dimension one and two},
journal = {RAIRO Informatique Th\'{e}orique et Applications},
volume = {31},
number = {1},
year = {1997},
pages = {67--79},
doi = {10.1051/ita/1997310100671},
}
@article{Ruo97a,
author = {Ruohonen, Keijo},
title = {Decidability and complexity of event detection problems for {ODE}s},
journal = {Complexity},
volume = {2},
number = {6},
year = {1997},
pages = {41--53},
doi = {10.1002/(SICI)1099-0526(199707/08)2:6<41::AID-CPLX9>3.0.CO;2-K},
}
@phdthesis{Rut13,
author = {Rute, Jason},
title = {Topics in algorithmic randomness and computable analysis},
school = {Carnegie Mellon University},
year = {2013},
month = Aug,
note = {{Ph.D.} thesis},
}
@article{Rut16,
author = {Rute, Jason},
title = {Computable randomness and betting for computable probability spaces},
journal = {Mathematical Logic Quarterly},
volume = {62},
number = {4-5},
year = {2016},
pages = {335--366},
doi = {10.1002/malq.201200089},
}
@article{Rut18,
author = {Rute, Jason},
title = {Schnorr randomness for noncomputable measures},
journal = {Information and Computation},
volume = {258},
year = {2018},
pages = {50--78},
doi = {10.1016/j.ic.2017.10.001},
}
@incollection{Rut20,
author = {Rute, Jason},
title = {Algorithmic randomness and constructive/computable measure theory},
editor = {Franklin, Johanna N.Y. and Porter, Christopher P.},
booktitle = {Algorithmic Randomness: Progress and Prospects},
series = {Lecture Notes in Logic},
volume = {50},
publisher = {Cambridge University Press},
year = {2020},
pages = {58--114},
doi = {10.1017/9781108781718.004},
}
@article{RV90,
author = {Rustem, Berc and Velupillai, Kumaraswamy},
title = {Rationality, computability, and complexity},
journal = {Journal of Economic Dynamics and Control},
volume = {14},
number = {2},
year = {1990},
pages = {419--432},
doi = {10.1016/0165-1889(90)90027-E},
}
@inproceedings{RW02,
author = {Rettinger, Robert and Weihrauch, Klaus},
title = {The Computational Complexity of Some {J}ulia Sets},
editor = {Brattka, Vasco and Schr{\"{o}}der, Matthias and Weihrauch, Klaus},
booktitle = {{CCA} 2002 Computability and Complexity in Analysis},
series = {Electronic Notes in Theoretical Computer Science},
volume = {66},
publisher = {Elsevier},
address = {Amsterdam},
year = {2002},
note = {5th International Workshop, {CCA} 2002, M{\'{a}}laga, Spain, July 12--13, 2002},
}
@inproceedings{RW03,
author = {Rettinger, Robert and Weihrauch, Klaus},
title = {The computational complexity of some {J}ulia sets},
editor = {Goemans, Michel X.},
booktitle = {Proceedings of the 35th Annual {ACM} Symposium on Theory of Computing},
publisher = {ACM Press},
address = {New York},
year = {2003},
pages = {177--185},
note = {San Diego, California, USA, June 9--11, 2003},
}
@article{RW13,
author = {Rettinger, Robert and Weihrauch, Klaus},
title = {Products of effective topological spaces and a uniformly computable {T}ychonoff Theorem},
journal = {Logical Methods in Computer Science},
volume = {9},
year = {2013},
pages = {4:14, 21},
doi = {10.2168/LMCS-9(4:14)2013},
}
@inproceedings{RW96,
author = {Richter, Marcel K. and Wong, Kam-Chau},
title = {Computable Economic Analysis},
editor = {Ko, Ker-I and M\"uller, Norbert and Weihrauch, Klaus},
booktitle = {Computability and Complexity in Analysis},
publisher = {Universit\"at Trier},
year = {1996},
pages = {81--90},
note = {Second CCA Workshop, Trier, August 22--23, 1996},
}
@article{RW99,
author = {Richter, Marcel K. and Wong, Kam-Chau},
title = {Computable preference and utility},
journal = {Journal of Mathematical Economics},
volume = {32},
number = {3},
year = {1999},
pages = {339--354},
}
@article{RW99a,
author = {Richter, Marcel K. and Wong, Kam-Chau},
title = {Non-computability of competitive equilibrium},
journal = {Economic Theory},
volume = {14},
number = {1},
year = {1999},
pages = {1--27},
}
@inproceedings{RWZ08,
author = {Rettinger, Robert and Weihrauch, Klaus and Zhong, Ning},
title = {Complexity of Blowup Problems (Extended Abstract)},
editor = {Brattka, Vasco and Dillhage, Ruth and Grubba, Tanja and Klutsch, Angela},
booktitle = {{CCA} 2008, Fifth International Conference on Computability and Complexity in Analysis},
series = {Electronic Notes in Theoretical Computer Science},
volume = {221},
publisher = {Elsevier},
year = {2008},
pages = {219--230},
note = {{CCA} 2008, Fifth International Conference, Hagen, Germany, August 21--24, 2008},
}
@article{RWZ09,
author = {Rettinger, Robert and Weihrauch, Klaus and Zhong, Ning},
title = {Topological complexity of blowup problems},
journal = {Journal of Universal Computer Science},
volume = {15},
number = {6},
year = {2009},
pages = {1301--1316},
doi = {10.3217/jucs-015-06-1301},
}
@article{RY19,
author = {Rojas, Cristobal and Yampolsky, Michael},
title = {Computational intractability of attractors in the real quadratic family},
journal = {Advances in Mathematics},
volume = {349},
year = {2019},
pages = {941--958},
doi = {10.1016/j.aim.2019.04.033},
}
@inproceedings{RY20,
author = {Rojas, Cristobal and Yampolsky, Michael},
title = {How to lose at {M}onte {C}arlo: a simple dynamical system whose typical statistical behavior is non-computable},
booktitle = {S{TOC} '20---{P}roceedings of the 52nd {A}nnual {ACM} {SIGACT} {S}ymposium on {T}heory of {C}omputing},
publisher = {ACM, New York},
year = {2020},
pages = {1066--1072},
doi = {10.1145/3357713.3384237},
}
@incollection{RY21,
author = {Rojas, Crist{\'o}bal and Yampolsky, Michael},
title = {Computable Geometric Complex Analysis and Complex Dynamics},
editor = {Brattka, Vasco and Hertling, Peter},
booktitle = {Handbook of Computability and Complexity in Analysis},
series = {Theory and Applications of Computability},
publisher = {Springer},
address = {Cham},
year = {2021},
pages = {143--172},
doi = {10.1007/978-3-030-59234-9_5},
}
@article{RY21a,
author = {Rojas, Cristobal and Yampolsky, Michael},
title = {Real quadratic {J}ulia sets can have arbitrarily high complexity},
journal = {Foundations of Computational Mathematics},
volume = {21},
number = {1},
year = {2021},
pages = {59--69},
doi = {10.1007/s10208-020-09457-w},
}
@inproceedings{RZ01,
author = {Rettinger, Robert and Zheng, Xizhong},
title = {Hierarchy of Monotonically Computable Real Numbers},
editor = {Sgall, Ji{\v{r}}{\'{\i}} and Pultr, Ale{\v{s}} and Kolman, Petr},
booktitle = {Mathematical Foundations of Computer Science 2001},
series = {Lecture Notes in Computer Science},
volume = {2136},
publisher = {Springer},
address = {Berlin},
year = {2001},
pages = {633--644},
note = {26th International Symposium, MFCS 2001, Mari{\'{a}}nsk{\'{e}} L{\'{a}}zn{\v{e}}, Czech Republic, August 27-31, 2001},
}
@article{RZ03,
author = {Rettinger, Robert and Zheng, Xizhong},
title = {On the hierarchy and extension of monotonically computable real numbers},
journal = {Journal of Complexity},
volume = {19},
year = {2003},
pages = {672--691},
}
@inproceedings{RZ05,
author = {Rettinger, Robert and Zheng, Xizhong},
title = {On the {T}uring Degrees of Divergence Bounded Computable Reals},
editor = {Cooper, S. Barry and L{\"o}we, Benedikt and Torenvliet, Leen},
booktitle = {New Computational Paradigms},
series = {Lecture Notes in Computer Science},
volume = {3526},
publisher = {Springer},
address = {Berlin},
year = {2005},
pages = {418--428},
note = {{F}irst Conference on Computability in Europe, CiE 2005, Amsterdam, The Netherlands, June 2005},
}
@inproceedings{RZ05b,
author = {Rettinger, Robert and Zheng, Xizhong},
title = {Solovay reducibility on d-c.e. real numbers},
editor = {Wang, Lusheng},
booktitle = {Computing and Combinatorics},
series = {Lecture Notes in Computer Science},
volume = {3595},
publisher = {Springer},
address = {Berlin},
year = {2005},
pages = {359--368},
note = {11th Annual International Conference, COCOON 2005, Kunming, China, August 16--19, 2005},
}
@article{RZ06,
author = {Rettinger, Robert and Zheng, Xizhong},
title = {A hierarchy of {T}uring degrees of divergence bounded computable real numbers},
journal = {Journal of Complexity},
volume = {22},
number = {6},
year = {2006},
pages = {818--826},
}
@inproceedings{RZ09,
author = {Rettinger, Robert and Zheng, Xizhong},
title = {Points on computable curves of computable lengths},
booktitle = {Mathematical Foundations of Computer Science 2009},
series = {Lecture Notes in Computer Science},
volume = {5734},
publisher = {Springer},
address = {Berlin},
year = {2009},
pages = {736--743},
doi = {10.1007/978-3-642-03816-7_62},
}
@incollection{RZ21,
author = {Rettinger, Robert and Zheng, Xizhong},
title = {Computability of Real Numbers},
editor = {Brattka, Vasco and Hertling, Peter},
booktitle = {Handbook of Computability and Complexity in Analysis},
series = {Theory and Applications of Computability},
publisher = {Springer},
address = {Cham},
year = {2021},
pages = {3--28},
doi = {10.1007/978-3-030-59234-9_1},
}
@inproceedings{RZB02,
author = {Rettinger, Robert and Zheng, Xizhong and von Braunm{\"{u}}hl, Burchard},
title = {Computable Real Functions of Bounded Variation and semi-Computable Real Numbers},
editor = {Ibarra, Oscar H. and Zhang, Louxin},
booktitle = {Computing and Combinatorics},
series = {Lecture Notes in Computer Science},
volume = {2387},
publisher = {Springer},
address = {Berlin},
year = {2002},
pages = {47--56},
note = {COCOON 2002, 8th Annual International Conference, August 15--17, 2002, Singapore},
}
@inproceedings{RZGB01,
author = {Rettinger, Robert and Zheng, Xizhong and Gengler, Romain and von Braunm{\"{u}}hl, Burchard},
title = {Monotonically Computable Real Numbers},
editor = {Calude, C.S. and Dinneen, M.J. and Sburlan, S.},
booktitle = {Combinatorics, Computability and Logic},
series = {Discrete Mathematics and Theoretical Computer Science},
publisher = {Springer},
address = {London},
year = {2001},
pages = {187--201},
note = {Proceedings of DMTCS 2001},
}
@inproceedings{RZGB01a,
author = {Rettinger, Robert and Zheng, Xizhong and Gengler, Romain and von Braunm{\"{u}}hl, Burchard},
title = {Weakly Computable Real Numbers and Total Computable Real Functions},
editor = {Wang, Jie},
booktitle = {Computing and Combinatorics},
series = {Lecture Notes in Computer Science},
volume = {2108},
publisher = {Springer},
address = {Berlin},
year = {2001},
pages = {586--595},
note = {7th Annual International Conference, COCOON 2001, Guilin, China, August 20-23, 2001},
}
@article{RZGB02,
author = {Rettinger, Robert and Zheng, Xizhong and Gengler, Romain and von Braunm{\"{u}}hl, Burchard},
title = {Monotonically Computable Real Numbers},
journal = {Mathematical Logic Quarterly},
volume = {48},
number = {3},
year = {2002},
pages = {459--479},
}
@article{Saf12,
author = {Safarik, Pavol},
title = {A quantitative nonlinear strong ergodic theorem for {H}ilbert spaces},
journal = {J. Math. Anal. Appl.},
volume = {391},
number = {1},
year = {2012},
pages = {26--37},
doi = {10.1016/j.jmaa.2012.02.038},
}
@article{Sam03,
author = {Sambin, Giovanni},
title = {Some points in formal topology},
journal = {Theoretical Computer Science},
volume = {305},
year = {2003},
pages = {347--408},
}
@inproceedings{Sam07,
author = {Sambin, Giovanni},
title = {Doing Without {T}uring Machines: Constructivism and Formal Topology},
editor = {Cooper, S. Barry and L{\"o}we, Benedikt and Sorbi, Andrea},
booktitle = {Computation and Logic in the Real World},
series = {Lecture Notes in Computer Science},
volume = {4497},
publisher = {Springer},
address = {Berlin},
year = {2007},
pages = {674--675},
note = {Third Conference on Computability in Europe, CiE 2007, Siena, Italy, June 18-23, 2007},
}
@article{San02,
author = {{\v{S}}anin, N.A.},
title = {On a finitary version of mathematical analysis},
journal = {Annals of Pure and Applied Logic},
volume = {113},
year = {2002},
pages = {261--295},
doi = {10.1016/S0168-0072(01)00062-8},
}
@article{San11,
author = {Sanders, Sam},
title = {{ERNA} and {F}riedman's reverse mathematics},
journal = {The Journal of Symbolic Logic},
volume = {76},
number = {2},
year = {2011},
pages = {637--664},
doi = {10.2178/jsl/1305810768},
}
@article{San13,
author = {Sanders, Sam},
title = {Reverse-engineering reverse mathematics},
journal = {Annals of Pure and Applied Logic},
volume = {164},
number = {5},
year = {2013},
pages = {528--541},
doi = {10.1016/j.apal.2012.11.006},
}
@article{San13a,
author = {Sanders, Sam},
title = {On the connection between nonstandard analysis and constructive analysis},
journal = {Logique et Analyse},
volume = {56},
number = {222},
year = {2013},
pages = {183--210},
}
@inproceedings{San13b,
author = {Sanders, Sam},
title = {On algorithm and robustness in a non-standard sense},
booktitle = {New challenges to philosophy of science},
series = {Philos. Sci. Eur. Perspect.},
volume = {4},
publisher = {Springer},
address = {Dordrecht},
year = {2013},
pages = {99--112},
}
@inproceedings{San16,
author = {Sanders, Sam},
title = {The computational content of nonstandard analysis},
booktitle = {Proceedings {S}ixth {I}nternational {W}orkshop on {C}lassical {L}ogic and {C}omputation},
series = {Electron. Proc. Theor. Comput. Sci. (EPTCS)},
volume = {213},
publisher = {EPTCS},
year = {2016},
pages = {24--40},
doi = {10.4204/EPTCS.213.3},
}
@article{San17,
author = {Sanders, Sam},
title = {{G}rilliot's trick in Nonstandard Analysis},
journal = {Logical Methods in Computer Science},
volume = {13},
number = {4},
year = {2017},
month = Nov,
doi = {10.23638/LMCS-13(4:23)2017},
}
@inproceedings{San17a,
author = {Sanders, Sam},
title = {From nonstandard analysis to various flavours of computability theory},
booktitle = {Theory and applications of models of computation},
series = {Lecture Notes in Computer Science},
volume = {10185},
publisher = {Springer},
address = {Cham},
year = {2017},
pages = {556--570},
}
@article{San18,
author = {Sanders, Sam},
title = {To be or not to be constructive, that is not the question},
journal = {Indagationes Mathematicae},
volume = {29},
number = {1},
year = {2018},
pages = {313--381},
doi = {10.1016/j.indag.2017.05.005},
}
@article{San18a,
author = {Sanders, Sam},
title = {The {G}andy-{H}yland functional and a computational aspect of nonstandard analysis},
journal = {Computability},
volume = {7},
number = {1},
year = {2018},
pages = {7--43},
doi = {10.3233/COM-170074},
}
@inproceedings{San19,
author = {Sanders, Sam},
title = {Nets and Reverse Mathematics},
editor = {Manea, Florin and Martin, Barnaby and Paulusma, Dani{\"e}l and Primiero, Giuseppe},
booktitle = {Computing with Foresight and Industry},
series = {Lecture Notes in Computer Science},
volume = {11558},
publisher = {Springer},
address = {Cham},
year = {2019},
pages = {253--264},
note = {15th Conference on Computability in Europe, CiE 2019, Durham, UK, July 15-19, 2019},
doi = {10.1007/978-3-030-22996-2_22},
}
@article{San21,
author = {Sanders, Sam},
title = {Nets and reverse mathematics},
journal = {Computability},
volume = {10},
number = {1},
year = {2021},
pages = {31--62},
doi = {10.3233/COM-190265},
}
@inproceedings{San21a,
author = {Sanders, Sam},
title = {Splittings and Robustness for the {H}eine-{B}orel Theorem},
editor = {De Mol, Liesbeth and Weiermann, Andreas and Manea, Florin and Fern{\'a}ndez-Duque, David},
booktitle = {Connecting with Computability},
publisher = {Springer},
address = {Cham},
year = {2021},
pages = {395--406},
doi = {10.1007/978-3-030-80049-9_39},
}
@article{San56,
author = {{\v{S}}anin, N.A.},
title = {Some problems of mathematical analysis in the light of constructive logic},
journal = {Zeitschrift f\"ur Mathematische Logik und Grundlagen der Mathematik},
volume = {2},
year = {1956},
pages = {27--36},
}
@book{San68,
author = {{\v{S}}anin, N.A.},
title = {Constructive Real Numbers and Constructive Function Spaces},
series = {Translations of Mathematical Monographs},
volume = {21},
publisher = {American Mathematical Society},
address = {Providence},
year = {1968},
}
@article{San73,
author = {{\v{S}}anin, N.A.},
title = {A hierarchy of ways of understanding judgments in constructive mathematics ({R}ussian)},
journal = {Trudy Mat. Inst. Steklov.},
series = {Problems in the Constructive Trend in Mathematics, 6},
volume = {129},
year = {1973},
pages = {203--266},
}
@article{San74,
author = {{\v{S}}anin, N.A.},
title = {The hierarchy of constructive {B}rouwer functionals ({R}ussian)},
journal = {Zap. Nau\v{c}n. Sem. Otdel. Mat. Inst. Steklov.},
series = {Ivestigations in Constructive Mathematics and Mathematical Logic, {VI}},
volume = {40},
year = {1974},
pages = {142--147},
note = {dedicated to A.A. Markov on the occasion of his seventieth birthday},
}
@article{San79,
author = {{\v{S}}anin, N.A.},
title = {Canonical recursive functions and operations ({R}ussian)},
journal = {Zap. Nau\v{c}n. Sem. Otdel. Mat. Inst. Steklov.},
series = {Studies in Constructive Mathematics and Mathematical Logic, {VIII}},
volume = {88},
year = {1979},
pages = {218--235,246--247},
}
@article{San95,
author = {{\v{S}}anin, N.A.},
title = {Georg {C}antor as the author of constructions that play fundamental roles in constructive mathematics ({R}ussian)},
journal = {Zap. Nau\v{c}n. Sem. Otdel. Mat. Inst. Steklov. POMI},
series = {Issled. po Konstrukt. Mat. i Logike. {IX}},
volume = {220},
year = {1995},
pages = {5--22,246--145},
}
@proceedings{SBO01,
title = {Reuniting the Antipodes - Constructive and Nonstandard Views of the Continuum},
editor = {Schuster, Peter and Berger, Ulrich and Osswald, Horst},
series = {Synthese Library},
volume = {306},
publisher = {Kluwer Academic Publishers},
address = {Dordrecht},
year = {2001},
note = {Proceedings of the symposium held in Venice, May 16--22, 1999},
}
@inproceedings{SBP19,
author = {Schaefer, R.F. and Boche, H. and Poor, H. V.},
title = {Turing Meets {S}hannon: On the Algorithmic Computability of the Capacities of Secure Communication Systems (Invited Paper)},
booktitle = {2019 IEEE 20th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC)},
year = {2019},
pages = {1--5},
doi = {10.1109/SPAWC.2019.8815442},
}
@article{SC10,
author = {Sella, Lorenzo and Collins, Pieter},
title = {Computation of symbolic dynamics for one-dimensional maps},
journal = {J. Comput. Appl. Math.},
volume = {234},
number = {2},
year = {2010},
pages = {418--436},
doi = {10.1016/j.cam.2009.12.034},
}
@article{SC11,
author = {Sella, Lorenzo and Collins, Pieter},
title = {Computation of symbolic dynamics for two-dimensional piecewise-affine maps},
journal = {Discrete Contin. Dyn. Syst. Ser. B},
volume = {15},
number = {3},
year = {2011},
pages = {739--767},
doi = {10.3934/dcdsb.2011.15.739},
}
@article{Sca63,
author = {Scarpellini, Bruno},
title = {Zwei unentscheidbare {P}robleme der {A}nalysis},
journal = {Zeitschrift f\"ur Mathematische Logik und Grundlagen der Mathematik},
volume = {9},
year = {1963},
pages = {265--289},
}
@article{Sca71,
author = {Scarpellini, Bruno},
title = {A model for barrecursion of higher types},
journal = {Compositio Mathematica},
volume = {23},
year = {1971},
pages = {123--153},
}
@article{Sce84,
author = {{\v{S}}{\v{c}}edrov, A.},
title = {Differential equations in constructive analysis and in the recursive realizability topos},
journal = {J. Pure Appl. Algebra},
volume = {33},
year = {1984},
pages = {69--80},
}
@article{Sce86,
author = {{\v{S}}{\v{c}}edrov, A.},
title = {Diagonalization of continuous matrices as a representation of intuitionistic reals},
journal = {Annals of Pure and Applied Logic},
volume = {30},
year = {1986},
pages = {201--206},
}
@article{Sch00a,
author = {Schuster, Peter},
title = {A constructive look at generalized {C}auchy reals},
journal = {Mathematical Logic Quarterly},
volume = {46},
number = {1},
year = {2000},
pages = {125--134},
}
@inproceedings{Sch00c,
author = {Schuster, Peter},
title = {Elementary choiceless constructive analysis},
editor = {Clote, Peter G. and Schwichtenberg, Helmut},
booktitle = {Computer Science Logic},
series = {Lecture Notes in Computer Science},
volume = {1862},
publisher = {Springer},
address = {Berlin},
year = {2000},
pages = {512--526},
note = {14th International Workshop, CSL 2000, Fischbachau, Germany, August 21--26, 2000},
}
@inproceedings{Sch01,
author = {Schr{\"o}der, Matthias},
title = {Admissible Representations of Limit Spaces},
editor = {Blanck, Jens and Brattka, Vasco and Hertling, Peter},
booktitle = {Computability and Complexity in Analysis},
series = {Lecture Notes in Computer Science},
volume = {2064},
publisher = {Springer},
address = {Berlin},
year = {2001},
pages = {273--295},
note = {4th International Workshop, CCA 2000, Swansea, UK, September 2000},
}
@article{Sch02,
author = {Schr{\"o}der, Matthias},
title = {Extended admissibility},
journal = {Theoretical Computer Science},
volume = {284},
number = {2},
year = {2002},
pages = {519--538},
}
@inproceedings{Sch02a,
author = {Schr{\"o}der, Matthias},
title = {A Natural Weak Limit Space with Admissible Representation which is not a Limit Space},
editor = {Brattka, Vasco and Schr{\"{o}}der, Matthias and Weihrauch, Klaus},
booktitle = {{CCA} 2002 Computability and Complexity in Analysis},
series = {Electronic Notes in Theoretical Computer Science},
volume = {66},
publisher = {Elsevier},
address = {Amsterdam},
year = {2002},
note = {5th International Workshop, {CCA} 2002, M{\'{a}}laga, Spain, July 12--13, 2002},
}
@article{Sch02b,
author = {Schr{\"o}der, Matthias},
title = {Effectivity in Spaces with Admissible Multirepresentations},
journal = {Mathematical Logic Quarterly},
volume = {48},
number = {Suppl. 1},
year = {2002},
pages = {78--90},
}
@phdthesis{Sch02c,
author = {Schr{\"o}der, Matthias},
title = {Admissible Representations for Continuous Computations},
school = {Fachbereich Informatik},
address = {FernUniversit\"{a}t Hagen},
year = {2002},
note = {{Ph.D.} thesis},
}
@article{Sch03a,
author = {Schuster, Peter M.},
title = {Unique existence, approximate solutions, and countable choice},
journal = {Theoretical Computer Science},
volume = {305},
year = {2003},
pages = {433--455},
}
@inproceedings{Sch03b,
author = {Schr\"oder, Matthias},
title = {Spaces allowing type-2 complexity theory revisited},
editor = {Brattka, Vasco and Schr{\"{o}}der, Matthias and Weihrauch, Klaus and Zhong, Ning},
booktitle = {Computability and Complexity in Analysis},
series = {Informatik Berichte},
volume = {302},
publisher = {FernUniversit\"at in Hagen},
year = {2003},
month = aug,
pages = {345--361},
note = {International Conference, CCA 2003, Cincinnati, USA, August 28--30, 2003},
}
@article{Sch04,
author = {Schr\"oder, Matthias},
title = {Spaces allowing Type-2 Complexity Theory revisited},
journal = {Mathematical Logic Quarterly},
volume = {50},
number = {4,5},
year = {2004},
pages = {443--459},
}
@article{Sch05,
author = {Schuster, Peter},
title = {What is Continuity, Constructively?},
journal = {Journal of Universal Computer Science},
volume = {11},
number = {12},
year = {2005},
pages = {2076--2085},
}
@article{Sch05a,
author = {Schwichtenberg, Helmut},
title = {A Direct Proof of the Equivalence between {B}rouwer's Fan Theorem and {K}{\"o}nig's Lemma with a Uniqueness Hypothesis},
journal = {Journal of Universal Computer Science},
volume = {11},
number = {12},
year = {2005},
pages = {2086--2095},
}
@inproceedings{Sch06,
author = {Schr\"oder, Matthias},
title = {Admissible Representations in Computable Analysis},
editor = {Beckmann, A. and Berger, U. and L{\"o}we, B. and Tucker, J.V.},
booktitle = {Logical Approaches to Computational Barriers},
series = {Lecture Notes in Computer Science},
volume = {3988},
publisher = {Springer},
address = {Berlin},
year = {2006},
pages = {471--480},
note = {Second Conference on Computability in Europe, CiE 2006, Swansea, UK, June 30-July 5, 2006},
}
@inproceedings{Sch06a,
author = {Schwichtenberg, Helmut},
title = {Inverting Monotone Continuous Functions in Constructive Analysis},
editor = {Beckmann, A. and Berger, U. and L{\"o}we, B. and Tucker, J.V.},
booktitle = {Logical Approaches to Computational Barriers},
series = {Lecture Notes in Computer Science},
volume = {3988},
publisher = {Springer},
address = {Berlin},
year = {2006},
pages = {490--504},
note = {Second Conference on Computability in Europe, CiE 2006, Swansea, UK, June 30-July 5, 2006},
}
@article{Sch06c,
author = {Schuster, Peter},
title = {Unique solutions},
journal = {Mathematical Logic Quarterly},
volume = {52},
number = {6},
year = {2006},
pages = {534--539},
}
@inproceedings{Sch07,
author = {Schr{\"o}der, Matthias},
title = {Admissible representations of probability measures},
editor = {Cenzer, Douglas and Dillhage, Ruth and Grubba, Tanja and Weihrauch, Klaus},
booktitle = {Proceedings of the Third International Conference on Computability and Complexity in Analysis},
series = {Electronic Notes in Theoretical Computer Science},
volume = {167},
publisher = {Elsevier},
address = {Amsterdam},
year = {2007},
pages = {61--78},
note = {{CCA} 2006, Gainesville, Florida, USA, November 1--5, 2006},
}
@inproceedings{Sch07a,
author = {Schuster, Peter},
title = {Problems as Solutions},
editor = {Cooper, S. Barry and L{\"o}we, Benedikt and Sorbi, Andrea},
booktitle = {Computation and Logic in the Real World},
series = {Lecture Notes in Computer Science},
volume = {4497},
publisher = {Springer},
address = {Berlin},
year = {2007},
pages = {676--684},
note = {Third Conference on Computability in Europe, CiE 2007, Siena, Italy, June 18-23, 2007},
}
@article{Sch07b,
author = {Schr{\"o}der, Matthias},
title = {Admissible representations for probability measures},
journal = {Mathematical Logic Quarterly},
volume = {53},
number = {4--5},
year = {2007},
pages = {431--445},
doi = {10.1002/malq.200710010},
}
@article{Sch07d,
author = {Schuster, Peter},
title = {Corrigendum to ``Unique solutions''},
journal = {Mathematical Logic Quarterly},
volume = {53},
number = {2},
year = {2007},
pages = {214},
}
@inproceedings{Sch08,
author = {Schr\"oder, Matthias},
title = {On the Relationship between Filter Spaces and Weak Limit Spaces},
editor = {Dillhage, Ruth and Grubba, Tanja and Sorbi, Andrea and Weihrauch, Klaus and Zhong, Ning},
booktitle = {Proceedings of the Fourth International Conference on Computability and Complexity in Analysis ({CCA} 2007)},
series = {Electronic Notes in Theoretical Computer Science},
volume = {202},
publisher = {Elsevier},
year = {2008},
pages = {267--277},
note = {{CCA} 2007, Siena, Italy, June 16--18, 2007},
}
@article{Sch08a,
author = {Schr\"{o}der, Matthias},
title = {On the Relationship between Filter Spaces and Weak Limit Spaces},
journal = {Journal of Universal Computer Science},
volume = {14},
number = {6},
year = {2008},
pages = {996--1015},
}
@inproceedings{Sch08b,
author = {Schr\"{o}der, Matthias},
title = {An Effective {T}ietze-{U}rysohn Theorem for {QCB}-Spaces (Extended Abstract)},
editor = {Brattka, Vasco and Dillhage, Ruth and Grubba, Tanja and Klutsch, Angela},
booktitle = {{CCA} 2008, Fifth International Conference on Computability and Complexity in Analysis},
series = {Electronic Notes in Theoretical Computer Science},
volume = {221},
publisher = {Elsevier},
year = {2008},
pages = {231--242},
note = {{CCA} 2008, Fifth International Conference, Hagen, Germany, August 21--24, 2008},
}
@article{Sch08c,
author = {Schwichtenberg, Helmut},
title = {Realizability interpretation of proofs in constructive analysis},
journal = {Theory of Computing Systems},
volume = {43},
number = {3-4},
year = {2008},
pages = {583--602},
doi = {10.1007/s00224-007-9027-4},
}
@incollection{Sch09,
author = {Schwichtenberg, Helmut},
title = {Program extraction in constructive analysis},
booktitle = {Logicism, intuitionism, and formalism},
series = {Synth. Libr.},
volume = {341},
publisher = {Springer},
address = {Dordrecht},
year = {2009},
pages = {255--275},
doi = {10.1007/978-1-4020-8926-8_13},
}
@article{Sch09a,
author = {Schr{\"o}der, Matthias},
title = {The sequential topology on {$\Bbb N^{\Bbb N^{\Bbb N}}$} is not regular},
journal = {Mathematical Structures in Computer Science},
volume = {19},
number = {5},
year = {2009},
pages = {943--957},
doi = {10.1017/S0960129509990065},
}
@article{Sch09b,
author = {Schr{\"o}der, Matthias},
title = {An effective {T}ietze-{U}rysohn theorem for {QCB}-spaces},
journal = {Journal of Universal Computer Science},
volume = {15},
number = {6},
year = {2009},
pages = {1317--1336},
}
@article{Sch10,
author = {Schuster, Peter},
title = {Problems, solutions, and completions},
journal = {J. Log. Algebr. Program.},
volume = {79},
number = {1},
year = {2010},
pages = {84--91},
doi = {10.1016/j.jlap.2009.02.007},
}
@article{Sch10a,
author = {Schr{\"o}der, Matthias},
title = {A note on closed subsets in quasi-zero-dimensional {Q}cb-spaces},
journal = {J.UCS},
volume = {16},
number = {18},
year = {2010},
pages = {2711--2732},
}
@phdthesis{Sch16,
author = {Schr{\"o}der, Matthias},
title = {The Coincidence Problem in Computable Analysis},
school = {Department of Mathematics, University of Darmstadt},
address = {Darmstadt, Germany},
year = {2016},
note = {Habilitation Thesis},
}
@article{Sch18,
author = {Schlicht, Philipp},
title = {Continuous reducibility and dimension of metric spaces},
journal = {Archive for Mathematical Logic},
volume = {57},
number = {3},
year = {2018},
pages = {329--359},
doi = {10.1007/s00153-017-0571-6},
}
@incollection{Sch21,
author = {Schr{\"o}der, Matthias},
title = {Admissibly Represented Spaces and {Qcb}-Spaces},
editor = {Brattka, Vasco and Hertling, Peter},
booktitle = {Handbook of Computability and Complexity in Analysis},
series = {Theory and Applications of Computability},
publisher = {Springer},
address = {Cham},
year = {2021},
pages = {305--346},
doi = {10.1007/978-3-030-59234-9\_9},
}
@book{Sch71,
author = {Schnorr, Claus Peter},
title = {Zuf{\"a}lligkeit und Wahrscheinlichkeit},
series = {Lecture Notes in Mathematics},
volume = {218},
publisher = {Springer},
address = {Berlin},
year = {1971},
}
@article{Sch71a,
author = {Schnorr, Claus Peter},
title = {Komplexit{\"a}t von {A}lgorithmen mit {A}nwendung auf die {A}nalysis},
journal = {Archiv f{\"u}r {M}athematische {L}ogik und {G}rundlagenforschung},
volume = {14},
year = {1971},
pages = {54--68},
}
@inproceedings{Sch95,
author = {Schr\"oder, Matthias},
title = {Topological spaces allowing type 2 complexity theory},
editor = {Ko, Ker-I and Weihrauch, Klaus},
booktitle = {Computability and Complexity in Analysis},
series = {Informatik Berichte},
volume = {190},
publisher = {FernUniversit\"at Hagen},
year = {1995},
month = sep,
pages = {41--53},
note = {CCA Workshop, Hagen, August 19--20, 1995},
}
@inproceedings{Sch97,
author = {Schr\"oder, Matthias},
title = {Fast Online Multiplication of Real Numbers},
editor = {Reischuk, R{\"u}diger and Morvan, Michel},
booktitle = {STACS 97},
series = {Lecture Notes in Computer Science},
volume = {1200},
publisher = {Springer},
address = {Berlin},
year = {1997},
pages = {81--92},
note = {14th Annual Symposium on Theoretical Aspects of Computer Science, L{\"u}beck, Germany, February 27--March 1, 1997},
doi = {10.1007/BFb0023450},
}
@inproceedings{Sch98,
author = {Schr\"oder, Matthias},
title = {Effective Metrization of Regular Spaces},
editor = {Ko, Ker-I and Nerode, Anil and Pour-El, Marian B. and Weihrauch, Klaus and Wiedermann, Ji{\v{r}}{\'{\i}}},
booktitle = {Computability and Complexity in Analysis},
series = {Informatik Berichte},
volume = {235},
publisher = {FernUniversit\"at Hagen},
year = {1998},
month = aug,
pages = {63--80},
note = {CCA Workshop, Brno, Czech Republic, August, 1998},
}
@inproceedings{Sch98a,
author = {Schulz, Holger},
title = {Type 2 Theory of Effectivity and Real {PCF}},
editor = {Ko, Ker-I and Nerode, Anil and Pour-El, Marian B. and Weihrauch, Klaus and Wiedermann, Ji{\v{r}}{\'{\i}}},
booktitle = {Computability and Complexity in Analysis},
series = {Informatik Berichte},
volume = {235},
publisher = {FernUniversit\"at Hagen},
year = {1998},
month = aug,
pages = {81--90},
note = {CCA Workshop, Brno, Czech Republic, August, 1998},
}
@article{Sch99,
author = {Schr{\"o}der, Matthias},
title = {Online computations of differentiable functions},
journal = {Theoretical Computer Science},
volume = {219},
year = {1999},
pages = {331--345},
}
@article{Sco68,
author = {Scott, Dana},
title = {Extending the topological interpretation to intuitionistic analysis},
journal = {Compositio Mathematica},
volume = {20},
year = {1968},
pages = {194--210},
}
@inproceedings{Sco70a,
author = {Scott, Dana},
title = {Extending the topological interpretation to intuitionistic analysis. {II}},
editor = {Kino, A. and Myhill, J. and Vesley, R. E.},
booktitle = {Intuitionism and {P}roof {T}heory ({P}roc. {C}onf., {B}uffalo, {N}.{Y}., 1968)},
series = {Studies in Logic and the Foundations of Mathematics},
volume = {60},
publisher = {North-Holland},
address = {Amsterdam},
year = {1970},
pages = {235--255},
}
@article{SCZ12,
author = {Sacerdoti Coen, Claudio and Zoli, Enrico},
title = {Lebesgue's dominated convergence theorem in {B}ishop's style},
journal = {Ann. Pure Appl. Logic},
volume = {163},
number = {2},
year = {2012},
pages = {140--150},
doi = {10.1016/j.apal.2011.06.020},
}
@inproceedings{Sel05,
author = {Selivanov, Victor L.},
title = {Variations on {W}adge Reducibility (Extended Abstract)},
editor = {Brattka, Vasco and Staiger, Ludwig and Weihrauch, Klaus},
booktitle = {Proceedings of the 6th Workshop on Computability and Complexity in Analysis},
series = {Electronic Notes in Theoretical Computer Science},
volume = {120},
publisher = {Elsevier},
address = {Amsterdam},
year = {2005},
pages = {159--171},
note = {6th International Workshop, {CCA} 2004, Wittenberg, Germany, August 16--20, 2004},
}
@article{Sel05a,
author = {Selivanov, Victor L.},
title = {Hierarchies in $\varphi$-spaces and applications},
journal = {Mathematical Logic Quarterly},
volume = {51},
number = {1},
year = {2005},
pages = {45--61},
}
@article{Sel05b,
author = {Selivanov, Victor L.},
title = {Variations on the {W}adge reducibility},
journal = {Siberian Advances in Math.},
volume = {15},
number = {3},
year = {2005},
pages = {44--80},
}
@article{Sel05c,
author = {Selivanov, Victor L.},
title = {Classifying countable {B}oolean terms},
journal = {Algebra and Logic},
volume = {44},
number = {2},
year = {2005},
pages = {95--108},
}
@article{Sel06,
author = {Selivanov, Victor L.},
title = {Towards a descriptive set theory for domain-like structures},
journal = {Theoretical Computer Science},
volume = {365},
number = {3},
year = {2006},
pages = {258--282},
doi = {10.1016/j.tcs.2006.07.053},
}
@article{Sel07,
author = {Selivanov, Victor L.},
title = {Hierarchies of {$\Delta^0_2$}--measurable $k$--partitions},
journal = {Mathematical Logic Quarterly},
volume = {53},
number = {4--5},
year = {2007},
pages = {446--461},
}
@inproceedings{Sel08,
author = {Selivanov, Victor},
title = {On the {W}adge Reducibility of $k$-Partitions},
editor = {Dillhage, Ruth and Grubba, Tanja and Sorbi, Andrea and Weihrauch, Klaus and Zhong, Ning},
booktitle = {Proceedings of the Fourth International Conference on Computability and Complexity in Analysis ({CCA} 2007)},
series = {Electronic Notes in Theoretical Computer Science},
volume = {202},
publisher = {Elsevier},
year = {2008},
pages = {59--71},
note = {{CCA} 2007, Siena, Italy, June 16--18, 2007},
}
@inproceedings{Sel08a,
author = {Selivanov, Victor},
title = {On the Difference Hierarchy in Countably Based $T_0$-Spaces},
editor = {Brattka, Vasco and Dillhage, Ruth and Grubba, Tanja and Klutsch, Angela},
booktitle = {{CCA} 2008, Fifth International Conference on Computability and Complexity in Analysis},
series = {Electronic Notes in Theoretical Computer Science},
volume = {221},
publisher = {Elsevier},
year = {2008},
pages = {257--269},
note = {{CCA} 2008, Fifth International Conference, Hagen, Germany, August 21--24, 2008},
}
@article{Sel13,
author = {Selivanov, Victor},
title = {Total Representations},
journal = {Logical Methods in Computer Science},
volume = {9},
year = {2013},
pages = {2:5, 30},
doi = {10.2168/LMCS-9(2:5)2013},
}
@inproceedings{Sel15,
author = {Selivanov, Victor},
title = {Towards the Effective Descriptive Set Theory},
editor = {Beckmann, Arnold and Mitrana, Victor and Soskova, Mariya},
booktitle = {Evolving Computability},
series = {Lecture Notes in Computer Science},
volume = {9136},
publisher = {Springer},
address = {Cham},
year = {2015},
pages = {324--333},
note = {11th Conference on Computability in Europe, CiE 2015, Bucharest, Romania, June 29--July 3, 2015},
doi = {10.1007/978-3-319-20028-6_33},
}
@inproceedings{Sel17,
author = {Selivanov, Victor L.},
title = {Extending {W}adge Theory to k-Partitions},
editor = {Kari, Jarkko and Manea, Florin and Petre, Ion},
booktitle = {Unveiling Dynamics and Complexity},
series = {Lecture Notes in Computer Science},
volume = {10307},
publisher = {Springer},
address = {Cham},
year = {2017},
pages = {387--399},
note = {13th Conference on Computability in Europe, CiE 2017, Turku, Finland, June 12-16, 2017},
doi = {10.1007/978-3-319-58741-7_36},
}
@article{Sel17a,
author = {Selivanov, Victor},
title = {Towards a descriptive theory of cb0-spaces},
journal = {Mathematical Structures in Computer Science},
volume = {27},
number = {8},
publisher = {Cambridge University Press},
year = {2017},
pages = {1553--1580},
doi = {10.1017/S0960129516000177},
}
@article{Sel20,
author = {Selivanov, Victor},
title = {Q-{W}adge degrees as free structures},
journal = {Computability},
volume = {9},
number = {3-4},
year = {2020},
pages = {327--341},
doi = {10.3233/COM-180241},
}
@article{Sel20a,
author = {Selivanov, V. L.},
title = {On degree spectra of topological spaces},
journal = {Lobachevskii Journal of Mathematics},
volume = {41},
number = {2},
year = {2020},
pages = {252--259},
doi = {10.1134/s1995080220020146},
}
@incollection{Sel20b,
author = {Selivanov, Victor},
title = {Well-quasi orders and hierarchy theory},
booktitle = {Well-quasi orders in computation, logic, language and reasoning---a unifying concept of proof theory, automata theory, formal languages and descriptive set theory},
series = {Trends Log. Stud. Log. Libr.},
volume = {53},
publisher = {Springer, Cham},
year = {2020},
pages = {271--319},
doi = {10.1007/978-3-030-30229-0\_10},
}
@inproceedings{Sel21,
author = {Selivanov, Victor},
title = {Non-collapse of the Effective {W}adge Hierarchy},
editor = {De Mol, Liesbeth and Weiermann, Andreas and Manea, Florin and Fern{\'a}ndez-Duque, David},
booktitle = {Connecting with Computability},
publisher = {Springer},
address = {Cham},
year = {2021},
pages = {407--416},
doi = {10.1007/978-3-030-80049-9_40},
}
@article{Sel21a,
author = {Selivanov, V. L.},
title = {Effective {W}adge hierarchy in computable quasi-{P}olish spaces},
journal = {Siberian Electronic Mathematical Reports},
volume = {18},
number = {1},
year = {2021},
pages = {121--135},
}
@incollection{Sel21b,
author = {Selivanov, Victor},
title = {Non-collapse of the effective {W}adge hierarchy},
booktitle = {Connecting with computability},
series = {Lecture Notes in Comput. Sci.},
volume = {12813},
publisher = {Springer, Cham},
year = {2021},
pages = {407--416},
doi = {10.1007/978-3-030-80049-9\_40},
}
@article{Sel22,
author = {Selivanov, Victor},
title = {A {$Q$}-{W}adge hierarchy in quasi-{P}olish spaces},
journal = {The Journal of Symbolic Logic},
volume = {87},
number = {2},
year = {2022},
pages = {732--757},
doi = {10.1017/jsl.2020.52},
}
@article{Sel22a,
author = {Selivanov, Victor},
title = {Non-collapse of the effective {W}adge hierarchy},
journal = {Computability},
volume = {11},
number = {3-4},
year = {2022},
pages = {335--358},
doi = {10.3233/COM-210376},
}
@phdthesis{Sem09,
author = {Semmes, Brian Thomas},
title = {A Game for the {B}orel Functions},
school = {Institute for Logic, Language and Computation, University of Amsterdam},
year = {2009},
note = {{Ph.D.} thesis},
}
@inproceedings{SG11,
author = {Skordev, Dimiter and Georgiev, Ivan},
title = {On a relative computability notion for real functions},
booktitle = {Models of computation in context},
series = {Lecture Notes in Comput. Sci.},
volume = {6735},
publisher = {Springer},
address = {Heidelberg},
year = {2011},
pages = {270--279},
doi = {10.1007/978-3-642-21875-0_29},
}
@article{She76,
author = {Shepherdson, J.C.},
title = {On the definition of computable function of a real variable},
journal = {Zeitschrift f\"ur Mathematische Logik und Grundlagen der Mathematik},
volume = {22},
year = {1976},
pages = {391--402},
}
@article{Sho59,
author = {Shoenfield, J.R.},
title = {On degrees of unsolvability},
journal = {Ann. of Math.},
volume = {69},
number = {2},
year = {1959},
pages = {644-653},
}
@inproceedings{Sim03,
author = {Simpson, Alex K.},
title = {Towards a Convenient Category of Topological Domains},
booktitle = {Proceedings of the 13th ALGI Workshop, RIMS, Kyoto University},
year = {2003},
}
@article{Sim05,
author = {Simonsen, Jakob G.},
title = {Specker sequences revisited},
journal = {Mathematical Logic Quarterly},
volume = {51},
number = {5},
year = {2005},
pages = {532--540},
}
@article{Sim06,
author = {Simonsen, Jakob G.},
title = {On local non-compactness in recursive mathematics},
journal = {Mathematical Logic Quarterly},
volume = {52},
number = {4},
year = {2006},
pages = {323--330},
}
@article{Sim07,
author = {Simpson, Stephen G.},
title = {Almost everywhere domination and superhighness},
journal = {Mathematical Logic Quarterly},
volume = {53},
number = {4--5},
year = {2007},
pages = {462--482},
}
@article{Sim07a,
author = {Simpson, Stephen G.},
title = {Mass problems and almost everywhere domination},
journal = {Mathematical Logic Quarterly},
volume = {53},
number = {4--5},
year = {2007},
pages = {483--492},
}
@article{Sim08,
author = {Simpson, Stephen G.},
title = {Mass problems and intuitionism},
journal = {Notre Dame Journal of Formal Logic},
volume = {49},
number = {2},
year = {2008},
pages = {127--136},
doi = {10.1215/00294527-2008-002},
}
@book{Sim09,
author = {Simpson, Stephen G.},
title = {Subsystems of Second Order Arithmetic},
edition = {2nd},
series = {Perspectives in Logic},
publisher = {Cambridge University Press},
year = {2009},
}
@article{Sim09a,
author = {Simpson, Stephen G.},
title = {Mass problems and measure-theoretic regularity},
journal = {Bulletin of Symbolic Logic},
volume = {15},
number = {4},
year = {2009},
pages = {385--409},
doi = {10.2178/bsl/1255526079},
}
@article{Sim11,
author = {Simpson, Stephen G.},
title = {Mass problems associated with effectively closed sets},
journal = {The Tohoku Mathematical Journal. Second Series},
volume = {63},
number = {4},
year = {2011},
pages = {489--517},
doi = {10.2748/tmj/1325886278},
}
@book{Sim99,
author = {Simpson, Stephen G.},
title = {Subsystems of Second Order Arithmetic},
series = {Perspectives in Mathematical Logic},
publisher = {Springer},
address = {Berlin},
year = {1999},
}
@article{Sip19,
author = {Sipo\c{s}, Andrei},
title = {Proof mining in {$L_p$} spaces},
journal = {The Journal of Symbolic Logic},
volume = {84},
number = {4},
year = {2019},
pages = {1612--1629},
doi = {10.1017/jsl.2019.55},
}
@article{SK10,
author = {Safarik, Pavol and Kohlenbach, Ulrich},
title = {On the computational content of the {B}olzano-{W}eierstra\ss{} Principle},
journal = {Mathematical Logic Quarterly},
volume = {50},
number = {5},
year = {2010},
pages = {508--532},
}
@article{SK12,
author = {Schade, K. and Kohlenbach, U.},
title = {Effective metastability for modified {H}alpern iterations in {CAT}(0) spaces},
journal = {Fixed Point Theory Appl.},
year = {2012},
pages = {2012:191, 19},
doi = {10.1186/1687-1812-2012-191},
}
@article{Ska83,
author = {Skandalis, Kostas},
title = {Programmability in the set of real numbers and second-order recursion},
journal = {Fundamenta Informaticae},
volume = {6},
number = {3--4},
year = {1983},
pages = {257--274},
}
@article{Ska84,
author = {Skandalis, Kostas},
title = {Programmable real numbers and functions},
journal = {Fundamenta Informaticae},
volume = {7},
number = {1},
year = {1984},
pages = {27--56},
}
@article{Ska90,
author = {Skandalis, Kostas},
title = {Non-Recursiveness of the Operations on Real Numbers},
journal = {Theoretical Computer Science},
volume = {71},
year = {1990},
pages = {425--429},
}
@inproceedings{Ska95,
author = {Skandalis, Kostas},
title = {Program computability over the real numbers},
editor = {Ko, Ker-I and Weihrauch, Klaus},
booktitle = {Computability and Complexity in Analysis},
series = {Informatik Berichte},
volume = {190},
publisher = {FernUniversit\"at Hagen},
year = {1995},
month = sep,
pages = {55--63},
note = {CCA Workshop, Hagen, August 19--20, 1995},
}
@inproceedings{Sko01,
author = {Skordev, Dimiter},
title = {Characterization of the Computable Real Numbers by Means of Primitive Recursive Functions},
editor = {Blanck, Jens and Brattka, Vasco and Hertling, Peter},
booktitle = {Computability and Complexity in Analysis},
series = {Lecture Notes in Computer Science},
volume = {2064},
publisher = {Springer},
address = {Berlin},
year = {2001},
pages = {296--309},
note = {4th International Workshop, CCA 2000, Swansea, UK, September 2000},
}
@article{Sko02,
author = {Skordev, Dimiter},
title = {Computability of Real Numbers by Using a Given Class of Functions in the Set of Natural Numbers},
journal = {Mathematical Logic Quarterly},
volume = {48},
number = {Suppl. 1},
year = {2002},
pages = {91--106},
}
@article{Sko04,
author = {Skordev, Dimiter},
title = {Some subrecursive versions of {G}rzegorczyk's {U}niformity {T}heorem},
journal = {Mathematical Logic Quarterly},
volume = {50},
number = {4,5},
year = {2004},
pages = {520--524},
}
@inproceedings{Sko08,
author = {Skordev, Dimiter},
title = {$\mathcal{E}^2$-computability of $e$, $\pi$ and other famous constants},
editor = {Dillhage, Ruth and Grubba, Tanja and Sorbi, Andrea and Weihrauch, Klaus and Zhong, Ning},
booktitle = {Proceedings of the Fourth International Conference on Computability and Complexity in Analysis ({CCA} 2007)},
series = {Electronic Notes in Theoretical Computer Science},
volume = {202},
publisher = {Elsevier},
year = {2008},
pages = {37--47},
note = {{CCA} 2007, Siena, Italy, June 16--18, 2007},
}
@article{Sko08a,
author = {Skordev, Dimiter},
title = {On the Subrecursive Computability of Several Famous Constants},
journal = {Journal of Universal Computer Science},
volume = {14},
number = {6},
year = {2008},
pages = {861--875},
}
@inproceedings{Sko11,
author = {Skordev, Dimiter},
title = {Uniform computability of real functions},
booktitle = {120 Years Faculty of Mathematics and Informatics, St. Kliment Ohridski University of Sofia, Proceedings},
publisher = {St. Kliment Ohridski University Press},
address = {Sofia},
year = {2011},
pages = {179--185},
}
@article{Sko13,
author = {Skordev, Dimiter},
title = {On Some Computability Notions for Real Functions},
journal = {Computability},
volume = {1},
number = {1},
year = {2013},
pages = {67--73},
doi = {10.3233/COM-13018},
}
@article{Sko13a,
author = {Skordev, Dimiter},
title = {Approximation systems for functions in topological and in metric spaces},
journal = {Logical Methods in Computer Science},
volume = {9},
year = {2013},
pages = {4:15, 21},
doi = {10.2168/LMCS-9(4:15)2013},
}
@article{Sko13b,
author = {Skordev, Dimiter},
title = {A simple characterization of the computability of real functions},
journal = {Annual Univ. Sofia Fac. Math. Inf.},
volume = {101},
year = {2013},
pages = {115--122},
}
@article{Sko16,
author = {Skordev, Dimiter},
title = {Some theorems on passing from local to global presence of properties of functions},
journal = {Logical Methods in Computer Science},
volume = {12},
number = {4},
year = {2016},
month = Oct,
doi = {10.2168/LMCS-12(4:3)2016},
}
@article{Sli64,
author = {Slisenko, A.O.},
title = {Examples of a nondiscontinuous but not continuous constructive operator in a metric space ({R}ussian)},
journal = {Trudy Mat.\ Inst.\ Steklov},
volume = {72},
year = {1964},
pages = {524--532},
note = {(English trans. in AMS Trans. 100, 1972)},
}
@article{Soa69,
author = {Soare, R.I.},
title = {Recursion theory and {D}edekind cuts},
journal = {Trans.\ Amer.\ Math.\ Soc.},
volume = {140},
year = {1969},
pages = {271--294},
}
@article{Soa69a,
author = {Soare, R.I.},
title = {Cohesive sets and recursively enumerable {D}edekind cuts},
journal = {Pacific J.\ Math.},
volume = {31},
year = {1969},
pages = {215--231},
}
@inproceedings{Sol16,
author = {Solomon, Reed},
title = {Computable Reductions and Reverse Mathematics},
editor = {Beckmann, Arnold and Bienvenu, Laurent and Jonoska, Nata\v{s}a},
booktitle = {Pursuit of the Universal},
series = {Lecture Notes in Computer Science},
volume = {9709},
publisher = {Springer},
address = {Switzerland},
year = {2016},
pages = {182--191},
note = {12th Conference on Computability in Europe, CiE 2016, Paris, France, June 27 - July 1, 2016},
doi = {10.1007/978-3-319-40189-8_19},
}
@inproceedings{Spa07,
author = {Spandl, Christoph},
title = {Computing the topological entropy of shifts},
editor = {Cenzer, Douglas and Dillhage, Ruth and Grubba, Tanja and Weihrauch, Klaus},
booktitle = {Proceedings of the Third International Conference on Computability and Complexity in Analysis},
series = {Electronic Notes in Theoretical Computer Science},
volume = {167},
publisher = {Elsevier},
address = {Amsterdam},
year = {2007},
pages = {131--155},
note = {{CCA} 2006, Gainesville, Florida, USA, November 1--5, 2006},
}
@article{Spa07a,
author = {Spandl, Christoph},
title = {Computing the topological entropy of shifts},
journal = {Mathematical Logic Quarterly},
volume = {53},
number = {4--5},
year = {2007},
pages = {493--510},
}
@inproceedings{Spa08,
author = {Spandl, Christoph},
title = {Computability of Topological Pressure for Shifts of Finite Type with Applications in Statistical Physics},
editor = {Dillhage, Ruth and Grubba, Tanja and Sorbi, Andrea and Weihrauch, Klaus and Zhong, Ning},
booktitle = {Proceedings of the Fourth International Conference on Computability and Complexity in Analysis ({CCA} 2007)},
series = {Electronic Notes in Theoretical Computer Science},
volume = {202},
publisher = {Elsevier},
year = {2008},
pages = {385--401},
note = {{CCA} 2007, Siena, Italy, June 16--18, 2007},
}
@article{Spa08a,
author = {Spandl, Christoph},
title = {Computability of Topological Pressure for Sofic Shifts with Applications in Statistical Physics},
journal = {Journal of Universal Computer Science},
volume = {14},
number = {6},
year = {2008},
pages = {876--895},
}
@article{Spa12,
author = {Spandl, Christoph},
title = {Computational complexity of iterated maps on the interval},
journal = {Math. Comput. Simulation},
volume = {82},
number = {8},
year = {2012},
pages = {1459--1477},
doi = {10.1016/j.matcom.2012.02.003},
}
@article{Spe49,
author = {Specker, Ernst},
title = {Nicht konstruktiv beweisbare {S}\"atze der {A}nalysis},
journal = {The Journal of Symbolic Logic},
volume = {14},
number = {3},
year = {1949},
pages = {145--158},
}
@inproceedings{Spe59,
author = {Specker, Ernst},
title = {Der {S}atz vom {M}aximum in der rekursiven {A}nalysis},
editor = {Heyting, A.},
booktitle = {Constructivity in Mathematics},
series = {Studies in Logic and the Foundations of Mathematics},
publisher = {North-Holland},
address = {Amsterdam},
year = {1959},
pages = {254--265},
note = {Proc. Colloq., Amsterdam, Aug. 26--31, 1957},
}
@inproceedings{Spe69,
author = {Specker, Ernst},
title = {The fundamental theorem of algebra in recursive analysis},
editor = {Dejon, B.\ and Henrici, P.},
booktitle = {Constructive Aspects of the Fundamental Theorem of Algebra},
publisher = {Wiley-Interscience},
address = {London},
year = {1969},
pages = {321--329},
}
@article{Spi02,
author = {Spitters, Bas},
title = {Located Operators},
journal = {Mathematical Logic Quarterly},
volume = {48},
number = {Suppl. 1},
year = {2002},
pages = {107--122},
}
@phdthesis{Spi02a,
author = {Spitters, Bas},
title = {Constructive and intuitionistic integration theory and functional analysis},
school = {University of Nijmegen},
year = {2002},
}
@article{Spi05,
author = {Spitters, Bas},
title = {Constructive Results on Operator Algebras},
journal = {Journal of Universal Computer Science},
volume = {11},
number = {12},
year = {2005},
pages = {2096--2113},
}
@article{Spi06,
author = {Spitters, Bas},
title = {A constructive view on ergodic theorems},
journal = {The Journal of Symbolic Logic},
volume = {71},
number = {2},
year = {2006},
pages = {611--623},
}
@article{Spi10,
author = {Spitters, Bas},
title = {Locatedness and overt sublocales},
journal = {Annals of Pure and Applied Logic},
volume = {162},
year = {2010},
pages = {36--54},
}
@article{Spr01,
author = {Spreen, Dieter},
title = {Representations versus numberings: on the relationship of two computability notions},
journal = {Theoretical Computer Science},
volume = {262},
year = {2001},
pages = {473--499},
}
@article{Spr01a,
author = {Spreen, Dieter},
title = {Can partial indexings be totalized?},
journal = {The Journal of Symbolic Logic},
volume = {66},
number = {3},
year = {2001},
pages = {1157--1185},
}
@article{Spr05,
author = {Spreen, Dieter},
title = {Strong reducibilities for partial numberings},
journal = {Archive for Mathematical Logic},
volume = {44},
number = {3},
year = {2005},
pages = {209--217},
}
@inproceedings{Spr08,
author = {Spreen, Dieter},
title = {On the Continuity of Effective Multifunctions},
editor = {Brattka, Vasco and Dillhage, Ruth and Grubba, Tanja and Klutsch, Angela},
booktitle = {{CCA} 2008, Fifth International Conference on Computability and Complexity in Analysis},
series = {Electronic Notes in Theoretical Computer Science},
volume = {221},
publisher = {Elsevier},
year = {2008},
pages = {271--286},
note = {{CCA} 2008, Fifth International Conference, Hagen, Germany, August 21--24, 2008},
}
@inproceedings{Spr08a,
author = {Spreen, Dieter},
title = {On some problems in computable topology},
booktitle = {Logic {C}olloquium 2005},
series = {Lect. Notes Log.},
volume = {28},
publisher = {Assoc. Symbol. Logic},
address = {Urbana, IL},
year = {2008},
pages = {221--254},
}
@article{Spr10,
author = {Spreen, Dieter},
title = {Effectivity and effective continuity of multifunctions},
journal = {J. Symbolic Logic},
volume = {75},
number = {2},
year = {2010},
pages = {602--640},
doi = {10.2178/jsl/1268917496},
}
@article{Spr14,
author = {David A. Sprecher},
title = {On computational algorithms for real-valued continuous functions of several variables},
journal = {Neural Networks},
volume = {59},
year = {2014},
pages = {16--22},
doi = {10.1016/j.neunet.2014.05.015},
}
@article{Spr17,
author = {Spreen, Dieter},
title = {Some results related to the continuity problem},
journal = {Mathematical Structures in Computer Science},
volume = {27},
number = {8},
publisher = {Cambridge University Press},
year = {2017},
pages = {1601--1624},
doi = {10.1017/S0960129516000190},
}
@inproceedings{Spr88,
author = {Spreen, Dieter},
title = {Computable one-to-one enumerations of effective domains},
editor = {Main, M. and Melton, A. and Mislove, M. and Schmidt, D.},
booktitle = {Mathematical foundations of programming language semantics},
series = {Lecture Notes in Computer Science},
volume = {298},
publisher = {Springer},
address = {Berlin},
year = {1988},
pages = {372--384},
}
@inproceedings{Spr90,
author = {Spreen, Dieter},
title = {A characterization of effective topological spaces},
editor = {Ambos-Spies, K. and M{\"u}ller, G. H. and Sacks, G. E.},
booktitle = {Recursion theory week},
series = {Lecture Notes in Mathematics},
volume = {1432},
publisher = {Springer},
address = {Berlin},
year = {1990},
pages = {363--387},
note = {Proceedings of the conference held at the Mathematisches Forschungsinstitut, Oberwolfach, March 19--25, 1989},
}
@article{Spr90a,
author = {Spreen, Dieter},
title = {Computable one-to-one enumerations of effective domains},
journal = {Information and Computation},
volume = {84},
year = {1990},
pages = {26--46},
}
@inproceedings{Spr91,
author = {Spreen, Dieter},
title = {A characterization of effective topological spaces {II}},
booktitle = {Topology and category theory in computer science},
publisher = {Oxford Univ. Press},
address = {New York},
year = {1991},
pages = {231--255},
note = {Oxford, 1989},
}
@inproceedings{Spr92,
author = {Spreen, Dieter},
title = {Effective operators and continuity revisited},
editor = {Nerode, A. and Ta{\u\i}tslin, M.},
booktitle = {Logical foundations of computer science},
series = {Lecture Notes in Computer Science},
volume = {620},
publisher = {Springer},
address = {Berlin},
year = {1992},
pages = {459--469},
}
@article{Spr95,
author = {Spreen, Dieter},
title = {On Some Decision Problems in Programming},
journal = {Information and Computation},
volume = {122},
number = {1},
year = {1995},
pages = {120--139},
note = {(Corrigendum: Inform. and Comp. 148, 241--244, 1999)},
}
@article{Spr96,
author = {Spreen, Dieter},
title = {Effective inseparability in a topological setting},
journal = {Annals of Pure and Applied Logic},
volume = {80},
year = {1996},
pages = {257--275},
}
@article{Spr98,
author = {Spreen, Dieter},
title = {On Effective Topological Spaces},
journal = {The Journal of Symbolic Logic},
volume = {63},
number = {1},
year = {1998},
pages = {185--221},
}
@article{SR97,
author = {Stallworth, Daniel T. and Roush, Fred W.},
title = {An undecidable property of definite integrals},
journal = {Proceedings of the American Mathematical Society},
volume = {125},
number = {7},
year = {1997},
pages = {2147--2148},
}
@inproceedings{SS01,
author = {Spreen, Dieter and Schulz, Holger},
title = {On the equivalence of some approaches to computability on the real line},
editor = {Keimel, Klaus and Zhang, Guo-Qiang and Liu, Ying Ming and Chen, Yixiang},
booktitle = {Domains and processes},
series = {Semantics Structures in Computation},
volume = {1},
publisher = {Kluwer},
address = {Dordrecht},
year = {2001},
pages = {67--101},
note = {Proceedings of the 1st International Symposium on Domain Theory},
}
@article{SS05a,
author = {Sofroniou, Mark and Spaletta, Giulia},
title = {Precise numerical computation},
journal = {The Journal of Logic and Algebraic Programming},
volume = {64},
year = {2005},
pages = {113--134},
}
@article{SS06,
author = {Schr{\"o}der, Matthias and Simpson, Alex},
title = {Representing probability measures using probabilistic processes},
journal = {Journal of Complexity},
volume = {22},
number = {6},
year = {2006},
pages = {768--782},
}
@article{SS07,
author = {Schr{\"o}der, Matthias and Simpson, Alex},
title = {Two preservation results for countable products of sequential spaces},
journal = {Mathematical Structures in Computer Science},
volume = {17},
year = {2007},
pages = {161--172},
}
@inproceedings{SS08,
author = {Selivanova, Svetlana and Selivanov, Victor},
title = {Computing Solutions of Symmetric Hyperbolic Systems of {PDE}'s},
editor = {Brattka, Vasco and Dillhage, Ruth and Grubba, Tanja and Klutsch, Angela},
booktitle = {{CCA} 2008, Fifth International Conference on Computability and Complexity in Analysis},
series = {Electronic Notes in Theoretical Computer Science},
volume = {221},
publisher = {Elsevier},
year = {2008},
pages = {243--255},
note = {{CCA} 2008, Fifth International Conference, Hagen, Germany, August 21--24, 2008},
}
@article{SS09,
author = {Selivanova, Svetlana and Selivanov, Victor},
title = {Computing the Solution Operators of Symmetric Hyperbolic Systems of {PDE}},
journal = {Journal of Universal Computer Science},
volume = {15},
number = {6},
year = {2009},
pages = {1337--1364},
doi = {10.3217/jucs-015-06-1337},
}
@inproceedings{SS14,
author = {Schr{\"o}der, Matthias and Selivanov, Victor},
title = {Hyperprojective hierarchy of {$qcb_0$}-spaces},
editor = {Beckmann, Arnold and Csuhaj-Varj{\'u}, Erzs{\'e}bet and Meer, Klaus},
booktitle = {Language, life, limits},
series = {Lecture Notes in Comput. Sci.},
volume = {8493},
publisher = {Springer, Cham},
year = {2014},
pages = {352--361},
doi = {10.1007/978-3-319-08019-2_37},
}
@article{SS15,
author = {Schr{\"o}der, Matthias and Selivanov, Victor},
title = {Hyperprojective hierarchy of {${\rm qcb}_0$}-spaces},
journal = {Computability},
volume = {4},
number = {1},
year = {2015},
pages = {1--17},
doi = {10.3233/COM-150031},
}
@article{SS15a,
author = {Schr{\"o}der, Matthias and Selivanov, Victor},
title = {Some hierarchies of {$QCB_0$}-spaces},
journal = {Mathematical Structures in Computer Science},
volume = {25},
year = {2015},
month = {12},
pages = {1799--1823},
doi = {10.1017/S0960129513000376},
}
@inproceedings{SS17,
author = {Schr{\"o}der, Matthias and Steinberg, Florian},
title = {Bounded time computation on metric spaces and Banach spaces},
booktitle = {32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)},
year = {2017},
pages = {1-12},
doi = {10.1109/LICS.2017.8005139},
}
@article{SS17a,
author = {Selivanova, Svetlana and Selivanov, Victor},
title = {Computing Solution Operators of Boundary-value Problems for Some Linear Hyperbolic Systems of {PDE}s},
journal = {Logical Methods in Computer Science},
volume = {13},
number = {4},
year = {2017},
month = Nov,
doi = {10.23638/LMCS-13(4:13)2017},
}
@article{SS17b,
author = {Selivanova, S. V. and Selivanov, V. L.},
title = {On constructive number fields and the computability of solutions of partial differential equations},
journal = {Doklady Akademii Nauk},
volume = {477},
number = {3},
year = {2017},
pages = {278--281},
doi = {10.1134/s1064562417060138},
}
@inproceedings{SS18,
author = {Selivanova, Svetlana V. and Selivanov, Victor L.},
title = {Bit complexity of computing solutions for symmetric hyperbolic systems of {PDE}s (extended abstract)},
editor = {Manea, F. and Miller, R.G. and Nowotka, D.},
booktitle = {Sailing Routes in the World of Computation},
series = {Lecture Notes in Computer Science},
volume = {10936},
publisher = {Springer},
address = {Cham},
year = {2018},
pages = {376--385},
doi = {10.1007/978-3-319-94418-0_3},
}
@article{SS21,
author = {Selivanova, Svetlana and Selivanov, Victor},
title = {Bit complexity of computing solutions for symmetric hyperbolic systems of {PDE}s with guaranteed precision},
journal = {Computability},
volume = {10},
number = {2},
year = {2021},
pages = {123--140},
doi = {10.3233/COM-180215},
}
@incollection{SS21a,
author = {Selivanov, Victor and Selivanova, Svetlana},
title = {Primitive recursive ordered fields and some applications},
booktitle = {Computer algebra in scientific computing},
series = {Lecture Notes in Comput. Sci.},
volume = {12865},
publisher = {Springer, Cham},
year = {2021},
pages = {353--369},
doi = {10.1007/978-3-030-85165-1\_20},
}
@article{SS23,
author = {Selivanov, Victor and Selivanova, Svetlana},
title = {Primitive recursive ordered fields and some applications},
journal = {Computability},
volume = {12},
number = {1},
year = {2023},
pages = {71--99},
doi = {10.3233/COM-210386},
}
@inproceedings{SSZ16,
author = {Schr\"oder, Matthias and Steinberg, Florian and Ziegler, Martin},
title = {Average-case bit-complexity theory of real functions},
editor = {Kotsireas, Ilias S. and Rump, Siegfried M. and Yap, Chee K.},
booktitle = {Mathematical aspects of computer and information sciences},
series = {Lecture Notes in Computer Science},
volume = {9582},
publisher = {Springer},
address = {Cham},
year = {2016},
pages = {505--519},
note = {6th International Conference, {MACIS} 2015, Berlin, Germany, November 11--13, 2015, Revised Selected Papers},
}
@article{ST03,
author = {Stoltenberg-Hansen, Viggo and Tucker, John V.},
title = {Computable and continuous partial homomorphisms on metric partial algebras},
journal = {Bulletin of Symbolic Logic},
volume = {9},
number = {3},
year = {2003},
pages = {299--334},
}
@article{ST08,
author = {Sorbi, Andrea and Terwijn, Sebastiaan A.},
title = {Intermediate logics and factors of the {M}edvedev lattice},
journal = {Annals of Pure and Applied Logic},
volume = {155},
number = {2},
year = {2008},
pages = {69--85},
doi = {10.1016/j.apal.2008.03.002},
}
@article{ST90,
author = {Shioji, Naoki and Tanaka, Kazuyuki},
title = {Fixed Point Theory in Weak Second-Order Arithmetic},
journal = {Annals of Pure and Applied Logic},
volume = {47},
year = {1990},
pages = {167--188},
}
@inproceedings{ST95,
author = {Stoltenberg-Hansen, Viggo and Tucker, John V.},
title = {Effective Algebras},
editor = {Abramsky, S. and Gabbay, D.M. and Maibaum, T.S.E.},
booktitle = {Handbook of Logic in Computer Science, Volume 4},
publisher = {Clarendon Press},
address = {Oxford},
year = {1995},
pages = {357--527},
}
@article{ST99,
author = {Stoltenberg-Hansen, Viggo and Tucker, John V.},
title = {Concrete models of computation for topological algebras},
journal = {Theoretical Computer Science},
volume = {219},
year = {1999},
pages = {347--378},
}
@article{Sta02,
author = {Staiger, Ludwig},
title = {How Large is the Set of Disjunctive Sequences?},
journal = {Journal of Universal Computer Science},
volume = {8},
number = {2},
year = {2002},
pages = {348--362},
}
@article{Sta02a,
author = {Staiger, Ludwig},
title = {The {K}olmogorov complexity of real numbers},
journal = {Theoretical Computer Science},
volume = {284},
number = {2},
year = {2002},
pages = {455--466},
}
@inproceedings{Sta08,
author = {Staiger, Ludwig},
title = {On Oscillation-free $\varepsilon$-random Sequences},
editor = {Brattka, Vasco and Dillhage, Ruth and Grubba, Tanja and Klutsch, Angela},
booktitle = {{CCA} 2008, Fifth International Conference on Computability and Complexity in Analysis},
series = {Electronic Notes in Theoretical Computer Science},
volume = {221},
publisher = {Elsevier},
year = {2008},
pages = {287--297},
note = {{CCA} 2008, Fifth International Conference, Hagen, Germany, August 21--24, 2008},
}
@article{Sta17,
author = {Staiger, Ludwig},
title = {Exact Constructive and Computable Dimensions},
journal = {Theory of Computing Systems},
volume = {61},
number = {4},
year = {2017},
pages = {1288--1314},
doi = {10.1007/s00224-017-9790-9},
}
@inproceedings{Sta99,
author = {Staiger, Ludwig},
title = {The {K}olmogorov Complexity of Real Numbers},
editor = {Ciobanu, G. and Paun, Gh.},
booktitle = {Fundamentals of Computation Theory},
series = {Lecture Notes in Computer Science},
volume = {1684},
publisher = {Springer},
address = {Berlin},
year = {1999},
pages = {536--546},
}
@article{Ste17,
author = {Steinberg, Florian},
title = {Complexity theory for spaces of integrable functions},
journal = {Logical Methods in Computer Science},
volume = {13},
number = {3},
year = {2017},
pages = {Paper No. 21, 39},
doi = {10.23638/LMCS-13(3:21)2017},
}
@inproceedings{Ste21,
author = {Steifer, Tomasz},
title = {Simple Betting and Stochasticity},
editor = {De Mol, Liesbeth and Weiermann, Andreas and Manea, Florin and Fern{\'a}ndez-Duque, David},
booktitle = {Connecting with Computability},
publisher = {Springer},
address = {Cham},
year = {2021},
pages = {424--433},
doi = {10.1007/978-3-030-80049-9_42},
}
@phdthesis{Ste99,
author = {Stewart, Kristian Jon},
title = {Concrete and Abstract Models of Computation over Metric Algebras},
school = {University of Wales Swansea},
address = {Singleton Park, Swansea, SA2 8PP, UK},
year = {1999},
}
@inproceedings{STT19,
author = {Steinberg, Florian and Th\'{e}ry, Laurent and Thies, Holger},
title = {Quantitative continuity and computable analysis in {C}oq},
booktitle = {10th {I}nternational {C}onference on {I}nteractive {T}heorem {P}roving},
series = {LIPIcs. Leibniz Int. Proc. Inform.},
volume = {141},
publisher = {Schloss Dagstuhl. Leibniz-Zent. Inform.},
address = {Wadern},
year = {2019},
pages = {Art. No. 28, 21},
}
@article{STT21,
author = {Steinberg, Florian and Thery, Laurent and Thies, Holger},
title = {Computable analysis and notions of continuity in {Coq}},
journal = {Logical Methods in Computer Science},
volume = {17},
number = {2},
year = {2021},
pages = {16:1--16:43},
doi = {10.23638/LMCS-17(2:16)2021},
}
@inproceedings{Stu18,
author = {Stull, Donald M.},
title = {Results on the Dimension Spectra of Planar Lines},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science ({MFCS} 2018)},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
volume = {117},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
year = {2018},
pages = {79:1--79:15},
doi = {10.4230/LIPIcs.MFCS.2018.79},
}
@incollection{Stu20,
author = {Stull, Donald M.},
title = {Resource bounded randomness and its applications},
editor = {Franklin, Johanna N.Y. and Porter, Christopher P.},
booktitle = {Algorithmic Randomness: Progress and Prospects},
series = {Lecture Notes in Logic},
volume = {50},
publisher = {Cambridge University Press},
year = {2020},
pages = {301--348},
doi = {10.1017/9781108781718.010},
}
@article{STY02,
author = {Simpson, Stephen G. and Tanaka, Kazuyuki and Yamazaki, Takeshi},
title = {Some conservation results on weak {K}{\"o}nig's lemma},
journal = {Annals of Pure and Applied Logic},
volume = {118},
number = {1-2},
year = {2002},
pages = {87--114},
doi = {10.1016/S0168-0072(01)00121-X},
}
@phdthesis{Sun94,
author = {S{\"u}nderhauf, Philipp},
title = {Discrete Approximation of Spaces, A Uniform Approach to Topologically Structured Datatypes and their Function Spaces},
school = {Fachbereich Mathematik, Technische Hochschule Darmstadt},
address = {Darmstadt, Germany},
year = {1994},
}
@article{Sun95,
author = {S{\"u}nderhauf, Philipp},
title = {A faithful computational model of the real numbers},
journal = {Theoretical Computer Science},
volume = {151},
year = {1995},
pages = {277--294},
}
@article{SV00,
author = {Spitters, Bas and Veldman, Wim},
title = {A constructive converse of the mean value theorem},
journal = {Indagationes Mathematicae},
volume = {11},
number = {1},
year = {2000},
pages = {151--157},
}
@article{SV23,
author = {Sold{\`a}, Giovanni and Valenti, Manlio},
title = {Algebraic properties of the first-order part of a problem},
journal = {Annals of Pure and Applied Logic},
year = {2023},
pages = {103270},
doi = {10.1016/j.apal.2023.103270},
}
@inproceedings{SVB01,
author = {Schuster, Peter and V{\^{\i}}{\c{t}}{\u{a}}, Lumini{\c{t}}a and Bridges, Douglas S.},
title = {Apartness as a Relation Between Subsets},
editor = {Calude, C.S. and Dinneen, M.J. and Sburlan, S.},
booktitle = {Combinatorics, Computability and Logic},
series = {Discrete Mathematics and Theoretical Computer Science},
publisher = {Springer},
address = {London},
year = {2001},
pages = {203--214},
note = {Proceedings of DMTCS 2001},
}
@article{SVB03,
author = {Schuster, Peter and V{\^{\i}}{\c{t}}{\u{a}}, Lumini{\c{t}}a and Bridges, Douglas S.},
title = {Strong versus uniform continuity: a constructive round},
journal = {Quaestiones Mathematicae},
volume = {26},
number = {2},
year = {2003},
pages = {171--190},
}
@inproceedings{SW05,
author = {Stephan, Frank and Wu, Guohua},
title = {Presentations of {K}-Trivial Reals and {K}olmogorov Complexity},
editor = {Cooper, S. Barry and L{\"{o}}we, Benedikt and Torenvliet, Leen},
booktitle = {New Computational Paradigms, First Conference on Computability in Europe, CiE 2005, Amsterdam, The Netherlands, June 8-12, 2005, Proceedings},
series = {Lecture Notes in Computer Science},
volume = {3526},
publisher = {Springer},
year = {2005},
pages = {461--469},
doi = {10.1007/11494645_57},
}
@article{Swa76,
author = {de Swart, H.},
title = {Elements of Intuitionistic Analysis. {R}olle's Theorem and Complete, Totally bounded, Metric Spaces},
journal = {Zeitschrift f\"ur Mathematische Logik und Grundlagen der Mathematik},
volume = {22},
number = {1},
year = {1976},
pages = {289--298},
}
@article{Swa76a,
author = {de Swart, H.},
title = {Elements of Intuitionistic Analysis {II} the {S}tone-{W}eierstrass Theorem and {A}scoli's Theorem},
journal = {Zeitschrift f\"ur Mathematische Logik und Grundlagen der Mathematik},
volume = {22},
number = {1},
year = {1976},
pages = {501--508},
}
@article{SWG12,
author = {Skordev, Dimiter and Weiermann, Andreas and Georgiev, Ivan},
title = {{$M^2$}-computable real numbers},
journal = {J. Logic Comput.},
volume = {22},
number = {4},
year = {2012},
pages = {899--925},
doi = {10.1093/logcom/exq050},
}
@article{SY11,
author = {Simpson, Stephen G. and Yokoyama, Keita},
title = {A nonstandard counterpart of {WWKL}},
journal = {Notre Dame J. Form. Log.},
volume = {52},
number = {3},
year = {2011},
pages = {229--243},
doi = {10.1215/00294527-1435429},
}
@article{SY12,
author = {Sanders, Sam and Yokoyama, Keita},
title = {The {D}irac delta function in two settings of reverse mathematics},
journal = {Archive for Mathematical Logic},
volume = {51},
number = {1-2},
year = {2012},
pages = {99--121},
doi = {10.1007/s00153-011-0256-5},
}
@article{SY15,
author = {Selinger, Nikita and Yampolsky, Michael},
title = {Constructive geometrization of {T}hurston maps},
journal = {C. R. Math. Acad. Sci. Soc. R. Can.},
volume = {37},
number = {3},
year = {2015},
pages = {100--113},
}
@article{SY15a,
author = {Selinger, Nikita and Yampolsky, Michael},
title = {Constructive geometrization of {T}hurston maps and decidability of {T}hurston equivalence},
journal = {Arnold Mathematical Journal},
volume = {1},
number = {4},
year = {2015},
pages = {361--402},
doi = {10.1007/s40598-015-0024-4},
}
@inproceedings{SY84,
author = {Spreen, Dieter and Young, Paul},
title = {Effective operators in a topological setting},
editor = {Richter, M.M. and B\"orger, E. and Oberschelp, W. and Schinzel, B. and Thomas, W.},
booktitle = {Computation and Proof Theory},
series = {Lecture Notes in Mathematics},
volume = {1104},
publisher = {Springer},
address = {Berlin},
year = {1984},
pages = {437--451},
note = {Proceedings of the Logic Colloquium, Aachen, July 18--23, 1983, Part II},
}
@article{SZ14,
author = {Sun, Shu-Ming and Zhong, Ning},
title = {On effective convergence of numerical solutions for differential equations},
journal = {ACM Transactions on Computation Theory},
volume = {6},
number = {1},
year = {2014},
pages = {Art. 4, 25},
doi = {10.1145/2578219},
}
@article{SZ15,
author = {Sun, Shu-Ming and Zhong, Ning},
title = {Computability aspects for 1st-order partial differential equations via characteristics},
journal = {Theoretical Computer Science},
volume = {583},
year = {2015},
pages = {27--39},
doi = {10.1016/j.tcs.2015.03.039},
}
@inproceedings{SZZ15,
author = {Sun, Shu Ming and Zhong, Ning and Ziegler, Martin},
title = {On Computability of {N}avier-{S}tokes' Equation},
editor = {Beckmann, Arnold and Mitrana, Victor and Soskova, Mariya},
booktitle = {Evolving Computability},
series = {Lecture Notes in Computer Science},
volume = {9136},
publisher = {Springer},
address = {Cham},
year = {2015},
pages = {334--342},
note = {11th Conference on Computability in Europe, CiE 2015, Bucharest, Romania, June 29--July 3, 2015},
doi = {10.1007/978-3-319-20028-6_34},
}
@incollection{SZZ20,
author = {Sun, Shu-Ming and Zhong, Ning and Ziegler, Martin},
title = {Computability of the Solutions to {N}avier-{S}tokes Equations via Effective Approximation},
editor = {Du, Ding-Zhu and Wang, Jie},
booktitle = {Complexity and Approximation: In Memory of {Ker-I Ko}},
publisher = {Springer},
address = {Cham},
year = {2020},
pages = {80--112},
doi = {10.1007/978-3-030-41672-0_7},
}
@inproceedings{Tad03,
author = {Tadaki, Kohtaro},
title = {Upper bound by {K}olmogorov complexity for the probability in computable quantum measurement},
editor = {Daumas, Marc et al.},
booktitle = {RNC'5 Real Numbers and Computers},
year = {2003},
pages = {193--214},
note = {Lyon, September 3--5, 2003},
}
@inproceedings{Tad04,
author = {Tadaki, Kohtaro},
title = {An extension of {C}haitin's halting probability $\Omega$ to measurement operator in infinite dimensional quantum system},
editor = {Frougny, Christiane and Brattka, Vasco and M{\"{u}}ller, Norbert},
booktitle = {RNC'6 Real Numbers and Computers},
year = {2004},
pages = {172--191},
note = {Dagstuhl, Germany, November 15--17, 2004},
}
@article{Tad06,
author = {Tadaki, Kohtaro},
title = {An extension of {C}haitin's halting probability {$\Omega$} to a measurement operator in an infinite dimensional quantum system},
journal = {Mathematical Logic Quarterly},
volume = {52},
number = {5},
year = {2006},
pages = {419--438},
}
@inproceedings{Tak01,
author = {Takeuti, Izumi},
title = {Effective Fixed Point Theorem Over a Non-computably Separable Metric Space},
editor = {Blanck, Jens and Brattka, Vasco and Hertling, Peter},
booktitle = {Computability and Complexity in Analysis},
series = {Lecture Notes in Computer Science},
volume = {2064},
publisher = {Springer},
address = {Berlin},
year = {2001},
pages = {310--322},
note = {4th International Workshop, CCA 2000, Swansea, UK, September 2000},
}
@inproceedings{Tak03,
author = {Takeuti, Izumi},
title = {Effective Limit in Computable Analysis},
editor = {Daumas, Marc et al.},
booktitle = {RNC'5 Real Numbers and Computers},
year = {2003},
pages = {161--175},
note = {Lyon, September 3--5, 2003},
}
@inproceedings{Tak05,
author = {Takeuti, Izumi},
title = {Transition Systems over Continuous Time-Space},
editor = {Brattka, Vasco and Staiger, Ludwig and Weihrauch, Klaus},
booktitle = {Proceedings of the 6th Workshop on Computability and Complexity in Analysis},
series = {Electronic Notes in Theoretical Computer Science},
volume = {120},
publisher = {Elsevier},
address = {Amsterdam},
year = {2005},
pages = {173--186},
note = {6th International Workshop, {CCA} 2004, Wittenberg, Germany, August 16--20, 2004},
}
@article{Tak11,
author = {Takamura, Hiroki},
title = {Powers of positive elements in {$C^*$}-algebras},
journal = {Math. Log. Q.},
volume = {57},
number = {5},
year = {2011},
pages = {481--484},
doi = {10.1002/malq.201010024},
}
@article{Tan11,
author = {Tanaka, Yasuhito},
title = {Equivalence between an approximate version of {B}rouwer's fixed point theorem and {S}perner's lemma: a constructive analysis},
journal = {Appl. Math. E-Notes},
volume = {11},
year = {2011},
pages = {238--243},
}
@article{Tan11a,
author = {Tanaka, Yasuhito},
title = {A proof of constructive version of {B}rouwer's fixed point theorem with uniform sequential continuity},
journal = {ISRN Appl. Math.},
year = {2011},
pages = {Art. ID 276040, 9},
}
@article{Tan12,
author = {Tanaka, Yasuhito},
title = {Constructive proof of {B}rouwer's fixed point theorem for sequentially locally non-constant and uniformly sequentially continuous functions},
journal = {IAENG Int. J. Appl. Math.},
volume = {42},
number = {1},
year = {2012},
pages = {1--6},
}
@article{Tas10,
author = {Taschner, Rudolf},
title = {The swap of integral and limit in constructive mathematics},
journal = {Math. Log. Q.},
volume = {56},
number = {5},
year = {2010},
pages = {533--540},
doi = {10.1002/malq.200910107},
}
@inproceedings{Tay05,
author = {Taylor, Paul},
title = {A lambda calculus for real analysis},
editor = {Grubba, Tanja and Hertling, Peter and Tsuiki, Hideki and Weihrauch, Klaus},
booktitle = {Computability and Complexity in Analysis},
series = {Informatik Berichte},
volume = {326},
publisher = {FernUniversit\"at in Hagen},
year = {2005},
month = jul,
pages = {227--266},
note = {Proccedings, Second International Conference, CCA 2005, Kyoto, Japan, August 25--29, 2005},
}
@article{Tay06,
author = {Taylor, Paul},
title = {Computably based locally compact spaces},
journal = {Logical Methods in Computer Science},
volume = {2},
number = {1},
year = {2006},
pages = {1:1, 70},
doi = {10.2168/LMCS-2(1:1)2006},
}
@article{Tay06a,
author = {Taylor, Walter},
title = {Equations on real intervals},
journal = {Algebra Universalis},
volume = {55},
number = {4},
year = {2006},
pages = {409--456},
}
@article{Tay10,
author = {Taylor, Paul},
title = {A lambda calculus for real analysis},
journal = {Journal of Logic and Analysis},
volume = {2},
year = {2010},
pages = {Paper 5, 115},
doi = {10.4115/jla.2010.2.5},
}
@incollection{Tay11,
author = {Taylor, Paul},
title = {Foundations {\it for} Computable Topology},
editor = {Sommaruga, Giovanni},
booktitle = {Foundational Theories of Classical and Constructive Mathematics},
series = {Western Ontario Series in Philosophy of Science},
volume = {76},
publisher = {Springer},
address = {Dordrecht},
year = {2011},
pages = {265--310},
doi = {10.1007/978-94-007-0431-2_14},
}
@book{TD88,
author = {Troelstra, A.S. and van Dalen, D.},
title = {Constructivism in Mathematics, Volume 1},
series = {Studies in Logic and the Foundations of Mathematics},
volume = {121},
publisher = {North-Holland},
address = {Amsterdam},
year = {1988},
}
@book{TD88a,
author = {Troelstra, A.S. and van Dalen, D.},
title = {Constructivism in Mathematics, Volume 2},
series = {Studies in Logic and the Foundations of Mathematics},
volume = {123},
publisher = {North-Holland},
address = {Amsterdam},
year = {1988},
}
@article{Ter06,
author = {Terwijn, Sebastiaan A.},
title = {The {M}edvedev lattice of computably closed sets},
journal = {Archive for Mathematical Logic},
volume = {45},
number = {2},
year = {2006},
pages = {179--190},
doi = {10.1007/s00153-005-0278-y},
}
@article{Ter06a,
author = {Terwijn, Sebastiaan A.},
title = {Constructive logic and the {M}edvedev lattice},
journal = {Notre Dame Journal of Formal Logic},
volume = {47},
number = {1},
year = {2006},
pages = {73--82 (electronic)},
doi = {10.1305/ndjfl/1143468312},
}
@inproceedings{Ter06b,
author = {Terwijn, Sebastiaan A.},
title = {Learning and computing in the limit},
booktitle = {Logic {C}olloquium '02},
series = {Lect. Notes Log.},
volume = {27},
publisher = {Assoc. Symbol. Logic},
address = {La Jolla, CA},
year = {2006},
pages = {349--359},
}
@article{Ter07,
author = {Terwijn, Sebastiaan A.},
title = {Kripke models, distributive lattices, and {M}edvedev degrees},
journal = {Studia Logica},
volume = {85},
number = {3},
year = {2007},
pages = {319--332},
doi = {10.1007/s11225-007-9054-9},
}
@article{Ter08,
author = {Terwijn, Sebastiaan A.},
title = {On the structure of the {M}edvedev lattice},
journal = {Journal of Symbolic Logic},
volume = {73},
number = {2},
year = {2008},
pages = {543--558},
doi = {10.2178/jsl/1208359059},
}
@article{Ter12,
author = {Terwijn, Sebastiaan A.},
title = {The finite intervals of the {M}uchnik lattice},
journal = {Trans. Amer. Math. Soc.},
volume = {364},
number = {5},
year = {2012},
pages = {2521--2538},
doi = {10.1090/S0002-9947-2011-05384-5},
}
@phdthesis{Ter98,
author = {Terwijn, Sebastiaan Augustinus},
title = {Computability and Measure},
school = {Institute for Logic, Language and Computation},
address = {University Amsterdam},
year = {1998},
}
@phdthesis{The84,
author = {Theobald, Konrad R.},
title = {Eine allgemeine Theorie der Stetigkeit und Berechenbarkeit f\"{u}r nat\"{u}rliche Halbordnungen},
school = {Fachbereich Mathematik und Informatik},
address = {FernUniversit\"{a}t Hagen},
year = {1984},
}
@phdthesis{Thi18,
author = {Thies, Holger},
title = {Uniform computational complexity of ordinary differential equations with applications to dynamical systems and exact real arithmetic},
school = {Graduate School of Arts and Sciences, University of Tokyo},
address = {Tokyo, Japan},
year = {2018},
}
@inproceedings{TMYT09,
author = {Tsujii, Yoshiki and Mori, Takakazu and Yasugi, Mariko and Tsuiki, Hideki},
title = {Fine-continuous functions and fractals defined by infinite systems of contractions},
booktitle = {Infinity in logic and computation},
series = {Lecture Notes in Comput. Sci.},
volume = {5489},
publisher = {Springer},
address = {Berlin},
year = {2009},
pages = {109--125},
doi = {10.1007/978-3-642-03092-5_9},
}
@book{Tod63,
author = {Todd, J.},
title = {Introduction to the Constructive Theory of Functions},
publisher = {Academic Press},
address = {New York},
year = {1963},
}
@inproceedings{Tof04,
author = {Toftdal, Michael},
title = {A calibration of ineffective theorems of analysis in a hierarchy of semi-classical logical principles (extended abstract)},
booktitle = {Automata, languages and programming},
series = {Lecture Notes in Computer Science},
volume = {3142},
publisher = {Springer},
address = {Berlin},
year = {2004},
pages = {1188--1200},
doi = {10.1007/978-3-540-27836-8_98},
}
@incollection{Tow20,
author = {Towsner, Henry},
title = {Algorithmic randomness in ergodic theory},
editor = {Franklin, Johanna N.Y. and Porter, Christopher P.},
booktitle = {Algorithmic Randomness: Progress and Prospects},
series = {Lecture Notes in Logic},
volume = {50},
publisher = {Cambridge University Press},
year = {2020},
pages = {40--57},
doi = {10.1017/9781108781718.003},
}
@article{Tro67,
author = {Troelstra, A.S.},
title = {Intuitionistic continuity},
journal = {Nieuw Arch. Wisk.},
volume = {15},
year = {1967},
pages = {2--6},
}
@book{Tro73,
title = {Metamathematical {I}nvestigation of {I}ntuitionistic {A}rithmetic and {A}nalysis},
editor = {Troelstra, A.S.},
series = {Lecture Notes in Mathematics},
volume = {344},
publisher = {Springer},
address = {Berlin},
year = {1973},
}
@inproceedings{Tro73a,
author = {Troelstra, A.S.},
title = {Models and computability},
editor = {Troelstra, A.S.},
booktitle = {Metamathematical Investigation of Intuitionistic Arithmetic and Analysis},
series = {Lecture Notes in Mathematics},
volume = {344},
year = {1973},
pages = {97--174},
}
@article{Tro77,
author = {Troelstra, A.S.},
title = {A note on non-extensional operations in connection with continuity and recursivness},
journal = {Nederl. Akad. Wetensch. Proc. Ser. A},
volume = {39},
year = {1977},
pages = {455--462},
}
@article{Tro80,
author = {Troelstra, A.S.},
title = {Intuitionistic extensions of the reals},
journal = {Nieuw Arch. Wisk.},
volume = {28},
year = {1980},
pages = {63--113},
}
@inproceedings{Tro80a,
author = {Troelstra, A.S.},
title = {Intuitionistic extensions of the reals, {II}},
booktitle = {Logic Colloq. '80},
series = {Studies in Logic and the Foundations of Mathematics},
volume = {108},
publisher = {North-Holland},
address = {Amsterdam},
year = {1980},
note = {Prague, 1980},
}
@inproceedings{Tro92,
author = {Troelstra, A.S.},
title = {Comparing the theory of representations and constructive mathematics},
editor = {B\"orger, E. and J\"ager, G. and Kleine B\"uning, H. and Richter, M.M.},
booktitle = {Computer Science Logic},
series = {Lecture Notes in Computer Science},
volume = {626},
publisher = {Springer},
address = {Berlin},
year = {1992},
pages = {382--395},
note = {Proceedings of the 5th Workshop, CSL'91, Berne Switzerland, October 1991},
}
@inproceedings{Tro93,
author = {Troelstra, A.S.},
title = {An intuitionistic look at the real numbers ({Dutch})},
booktitle = {Summer course 1993: the real numbers, {CWI} {S}yllabi},
volume = {35},
year = {1993},
pages = {67--81},
note = {Math. Centrum, 1993},
}
@inproceedings{Tsu01,
author = {Tsuiki, Hideki},
title = {Computational Dimension of Topological Spaces},
editor = {Blanck, Jens and Brattka, Vasco and Hertling, Peter},
booktitle = {Computability and Complexity in Analysis},
series = {Lecture Notes in Computer Science},
volume = {2064},
publisher = {Springer},
address = {Berlin},
year = {2001},
pages = {323--335},
note = {4th International Workshop, CCA 2000, Swansea, UK, September 2000},
}
@article{Tsu02,
author = {Tsuiki, Hideki},
title = {Real number computation through {G}ray code embedding},
journal = {Theoretical Computer Science},
volume = {284},
number = {2},
year = {2002},
pages = {467--485},
}
@inproceedings{Tsu02a,
author = {Tsuiki, Hideki},
title = {Representations of Complete Uniform Spaces via Uniform Domains},
editor = {Brattka, Vasco and Schr{\"{o}}der, Matthias and Weihrauch, Klaus},
booktitle = {{CCA} 2002 Computability and Complexity in Analysis},
series = {Electronic Notes in Theoretical Computer Science},
volume = {66},
publisher = {Elsevier},
address = {Amsterdam},
year = {2002},
note = {5th International Workshop, {CCA} 2002, M{\'{a}}laga, Spain, July 12--13, 2002},
}
@article{Tsu04,
author = {Tsuiki, Hideki},
title = {Dyadic subbases and efficiency properties of the induced $\{0, 1, \bot\}^\omega$--representations},
journal = {Topology Proceedings},
volume = {28},
number = {2},
year = {2004},
pages = {673--687},
}
@article{Tsu04a,
author = {Tsuiki, Hideki},
title = {Compact metric spaces as minimal-limit sets in domains of bottomed sequences},
journal = {Mathematical Structures in Computer Science},
volume = {14},
year = {2004},
pages = {853--878},
}
@article{Tsu05,
author = {Tsuiki, Hideki},
title = {Real number computation with committed choice logic programming languages},
journal = {The Journal of Logic and Algebraic Programming},
volume = {64},
year = {2005},
pages = {61--84},
}
@inproceedings{Tsu98,
author = {Tsuiki, Hideki},
title = {Grey Code Representation of Exact Real Numbers},
editor = {Ko, Ker-I and Nerode, Anil and Pour-El, Marian B. and Weihrauch, Klaus and Wiedermann, Ji{\v{r}}{\'{\i}}},
booktitle = {Computability and Complexity in Analysis},
series = {Informatik Berichte},
volume = {235},
publisher = {FernUniversit\"at Hagen},
year = {1998},
month = aug,
pages = {91--102},
note = {CCA Workshop, Brno, Czech Republic, August, 1998},
}
@inproceedings{TT13,
author = {Terayama, Kei and Tsuiki, Hideki},
title = {A stream calculus of bottomed sequences for real number computation},
booktitle = {Proceedings of the {T}wenty-{N}inth {C}onference on the {M}athematical {F}oundations of {P}rogramming {S}emantics, {MFPS} {XXIX}},
series = {Electron. Notes Theor. Comput. Sci.},
volume = {298},
publisher = {Elsevier Sci. B. V.},
address = {Amsterdam},
year = {2013},
pages = {383--402},
doi = {10.1016/j.entcs.2013.09.023},
}
@article{TT15,
author = {Tsuiki, Hideki and Tsukamoto, Yasuyuki},
title = {Domain representations induced by dyadic subbases},
journal = {Logical Methods in Computer Science},
volume = {11},
number = {1},
year = {2015},
pages = {1:17, 19},
doi = {10.2168/LMCS-11(1:17)2015},
}
@article{TT17,
author = {Tsukamoto, Yasuyuki and Tsuiki, Hideki},
title = {Properties of domain representations of spaces through dyadic subbases},
journal = {Mathematical Structures in Computer Science},
volume = {27},
number = {8},
publisher = {Cambridge University Press},
year = {2017},
pages = {1625--1638},
doi = {10.1017/S0960129516000207},
}
@article{TTZ09,
author = {Thompson, B. C. and Tucker, J. V. and Zucker, J. I.},
title = {Unifying computers and dynamical systems using the theory of synchronous concurrent algorithms},
journal = {Appl. Math. Comput.},
volume = {215},
number = {4},
year = {2009},
pages = {1386--1403},
doi = {10.1016/j.amc.2009.04.058},
}
@inproceedings{Tur21,
author = {Turner, D. A.},
title = {Constructive Mathematics, {C}hurch's Thesis, and Free Choice Sequences},
editor = {De Mol, Liesbeth and Weiermann, Andreas and Manea, Florin and Fern{\'a}ndez-Duque, David},
booktitle = {Connecting with Computability},
publisher = {Springer},
address = {Cham},
year = {2021},
pages = {446--456},
doi = {10.1007/978-3-030-80049-9_44},
}
@article{Tur37,
author = {Turing, Alan M.},
title = {On computable numbers, with an application to the {E}ntscheidungsproblem},
journal = {Proceedings of the London Mathematical Society},
volume = {42},
number = {2},
year = {1937},
pages = {230--265},
}
@article{Tur38,
author = {Turing, Alan M.},
title = {On computable numbers, with an application to the {E}ntscheidungsproblem. {A} correction.},
journal = {Proceedings of the London Mathematical Society},
volume = {43},
number = {2},
year = {1938},
pages = {544--546},
}
@article{Tur39,
author = {Turing, Alan M.},
title = {Systems of Logic Based on Ordinals},
journal = {Proceedings of the London Mathematical Society},
volume = {s2-45},
number = {1},
year = {1939},
pages = {161--228},
doi = {10.1112/plms/s2-45.1.161},
}
@article{TW11,
author = {Tavana, Nazanin R.\ and Weihrauch, Klaus},
title = {Turing machines on represented sets, a model of computation for analysis},
journal = {Logical Methods in Computer Science},
volume = {7},
number = {2},
year = {2011},
pages = {2:19, 21},
doi = {10.2168/LMCS-7(2:19)2011},
}
@inproceedings{TY08,
author = {Tsuiki, Hideki and Yamada, Shuji},
title = {On Finite-time Computability Preserving Conversions},
editor = {Brattka, Vasco and Dillhage, Ruth and Grubba, Tanja and Klutsch, Angela},
booktitle = {{CCA} 2008, Fifth International Conference on Computability and Complexity in Analysis},
series = {Electronic Notes in Theoretical Computer Science},
volume = {221},
publisher = {Elsevier},
year = {2008},
pages = {299--308},
note = {{CCA} 2008, Fifth International Conference, Hagen, Germany, August 21--24, 2008},
}
@inproceedings{TYM01,
author = {Tsujii, Yoshiki and Yasugi, Mariko and Mori, Takakazu},
title = {Some Properties of the Effective Uniform Topological Space},
editor = {Blanck, Jens and Brattka, Vasco and Hertling, Peter},
booktitle = {Computability and Complexity in Analysis},
series = {Lecture Notes in Computer Science},
volume = {2064},
publisher = {Springer},
address = {Berlin},
year = {2001},
pages = {336--356},
note = {4th International Workshop, CCA 2000, Swansea, UK, September 2000},
}
@inproceedings{TYM05,
author = {Tsujii, Yoshiki and Yasugi, Mariko and Mori, Takakazu},
title = {Sequential Computability of a Function: Diagonal Space and Limiting Recursion},
editor = {Brattka, Vasco and Staiger, Ludwig and Weihrauch, Klaus},
booktitle = {Proceedings of the 6th Workshop on Computability and Complexity in Analysis},
series = {Electronic Notes in Theoretical Computer Science},
volume = {120},
publisher = {Elsevier},
address = {Amsterdam},
year = {2005},
pages = {187--199},
note = {6th International Workshop, {CCA} 2004, Wittenberg, Germany, August 16--20, 2004},
}
@inproceedings{TZ00,
author = {Tucker, J.V. and Zucker, J.I.},
title = {Computable Functions and Semicomputable Sets on Many-Sorted Algebras},
editor = {Abramsky, S. and Gabbay, D.M. and Maibaum, T.S.E.},
booktitle = {Handbook of Logic in Computer Science, Volume 5},
publisher = {Oxford University Press},
address = {Oxford},
year = {2000},
pages = {317--523},
}
@article{TZ02,
author = {Tucker, J.V. and Zucker, J.I.},
title = {Abstract computability and algebraic specification},
journal = {ACM Transactions on Computational Logic},
volume = {3},
number = {2},
year = {2002},
pages = {279--333},
}
@article{TZ04,
author = {Tucker, J.V. and Zucker, J.I.},
title = {Abstract versus concrete computation on metric partial algebras},
journal = {ACM Transactions on Computational Logic},
volume = {5},
number = {4},
year = {2004},
pages = {611--668},
}
@article{TZ05,
author = {Tucker, J.V. and Zucker, J.I.},
title = {Computable total functions on metric algebras, universal algebraic specifications and dynamical systems},
journal = {The Journal of Logic and Algebraic Programming},
volume = {62},
year = {2005},
pages = {71--108},
}
@inproceedings{TZ05a,
author = {Tucker, John V. and Zucker, Jeffery I.},
title = {A Network Model of Analogoue Computation over Metric Algebras},
editor = {Cooper, Barry S. and L{\"o}we, Benedikt and Torenvliet, Leen},
booktitle = {New Computational Paradigms},
series = {Lecture Notes in Computer Science},
volume = {3526},
publisher = {Springer},
address = {Berlin},
year = {2005},
pages = {515--529},
note = {First Conference on Computability in Europe, CiE 2005, Amsterdam, The Netherlands, June 2005},
}
@article{TZ07,
author = {Tucker, John V. and Zucker, Jeffery I.},
title = {Computability of analog networks},
journal = {Theoretical Computer Science},
volume = {371},
number = {1--2},
year = {2007},
pages = {115--146},
}
@article{TZ10,
author = {Tent, Katrin and Ziegler, Martin},
title = {Computable functions of reals},
journal = {M\"unster J. Math.},
volume = {3},
year = {2010},
pages = {43--65},
}
@article{TZ11,
author = {Tucker, J. V. and Zucker, J. I.},
title = {Continuity of operators on continuous and discrete time streams},
journal = {Theoret. Comput. Sci.},
volume = {412},
number = {28},
year = {2011},
pages = {3378--3403},
doi = {10.1016/j.tcs.2011.04.012},
}
@article{TZ14,
author = {Tucker, J. V. and Zucker, J. I.},
title = {Computability of operators on continuous and discrete time streams},
journal = {Computability},
volume = {3},
number = {1},
year = {2014},
pages = {9--44},
}
@incollection{TZ15,
author = {Tucker, J. V. and Zucker, J. I.},
title = {Generalizing computability theory to abstract algebras},
editor = {Sommaruga, Giovanni and Strahm, Thomas},
booktitle = {Turing's Revolution},
publisher = {Birkh\"{a}user/Springer},
address = {Cham},
year = {2015},
pages = {127--160},
}
@inproceedings{TZ92,
author = {Tucker, J.V. and Zucker, J.I.},
title = {Examples of semicomputable sets of real and complex numbers},
editor = {Myers, J.P. and O'Donnell, M.J.},
booktitle = {Constructivity in computer science},
publisher = {Springer},
address = {Berlin},
year = {1992},
pages = {179--198},
note = {Summer Symposium San Antonio, TX, June 19--22, 1991},
}
@article{TZ99,
author = {Tucker, J.V. and Zucker, J.I.},
title = {Computation by `{W}hile' Programs on Topological Partial Algebras},
journal = {Theoretical Computer Science},
volume = {219},
year = {1999},
pages = {379--420},
}
@article{Uft21,
author = {Uftring, Patrick},
title = {The characterization of {W}eihrauch reducibility in systems containing {E-PA$^{\omega}$} + {QF-AC$^{0,0}$}},
journal = {The Journal of Symbolic Logic},
volume = {86},
number = {1},
year = {2021},
pages = {224--261},
doi = {10.1017/jsl.2020.53},
}
@book{Usp60,
author = {Uspensky, V.A.},
title = {Lectures on Computable Functions ({R}ussian)},
series = {Mathematical Logic and the Foundations of Mathematics},
publisher = {Fiz-MatGiz},
address = {Moscow},
year = {1960},
}
@article{Usp60a,
author = {Uspensky, V.A.},
title = {On the relation between various systems of constructive real numbers ({R}ussian)},
journal = {Izv.\ Vy{\v{s}}.\ U{\v{c}}ebn.\ Zaved\. Matematika},
number = {2(15)},
year = {1960},
pages = {199--208},
}
@phdthesis{Val21,
author = {Valenti, Manlio},
title = {A journey through computability, topology and analysis},
school = {Universit{\'a} degli Studi di Udine},
year = {2021},
}
@article{VB03,
author = {V{\^{\i}}{\c{t}}{\u{a}}, Lumini{\c{t}}a S. and Bridges, Douglas S.},
title = {A constructive theory of point-set nearness},
journal = {Theoretical Computer Science},
volume = {305},
year = {2003},
pages = {473--489},
}
@article{VB04,
author = {V{\^{\i}}{\c{t}}{\u{a}}, Lumini{\c{t}}a and Bridges, Douglas S.},
title = {More on {C}auchy nets in apartness spaces},
journal = {Scientiae Mathematicae Japonicae},
volume = {59},
number = {3},
year = {2004},
pages = {547--552},
}
@article{vDal11,
author = {van Dalen, Dirk},
title = {Brouwer's {$\epsilon$}-fixed point and {S}perner's lemma},
journal = {Theoret. Comput. Sci.},
volume = {412},
number = {28},
year = {2011},
pages = {3140--3144},
doi = {10.1016/j.tcs.2011.04.002},
}
@article{Vel04,
author = {Velupillai, K. Vela},
title = {Constructivity, computability and computers in economic theory: some cautionary notes},
journal = {Metroeconomica},
volume = {55},
number = {2-3},
year = {2004},
pages = {121--140},
doi = {10.1111/j.0026-1386.2004.00186.x},
}
@article{Vel04a,
author = {Velupillai, K. Vela},
title = {Economic dynamics and computation---resurrecting the {I}carus tradition},
journal = {Metroeconomica},
volume = {55},
number = {2-3},
year = {2004},
pages = {239--264},
doi = {10.1111/j.0026-1386.2004.00192.x},
}
@article{Vel06,
author = {Velupillai, K. Vela},
title = {Algorithmic foundations of {\it computable} general equilibrium theory},
journal = {Applied Mathematics and Computation},
volume = {179},
number = {1},
year = {2006},
pages = {360--369},
doi = {10.1016/j.amc.2005.11.113},
}
@article{Vel09,
author = {Velupillai, K. Vela},
title = {Uncomputability and undecidability in economic theory},
journal = {Appl. Math. Comput.},
volume = {215},
number = {4},
year = {2009},
pages = {1404--1416},
doi = {10.1016/j.amc.2009.04.051},
}
@incollection{Vel09a,
author = {Veldman, Wim},
title = {Brouwer's approximate fixed-point theorem is equivalent to {B}rouwer's fan theorem},
booktitle = {Logicism, intuitionism, and formalism},
series = {Synth. Libr.},
volume = {341},
publisher = {Springer, Dordrecht},
year = {2009},
pages = {277--299},
doi = {10.1007/978-1-4020-8926-8_14},
}
@article{Vel12,
author = {Velupillai, K. Vela},
title = {Taming the incomputable, reconstructing the nonconstructive and deciding the undecidable in mathematical economics},
journal = {New Math. Nat. Comput.},
volume = {8},
number = {1},
year = {2012},
pages = {5--51},
doi = {10.1142/S1793005712400017},
}
@article{Vel12a,
author = {Velupillai, K. Vela},
title = {Reflections on mathematical economics in the algorithmic mode},
journal = {New Math. Nat. Comput.},
volume = {8},
number = {1},
year = {2012},
pages = {139--152},
doi = {10.1142/S1793005712400091},
}
@article{Vel14,
author = {Velupillai, K. Vela},
title = {{\it {C}onstructive} and {\it computable} {H}ahn-{B}anach theorems for the (second) fundamental theorem of welfare economics},
journal = {Journal of Mathematical Economics},
volume = {54},
year = {2014},
pages = {36--39},
doi = {10.1016/j.jmateco.2014.08.004},
}
@article{Vel14a,
author = {Veldman, Wim},
title = {{B}rouwer's Fan Theorem as an axiom and as a contrast to {K}leene's alternative},
journal = {Archive for Mathematical Logic},
volume = {53},
number = {5},
year = {2014},
pages = {621--693},
doi = {10.1007/s00153-014-0384-9},
}
@phdthesis{Vel81,
author = {Veldman, W.},
title = {Investigations in {I}ntuitionistic {H}ierarchy {T}heory},
school = {Katholieke Universiteit, Nijmegen},
address = {Nijmegen, The Netherlands},
year = {1981},
}
@incollection{Vel90,
author = {Veldman, Wim},
title = {A Survey of Intuitionistic Descriptive Set Theory},
editor = {Petkov, Petio Petrov},
booktitle = {Mathematical Logic},
publisher = {Springer},
address = {Boston, MA},
year = {1990},
pages = {155--174},
doi = {10.1007/978-1-4613-0609-2_12},
}
@article{Vel97,
author = {Velupillai, K.},
title = {Expository notes on computability and complexity in (arithmetical) games},
journal = {Journal of Economic Dynamics and Control},
volume = {21},
number = {6},
year = {1997},
pages = {955--979},
note = {Society of Computational Economics Conference (Austin, TX, 1995)},
doi = {10.1016/S0165-1889(97)00012-2},
}
@article{Ves72,
author = {Vesley, R.E.},
title = {Choice sequences and {M}arkov's principle},
journal = {Compositio Mathematica},
volume = {24},
year = {1972},
pages = {33--53},
}
@article{Vid19,
author = {Vidick, Thomas},
title = {From operator algebras to complexity theory and back},
journal = {Notices of the American Mathematical Society},
volume = {66},
number = {10},
year = {2019},
pages = {1618--1627},
}
@phdthesis{Vit00,
author = {V{\^{\i}}{\c{t}}{\u{a}}, Lumini{\c{t}}a Simona},
title = {A Constructive Development of Operator Algebra Theory},
school = {Department of Mathematics \& Statistics, University of Canterbury},
address = {Christchurch},
year = {2000},
}
@article{Vit05,
author = {V{\^{\i}}{\c{t}}{\u{a}}, Lumini{\c{t}}a Simona},
title = {On Complements of Sets and the {E}fremovi{\v{c}} Condition in Pre-apartness Spaces},
journal = {Journal of Universal Computer Science},
volume = {11},
number = {12},
year = {2005},
pages = {2159--2164},
}
@phdthesis{vLam87,
author = {van Lambalgen, Michiel},
title = {Random sequences},
school = {Department of Mathematics, University of Amsterdam},
year = {1987},
note = {{Ph.D.} thesis},
}
@incollection{VN74,
author = {Va{\u\i}nberg, Ju. R. and Nogina, Elena Ju.},
title = {Categories of effectively topological spaces},
booktitle = {Studies in formalized languages and nonclassical logics ({R}ussian)},
publisher = {Izdat. ``Nauka'', Moscow},
year = {1974},
pages = {253--273},
}
@incollection{VN76,
author = {Va{\u\i}nberg, Ju. R. and Nogina, Elena Ju.},
title = {Two types of continuity of computable mappings of numerated topological spaces},
booktitle = {Studies in the theory of algorithms and mathematical logic, Vol. 2 ({R}ussian)},
publisher = {Vy{\v{c}}isl. Centr Akad. Nauk SSSR, Moscow},
year = {1976},
pages = {84--99, 159},
}
@article{Vy01,
author = {{V'yugin}, Vladimir V.},
title = {Non-robustness property of the individual ergodic theorem},
journal = {Problems of Information Transmission},
volume = {37},
number = {2},
year = {2001},
pages = {27--39},
}
@article{Vy97,
author = {{V'yugin}, Vladimir V.},
title = {Effective Convergence in Probability and an Ergodic Theorem for Individual Random Sequences},
journal = {SIAM Theory of Probability and Its Applications},
volume = {42},
number = {1},
year = {1997},
pages = {39--50},
}
@article{Vy98,
author = {{V'yugin}, Vladimir V.},
title = {Ergodic Theorems for Individual Random Sequences},
journal = {Theoretical Computer Science},
volume = {207},
number = {4},
year = {1998},
pages = {343--361},
}
@article{Waa05,
author = {Waaldijk, Frank},
title = {On the foundations of constructive mathematics - especially in relation to the theory of continuous functions},
journal = {Foundations of Science},
volume = {10},
number = {3},
year = {2005},
pages = {249--324},
}
@phdthesis{Waa96,
author = {Waaldijk, Frank},
title = {Modern Intuitionistic Topology},
school = {Radboud University Nijmegen},
year = {1996},
}
@article{Wag76,
author = {Wagner, Klaus},
title = {Arithmetische {O}peratoren},
journal = {Zeitschrift f\"ur Mathematische Logik und Grundlagen der Mathematik},
volume = {22},
year = {1976},
pages = {553--570},
}
@article{Wag77,
author = {Wagner, Klaus},
title = {Arithmetische und {B}airesche {O}peratoren},
journal = {Zeitschrift f\"ur Mathematische Logik und Grundlagen der Mathematik},
volume = {23},
year = {1977},
pages = {181--191},
}
@article{Wan74,
author = {Wang, Paul S.},
title = {The undecidability of the existence of zeros of real elementary functions},
journal = {Journal of the Association for Computing Machinery},
volume = {21},
year = {1974},
pages = {586--589},
}
@inproceedings{Wan82,
author = {Wang, Hao},
title = {Specker's mathematical work from 1949 to 1979},
booktitle = {Logic and Algorithmic ({Z}\"urich, 1980)},
journal = {Monograph. Enseign. Math.},
volume = {30},
publisher = {Univ. Geneva},
year = {1982},
pages = {11--24},
}
@phdthesis{Wan97,
author = {Wang, Michael Yuchuan},
title = {Constructive Analysis of Partial Differential Equations},
school = {Department of Mathematics, University of Waikato},
address = {Hamilton, New Zealand},
year = {1997},
}
@article{Was95,
author = {Washihara, Masako},
title = {Computability and {F}r\'{e}chet spaces},
journal = {Mathematica Japonica},
volume = {42},
number = {1},
year = {1995},
pages = {1--13},
}
@article{Was99,
author = {Washihara, Masako},
title = {Computability and tempered distributions},
journal = {Mathematica Japonica},
volume = {50},
number = {1},
year = {1999},
pages = {1--7},
}
@article{WD05,
author = {Wu, Yongcheng and Ding, Decheng},
title = {Computability of measurable sets via effective metrics},
journal = {Mathematical Logic Quarterly},
volume = {51},
number = {6},
year = {2005},
pages = {543--559},
}
@article{WD06,
author = {Wu, Yongcheng and Ding, Decheng},
title = {Computability of measurable sets via effective topologies},
journal = {Archive for Mathematical Logic},
volume = {45},
number = {3},
year = {2006},
pages = {365--379},
}
@book{Wei00,
author = {Weihrauch, Klaus},
title = {Computable Analysis},
publisher = {Springer},
address = {Berlin},
year = {2000},
}
@inproceedings{Wei01,
author = {Weihrauch, Klaus},
title = {On Computable Metric Spaces {T}ietze-{U}rysohn Extension is Computable},
editor = {Blanck, Jens and Brattka, Vasco and Hertling, Peter},
booktitle = {Computability and Complexity in Analysis},
series = {Lecture Notes in Computer Science},
volume = {2064},
publisher = {Springer},
address = {Berlin},
year = {2001},
pages = {357--368},
note = {4th International Workshop, CCA 2000, Swansea, UK, September 2000},
}
@inproceedings{Wei02a,
author = {Weihrauch, Klaus},
title = {Computable Analysis},
editor = {B.D. Masurov et al.},
booktitle = {Proceedings of the international conference ``Logic and Applications'' honouring {Y}u.\ {L}.\ {E}rshov on his 60th birthday},
publisher = {University of Novosibirsk},
address = {Novosibirsk},
year = {2002},
pages = {165--178},
}
@article{Wei03,
author = {Weihrauch, Klaus},
title = {Computational complexity on computable metric spaces},
journal = {Mathematical Logic Quarterly},
volume = {49},
number = {1},
year = {2003},
pages = {3--21},
}
@inproceedings{Wei03a,
author = {Weihrauch, Klaus},
title = {Continuity in computable analysis (Abstract)},
editor = {Brattka, Vasco and Schr{\"{o}}der, Matthias and Weihrauch, Klaus and Zhong, Ning},
booktitle = {Computability and Complexity in Analysis},
series = {Informatik Berichte},
volume = {302},
publisher = {FernUniversit\"at in Hagen},
year = {2003},
month = aug,
pages = {99--100},
note = {International Conference, CCA 2003, Cincinnati, USA, August 28--30, 2003},
}
@book{Wei04,
author = {Weinberger, Shmuel},
title = {Computers, Rigidity, and Moduli: The Large-Scale Fractal Geometry of {R}iemannian Moduli Space},
publisher = {Princeton University Press},
address = {New Jersey},
year = {2004},
}
@inproceedings{Wei05,
author = {Weihrauch, Klaus},
title = {Multi-functions on multi-represented sets are closed under flowchart programming},
editor = {Grubba, Tanja and Hertling, Peter and Tsuiki, Hideki and Weihrauch, Klaus},
booktitle = {Computability and Complexity in Analysis},
series = {Informatik Berichte},
volume = {326},
publisher = {FernUniversit\"at in Hagen},
year = {2005},
month = jul,
pages = {267--300},
note = {Proccedings, Second International Conference, CCA 2005, Kyoto, Japan, August 25--29, 2005},
}
@article{Wei08,
author = {Weihrauch, Klaus},
title = {The Computable Multi-Functions on Multi-represented Sets are Closed under Programming},
journal = {Journal of Universal Computer Science},
volume = {14},
number = {6},
year = {2008},
pages = {801--844},
}
@article{Wei10,
author = {Weihrauch, Klaus},
title = {Computable separation in topology, from {$T_0$} to {$T_2$}},
journal = {Journal of Universal Computer Science},
volume = {16},
number = {18},
year = {2010},
pages = {2733--2753},
}
@article{Wei13,
author = {Weihrauch, Klaus},
title = {Computably regular topological spaces},
journal = {Logical Methods in Computer Science},
volume = {9},
year = {2013},
pages = {3:5, 24},
doi = {10.2168/LMCS-9(3:5)2013},
}
@article{Wei17,
author = {Weihrauch, Klaus},
title = {Computability on measurable functions},
journal = {Computability},
volume = {6},
number = {1},
year = {2017},
pages = {79--104},
doi = {10.3233/COM-160058},
}
@article{Wei19,
author = {Weihrauch, Klaus},
title = {Computable planar curves intersect in a computable point},
journal = {Computability},
volume = {8},
number = {3, 4},
year = {2019},
pages = {399--415},
doi = {10.3233/COM-180102},
}
@article{Wei22,
author = {Weihrauch, Klaus},
title = {Intersection points of planar curves can be computed},
journal = {Computability},
volume = {11},
number = {2},
year = {2022},
pages = {113--133},
doi = {10.3233/com-210311},
}
@inproceedings{Wei77b,
author = {Weihrauch, Klaus},
title = {A generalized computability thesis},
editor = {Karpinski, Marek},
booktitle = {Fundamentals of Computation Theory},
series = {Lecture Notes in Computer Science},
volume = {56},
publisher = {Springer},
year = {1977},
pages = {538--542},
note = {Proceedings of the 1977 International FCT-Conference, Poznan-Kornik, Poland, September 19--23, 1977},
}
@inproceedings{Wei81,
author = {Weihrauch, Klaus},
title = {Recursion and complexity theory on cpo-s},
editor = {Deussen, Peter},
booktitle = {Theoretical Computer Science},
series = {Lecture Notes in Computer Science},
volume = {104},
publisher = {Springer},
year = {1981},
note = {5th GI-Conference, Karlsruhe, March 23--25, 1981},
}
@article{Wei85,
author = {Weihrauch, Klaus},
title = {Type 2 recursion theory},
journal = {Theoretical Computer Science},
volume = {38},
year = {1985},
pages = {17--33},
}
@book{Wei87,
author = {Weihrauch, Klaus},
title = {Computability},
series = {EATCS Monographs on Theoretical Computer Science},
volume = {9},
publisher = {Springer},
address = {Berlin},
year = {1987},
}
@article{Wei91,
author = {Weihrauch, Klaus},
title = {On the complexity of online computations of real functions},
journal = {Journal of Complexity},
volume = {7},
year = {1991},
pages = {380--394},
doi = {10.1016/0885-064X(91)90026-T},
}
@article{Wei93,
author = {Weihrauch, Klaus},
title = {Computability on computable metric spaces},
journal = {Theoretical Computer Science},
volume = {113},
year = {1993},
pages = {191--210},
}
@inproceedings{Wei97,
author = {Weihrauch, Klaus},
title = {A Foundation for Computable Analysis},
editor = {Bridges, Douglas S. and Calude, Cristian S. and Gibbons, Jeremy and Reeves, Steve and Witten, Ian H.},
booktitle = {Combinatorics, Complexity, and Logic},
series = {Discrete Mathematics and Theoretical Computer Science},
publisher = {Springer},
address = {Singapore},
year = {1997},
pages = {66--89},
note = {Proceedings of DMTCS'96},
}
@article{Wei98,
author = {Weihrauch, Klaus},
title = {A Refined Model of Computation for Continuous Problems},
journal = {Journal of Complexity},
volume = {14},
year = {1998},
pages = {102--121},
}
@article{Wei99a,
author = {Weihrauch, Klaus},
title = {Computability on the probability measures on the {B}orel sets of the unit interval},
journal = {Theoretical Computer Science},
volume = {219},
year = {1999},
pages = {421--437},
}
@article{Wel08,
author = {Welch, P.D.},
title = {The extent of computation in {M}alament-{H}ogarth spacetimes},
journal = {British Journal for the Philosophy of Science},
volume = {59},
number = {4},
year = {2008},
pages = {659--674},
}
@article{Wel21,
author = {Welch, Philip},
title = {Characterisations of variant transfinite computational models: infinite time {T}uring, ordinal time {T}uring, and {B}lum-{S}hub-{S}male machines},
journal = {Computability},
volume = {10},
number = {2},
year = {2021},
pages = {159--180},
doi = {10.3233/com-200301},
}
@article{Wes14,
author = {Westrick, Linda Brown},
title = {A lightface analysis of the differentiability rank},
journal = {Journal of Symbolic Logic},
volume = {79},
number = {1},
year = {2014},
pages = {240--265},
doi = {10.1017/jsl.2013.23},
}
@phdthesis{Wes14a,
author = {Westrick, Linda Brown},
title = {Computability in {O}rdinal {R}anks and {S}ymbolic {D}ynamics},
school = {University of California, Berkeley},
year = {2014},
pages = {106},
}
@article{Wes21,
author = {Westrick, Linda},
title = {A note on the diamond operator},
journal = {Computability},
volume = {10},
number = {2},
year = {2021},
pages = {107--110},
doi = {10.3233/COM-200295},
}
@book{Wey18,
author = {Weyl, H.},
title = {Das {K}ontinuum},
publisher = {Veit},
address = {Leipzig},
year = {1978},
}
@article{WG09,
author = {Weihrauch, Klaus and Grubba, Tanja},
title = {Elementary computable topology},
journal = {Journal of Universal Computer Science},
volume = {15},
number = {6},
year = {2009},
pages = {1381--1422},
}
@phdthesis{Why18,
author = {Whyman, Richard Arthur James},
title = {Characterising Computational Devices with Logical Systems},
school = {School of Mathematics, University of Leeds},
year = {2018},
}
@incollection{Why18b,
author = {Whyman, Richard},
title = {Physical computation and first-order logic},
editor = {Durand-Lose, J\'{e}r\^{o}me and Verlan, Sergey},
booktitle = {Machines, Computations, and Universality},
series = {Lecture Notes in Computer Science},
volume = {10881},
publisher = {Springer},
year = {2018},
pages = {153--169},
note = {8th International Conference, MCU 2018, Fontainebleau, France, June 28--30, 2018, Held at the University of Paris-Est Cr\'{e}teil},
doi = {10.1007/978-3-319-92402-1_9},
}
@article{Wie80,
author = {Wiedmer, E.},
title = {Computing with infinite objects},
journal = {Theoretical Computer Science},
volume = {10},
year = {1980},
pages = {133--155},
}
@article{WK22,
author = {Wiesnet, Franziskus and K{\"o}pp, Nils},
title = {Limits of real numbers in the binary signed digit representation},
journal = {Logical Methods in Computer Science},
volume = {18},
number = {3},
year = {2022},
month = Aug,
pages = {24:1--24:28},
doi = {10.46298/lmcs-18(3:24)2022},
}
@article{WK87,
author = {Weihrauch, Klaus and Kreitz, Christoph},
title = {Representations of the real numbers and of the open subsets of the set of real numbers},
journal = {Annals of Pure and Applied Logic},
volume = {35},
year = {1987},
pages = {247--260},
}
@article{WK91,
author = {Weihrauch, Klaus and Kreitz, Christoph},
title = {Type 2 computational complexity of functions on {C}antor's space},
journal = {Theoretical Computer Science},
volume = {82},
year = {1991},
pages = {1--18},
}
@inproceedings{WL02,
author = {Wiedermann, Ji{\v{r}}{\'{\i}} and {van Leeuwen}, Jan},
title = {Relativistic Computers and Non-uniform Complexity Theory},
editor = {Calude, Cristian S. and Dinneen, Michael J. and Peper, Ferdinand},
booktitle = {Unconventional models of computation},
series = {Lecture Notes in Computer Science},
volume = {2509},
publisher = {Springer},
address = {Berlin},
year = {2002},
pages = {287--299},
note = {Proceedings of the 3rd International Conference (UMC 2002) held in Kobe, Japan, October 15--19, 2002},
}
@article{Won96,
author = {Wong, Kam-Chau},
title = {Computability of Minimizers and Separating Hyperplanes},
journal = {Mathematical Logic Quarterly},
volume = {42},
year = {1996},
pages = {564--568},
}
@article{Woz99,
author = {Wo{\'{z}}niakowski, Henryk},
title = {Why does information-based complexity use the real number model?},
journal = {Theoretical Computer Science},
volume = {219},
year = {1999},
pages = {451--465},
}
@inproceedings{WS79,
author = {Weihrauch, Klaus and Schreiber, Ulrich},
title = {Metric spaces defined by weighted algebraic cpo-s},
editor = {Budach, Lothar},
booktitle = {Fundamentals of Computation Theory, FCT'79},
publisher = {Akademie-Verlag},
address = {Berlin},
year = {1979},
pages = {516--522},
note = {Proceedings of the Conference on Algebraic, Arithmetic, and Categorial Methods in Computation Theory, Berlin, September 17--21, 1979},
}
@article{WS81,
author = {Weihrauch, Klaus and Schreiber, Ulrich},
title = {Embedding metric spaces into cpo's},
journal = {Theoretical Computer Science},
volume = {16},
year = {1981},
pages = {5--24},
}
@inproceedings{WS81a,
author = {Weihrauch, Klaus and Sch\"afer, Giesela},
title = {Admissible representations of effective cpo's},
editor = {Gruska, J. and Chytil, M.},
booktitle = {Mathematical Foundations of Computer Science 1981},
series = {Lecture Notes in Computer Science},
volume = {118},
publisher = {Springer},
year = {1981},
note = {Proceedings, 10th Sympsoium \v{S}trbsk\'{e} Pleso, Czechoslovakia, August 31--September 4, 1981},
}
@article{WS83,
author = {Weihrauch, Klaus and Sch{\"a}fer, G.},
title = {Admissible representations of effective cpo's},
journal = {Theoretical Computer Science},
volume = {26},
year = {1983},
pages = {131--147},
}
@article{WT14,
author = {Weihrauch,Klaus and Tavana-Roshandel, Nazanin},
title = {Representations of measurable sets in computable measure theory},
journal = {Logical Methods in Computer Science},
volume = {10},
year = {2014},
pages = {3:7,21},
doi = {10.2168/LMCS-10(3:7)2014},
}
@article{Wu05a,
author = {Wu, Guohua},
title = {Regular reals},
journal = {Mathematical Logic Quarterly},
volume = {51},
number = {2},
year = {2005},
pages = {111--119},
}
@article{Wu12,
author = {Wu, Yongcheng},
title = {Computability on random events and variables in a computable probability space},
journal = {Theoret. Comput. Sci.},
volume = {460},
year = {2012},
pages = {54--69},
doi = {10.1016/j.tcs.2012.06.027},
}
@inproceedings{WW05,
author = {Yongcheng Wu and Klaus Weihrauch},
title = {A Computable Version of the {D}aniell-{S}tone Theorem on Integration and Linear Functionals},
editor = {Brattka, Vasco and Staiger, Ludwig and Weihrauch, Klaus},
booktitle = {Proceedings of the 6th Workshop on Computability and Complexity in Analysis},
series = {Electronic Notes in Theoretical Computer Science},
volume = {120},
publisher = {Elsevier},
address = {Amsterdam},
year = {2005},
pages = {217--230},
note = {6th International Workshop, {CCA} 2004, Wittenberg, Germany, August 16--20, 2004},
}
@article{WW06,
author = {Wu, Yongcheng and Weihrauch, Klaus},
title = {A computable version of the {D}aniell-{S}tone theorem on integration and linear functionals},
journal = {Theoretical Computer Science},
volume = {359},
number = {1--3},
year = {2006},
pages = {28--42},
}
@article{WWD09,
author = {Weihrauch, Klaus and Wu, Yongcheng and Ding, Decheng},
title = {Absolutely non-computable predicates and functions in analysis},
journal = {Mathematical Structures in Computer Science},
volume = {19},
number = {1},
year = {2009},
pages = {59--71},
doi = {10.1017/S096012950800724X},
}
@article{WY96,
author = {Washihara, Masako and Yasugi, Mariko},
title = {Computability and metrics in a {F}r\'{e}chet space},
journal = {Mathematica Japonica},
volume = {43},
number = {3},
year = {1996},
pages = {431--443},
}
@article{WZ00,
author = {Weihrauch, Klaus and Zheng, Xizhong},
title = {Computability on continuous, lower semi-continuous and upper semi-continuous real functions},
journal = {Theoretical Computer Science},
volume = {234},
year = {2000},
pages = {109--133},
}
@inproceedings{WZ01,
author = {Weihrauch, Klaus and Zhong, Ning},
title = {Is the Linear {S}chr{\"o}dinger Propagator {T}uring Computable?},
editor = {Blanck, Jens and Brattka, Vasco and Hertling, Peter},
booktitle = {Computability and Complexity in Analysis},
series = {Lecture Notes in Computer Science},
volume = {2064},
publisher = {Springer},
address = {Berlin},
year = {2001},
pages = {369--377},
note = {4th International Workshop, CCA 2000, Swansea, UK, September 2000},
}
@inproceedings{WZ01b,
author = {Weihrauch, Klaus and Zhong, Ning},
title = {{T}uring Computability of a Nonlinear {S}chr{\"o}dinger Propagator},
editor = {Wang, Jie},
booktitle = {Computing and Combinatorics},
series = {Lecture Notes in Computer Science},
volume = {2108},
publisher = {Springer},
address = {Berlin},
year = {2001},
pages = {596--599},
note = {7th Annual International Conference, COCOON 2001, Guilin, China, August 20-23, 2001},
}
@inproceedings{WZ02,
author = {Weihrauch, Klaus and Zhong, Ning},
title = {The Solution Operator of the {K}orteweg-de {V}ries Equation is Computable},
editor = {Brattka, Vasco and Schr{\"{o}}der, Matthias and Weihrauch, Klaus},
booktitle = {{CCA} 2002 Computability and Complexity in Analysis},
series = {Electronic Notes in Theoretical Computer Science},
volume = {66},
publisher = {Elsevier},
address = {Amsterdam},
year = {2002},
note = {5th International Workshop, {CCA} 2002, M{\'{a}}laga, Spain, July 12--13, 2002},
}
@article{WZ02a,
author = {Weihrauch, Klaus and Zhong, Ning},
title = {Is wave propagation computable or can wave computers beat the {T}uring machine?},
journal = {Proceedings of the London Mathematical Society},
volume = {85},
number = {2},
year = {2002},
pages = {312--332},
}
@inproceedings{WZ05,
author = {Weihrauch, Klaus and Zhong, Ning},
title = {An Algorithm for Computing Fundamental Solutions},
editor = {Brattka, Vasco and Staiger, Ludwig and Weihrauch, Klaus},
booktitle = {Proceedings of the 6th Workshop on Computability and Complexity in Analysis},
series = {Electronic Notes in Theoretical Computer Science},
volume = {120},
publisher = {Elsevier},
address = {Amsterdam},
year = {2005},
pages = {201--215},
note = {6th International Workshop, {CCA} 2004, Wittenberg, Germany, August 16--20, 2004},
}
@article{WZ05a,
author = {Weihrauch, Klaus and Zhong, Ning},
title = {Computing the solution of the {K}orteweg-de {V}ries equation with arbitrary precision on {T}uring machines},
journal = {Theoretical Computer Science},
volume = {332},
number = {1--3},
year = {2005},
pages = {337--366},
}
@article{WZ06,
author = {Weihrauch, Klaus and Zhong, Ning},
title = {An algorithm for computing fundamental solutions},
journal = {SIAM Journal on Computing},
volume = {35},
number = {6},
year = {2006},
pages = {1283--1294},
}
@article{WZ06b,
author = {Weihrauch, Klaus and Zhong, Ning},
title = {Computing {S}chr{\"o}dinger propagators on {T}ype-2 {T}uring machines},
journal = {Journal of Complexity},
volume = {22},
number = {6},
year = {2006},
pages = {918--935},
}
@inproceedings{WZ06c,
author = {Weihrauch, Klaus and Zhong, Ning},
title = {Beyond the first main theorem---when is the solution of a linear {C}auchy problem computable?},
booktitle = {Theory and applications of models of computation},
series = {Lecture Notes in Comput. Sci.},
volume = {3959},
publisher = {Springer},
address = {Berlin},
year = {2006},
pages = {783--792},
doi = {10.1007/11750321_75},
}
@inproceedings{WZ07,
author = {Weihrauch, Klaus and Zhong, Ning},
title = {Computable analysis of the abstract {C}auchy problem in a {B}anach space and its applications {(I)}},
editor = {Cenzer, Douglas and Dillhage, Ruth and Grubba, Tanja and Weihrauch, Klaus},
booktitle = {Proceedings of the Third International Conference on Computability and Complexity in Analysis},
series = {Electronic Notes in Theoretical Computer Science},
volume = {167},
publisher = {Elsevier},
address = {Amsterdam},
year = {2007},
pages = {33--59},
note = {{CCA} 2006, Gainesville, Florida, USA, November 1--5, 2006},
}
@article{WZ07a,
author = {Weihrauch, Klaus and Zhong, Ning},
title = {Computable analysis of the abstract {C}auchy problem in a {B}anach space and its applications {I}},
journal = {Mathematical Logic Quarterly},
volume = {53},
number = {4--5},
year = {2007},
pages = {511--531},
}
@inproceedings{WZ97,
author = {Weihrauch, Klaus and Zheng, Xizhong},
title = {Computability on Continuous, Lower Semi-Continuous and Upper Semi-Continuous Real Functions},
editor = {Jiang, Tao and Lee, D.T.},
booktitle = {Computing and Combinatorics},
series = {Lecture Notes in Computer Science},
volume = {1276},
publisher = {Springer},
address = {Berlin},
year = {1997},
pages = {166--175},
note = {Third Annual Conference, COCOON'97, Shanghai, China, August 1997},
}
@inproceedings{WZ98,
author = {Weihrauch, Klaus and Zheng, Xizhong},
title = {A Finite Hierarchy of the Recursively Enumerable Real Numbers},
editor = {Brim, Lubo{\v{s}} and Gruska, Jozef and Zlatu{\v{s}}ka, Ji{\v{r}}{\'{\i}}},
booktitle = {Mathematical Foundations of Computer Science 1998},
series = {Lecture Notes in Computer Science},
volume = {1450},
publisher = {Springer},
address = {Berlin},
year = {1998},
pages = {798--806},
note = {23rd International Symposium, MFCS'98, Brno, Czech Republic, August, 1998},
}
@article{WZ99,
author = {Weihrauch, Klaus and Zheng, Xizhong},
title = {Effectiveness of the global modulus of continuity on metric spaces},
journal = {Theoretical Computer Science},
volume = {219},
year = {1999},
pages = {439--450},
}
@inproceedings{WZ99a,
author = {Weihrauch, Klaus and Zhong, Ning},
title = {The Wave Propagator is {T}uring Computable},
editor = {Wiedermann, Ji{\v{r}}{\'{\i}} and van Emde Boas, Peter and Nielsen, Mogens},
booktitle = {Automata, Languages and Programming},
series = {Lecture Notes in Computer Science},
volume = {1644},
publisher = {Springer},
address = {Berlin},
year = {1999},
pages = {697--706},
note = {26th International Colloquium, ICALP'99, Prague, Czech Republic, July, 1999},
}
@article{XFZ15,
author = {Xie, Bo and Fu, Ming Quan and Zucker, Jeffery},
title = {Characterizations of semicomputable sets of real numbers},
journal = {Journal of Logical and Algebraic Methods in Programming},
volume = {84},
number = {1},
year = {2015},
pages = {124--154},
doi = {10.1016/j.jlap.2013.11.001},
}
@inproceedings{XG07,
author = {Xu, Yatao and Grubba, Tanja},
title = {Computability on Subsets of Locally Compact Spaces},
editor = {Cai, J.-Y. and Cooper, S.B. and Zhu, H.},
booktitle = {Theory and Applications of Models of Computation},
series = {Lecture Notes in Computer Science},
volume = {4484},
publisher = {Springer},
address = {Berlin},
year = {2007},
pages = {100--114},
note = {4th International Conference, TAMC 2007, Shanghai, China, May 2007},
}
@article{XG09,
author = {Xu, Yatao and Grubba, Tanja},
title = {On computably locally compact {H}ausdorff spaces},
journal = {Math. Structures Comput. Sci.},
volume = {19},
number = {1},
year = {2009},
pages = {101--117},
doi = {10.1017/S0960129508007366},
}
@article{Yas00,
author = {Yasugi, Mariko},
title = {How to understand the computability aspects of step functions},
journal = {S\={u}rikaisekikenky\={u}sho K\={o}ky\={u}roku},
volume = {1169},
year = {2000},
pages = {84--91},
note = {Research Institute for Mathematical Sciences Kyoto},
}
@article{Yas96,
author = {Yasugi, Mariko},
title = {Computability in analysis},
journal = {Surikaisekikenkyusho-Kokyuroku},
volume = {850},
year = {1993},
pages = {207--214},
note = {Workshop on Stochastic Numerics, Kyoto},
}
@inproceedings{Yas98,
author = {Yasugi, Mariko},
title = {Computability problem of {G}aussian function},
editor = {Ko, Ker-I and Nerode, Anil and Pour-El, Marian B. and Weihrauch, Klaus and Wiedermann, Ji{\v{r}}{\'{\i}}},
booktitle = {Computability and Complexity in Analysis},
series = {Informatik Berichte},
volume = {235},
publisher = {FernUniversit\"at Hagen},
year = {1998},
month = aug,
pages = {157--165},
note = {CCA Workshop, Brno, Czech Republic, August, 1998},
}
@article{YBW01,
author = {Yasugi, Mariko and Brattka, Vasco and Washihara, Masako},
title = {Computability aspects of some discontinuous functions},
journal = {Scientiae Mathematicae Japonicae Online},
volume = {5},
year = {2001},
pages = {405--419},
}
@article{YBW02,
author = {Yasugi, Mariko and Brattka, Vasco and Washihara, Masako},
title = {Computability aspects of some discontinuous functions},
journal = {Scientiae Mathematicae Japonicae},
volume = {55},
number = {3},
year = {2002},
pages = {427--441},
}
@inproceedings{YBW02a,
author = {Yasugi, Mariko and Brattka, Vasco and Washihara, Masako},
title = {Limit computation of some discontinuous functions},
booktitle = {Theoretical development and feasibility of mathematical analysis on the computer},
series = {S\={u}rikaisekikenky\={u}sho K\={o}ky\={u}roku},
volume = {1286},
publisher = {Research Institute for Mathematical Sciences},
address = {Kyoto},
year = {2002},
pages = {79--84},
}
@article{YCK06,
author = {Yu, Fuxiang and Chou, Arthur and Ko, Ker-I},
title = {On the complexity of finding circumscribed rectangles and squares for a two-dimensional domain},
journal = {Journal of Complexity},
volume = {22},
number = {6},
year = {2006},
pages = {803--817},
}
@article{YDD04,
author = {Yu, Liang and Ding, Decheng and Downey, Rodney},
title = {The {K}olmogorov complexity of random reals},
journal = {Annals of Pure and Applied Logic},
volume = {129},
number = {1--3},
year = {2004},
pages = {163--180},
}
@article{Ye02,
author = {Ye, Feng},
title = {Toward a constructive theory of unbounded linear operators},
journal = {The Journal of Symbolic Logic},
volume = {65},
number = {1},
year = {2000},
pages = {357--370},
}
@article{YK13,
author = {Yu, Fuxiang and Ko, Ker-I},
title = {On logarithmic-space computable real numbers},
journal = {Theoret. Comput. Sci.},
volume = {469},
year = {2013},
pages = {127--133},
doi = {10.1016/j.tcs.2012.10.004},
}
@article{YK13a,
author = {Yu, Fuxiang and Ko, Ker-I},
title = {On parallel complexity of analytic functions},
journal = {Theoret. Comput. Sci.},
volume = {489/490},
year = {2013},
pages = {48--57},
doi = {10.1016/j.tcs.2013.04.008},
}
@article{YK99,
author = {Yamakawa, Takeshi and Kreinovich, Vladik},
title = {Why fundamental physical equations are of second order?},
journal = {International Journal of Theoretical Physics},
volume = {38},
number = {6},
year = {1999},
pages = {1763--1770},
}
@inproceedings{YMT05,
author = {Yasugi, Mariko and Mori, Takakazu and Tsujii, Yoshiki},
title = {Effective sequence of uniformities and its effective limit},
editor = {Grubba, Tanja and Hertling, Peter and Tsuiki, Hideki and Weihrauch, Klaus},
booktitle = {Computability and Complexity in Analysis},
series = {Informatik Berichte},
volume = {326},
publisher = {FernUniversit\"at in Hagen},
year = {2005},
month = jul,
pages = {301--318},
note = {Proccedings, Second International Conference, CCA 2005, Kyoto, Japan, August 25--29, 2005},
}
@article{YMT07,
author = {Yasugi, Mariko and Mori, Takakazu and Tsujii, Yoshiki},
title = {The effective sequence of uniformities and its limit as a methodology in computable analysis},
journal = {Annals of the Japan Association for Philosophy of Science},
volume = {15},
number = {2},
year = {2007},
pages = {99--121},
doi = {10.4288/jafpos1956.15.99},
}
@article{YMT99,
author = {Yasugi, Mariko and Mori, Takakazu and Tsujii, Yoshiki},
title = {Effective properties of sets and functions in metric spaces with computability structure},
journal = {Theoretical Computer Science},
volume = {219},
year = {1999},
pages = {467--486},
}
@article{Yos02,
author = {Yoshikawa, Atsushi},
title = {Interpolation functor and computability},
journal = {Theoretical Computer Science},
volume = {284},
number = {2},
year = {2002},
pages = {487--498},
}
@article{Yos03,
author = {Yoshikawa, Atsushi},
title = {On an ad hoc computability structure in a {H}ilbert space},
journal = {Proc. Japan Acad. Ser. A},
volume = {79},
number = {3},
year = {2003},
pages = {65--70},
}
@article{Yos05,
author = {Yoshida, Satoru},
title = {The constructive completion of the space ${\cal D}(R)$},
journal = {Mathematical Logic Quarterly},
volume = {51},
number = {1},
year = {2005},
pages = {77--82},
}
@article{Yos06,
author = {Yoshida, Satoru},
title = {Generalized functions with pseudobounded support in constructive mathematics},
journal = {Journal of Complexity},
volume = {22},
number = {6},
year = {2006},
pages = {783--802},
}
@article{Yos07,
author = {Yoshikawa, Atsushi},
title = {On computability of the {G}alerkin procedure},
journal = {Proc. Japan Acad. Ser. A},
volume = {83},
number = {5},
year = {2007},
pages = {69--72},
}
@inproceedings{YT02,
author = {Yasugi, Mariko and Tsujii, Yoshiki},
title = {Two Notions of Sequential Computability of a Function with Jumps},
editor = {Brattka, Vasco and Schr{\"{o}}der, Matthias and Weihrauch, Klaus},
booktitle = {{CCA} 2002 Computability and Complexity in Analysis},
series = {Electronic Notes in Theoretical Computer Science},
volume = {66},
publisher = {Elsevier},
address = {Amsterdam},
year = {2002},
note = {5th International Workshop, {CCA} 2002, M{\'{a}}laga, Spain, July 12--13, 2002},
}
@article{YT05,
author = {Yasugi, Mariko and Tsujii, Yoshiki},
title = {Computability of a function with jumps -- Effective uniformity and limiting recursion},
journal = {Topology and its Applications},
volume = {146-147},
year = {2005},
pages = {563--582},
}
@article{YTM02,
author = {Yasugi, Mariko and Tsujii, Yoshiki and Mori, Takakazu},
title = {Metrization of the Uniform Space and Effective Convergence},
journal = {Mathematical Logic Quarterly},
volume = {48},
number = {Suppl. 1},
year = {2002},
pages = {123--130},
}
@article{YTM05,
author = {Yasugi, Mariko and Tsujii, Yoshiki and Mori, Takakazu},
title = {Sequential Computability of a Function. Effective {F}ine Space and Limiting Recursion},
journal = {Journal of Universal Computer Science},
volume = {11},
number = {12},
year = {2005},
pages = {2179--2191},
}
@inproceedings{YTM21,
author = {Yasugi, Mariko and Tsujii, Yoshiki and Mori, Takakazu},
title = {Irrational-based computability of functions},
editor = {Arai, Toshiyasu and Kikuchi, Makoto and Kuroda, Satoru and Okada, Mitsuhiro and Yorioka, Teruyuki},
booktitle = {Advances in mathematical logic},
series = {Springer Proc. Math. Stat.},
volume = {369},
publisher = {Springer},
address = {Singapore},
year = {2021},
pages = {181--204},
doi = {10.1007/978-981-16-4173-2\_9},
}
@inproceedings{YTM22,
author = {Yasugi, Mariko and Tsujii, Yoshiki and Mori, Takakazu},
title = {A effective study of continued ractions and applications},
editor = {Ikeda, Kazuma},
booktitle = {Theory and Applications of Proof and Computation},
series = {RIMS K{\^{o}}ky{\^{u}}roku},
volume = {2228},
publisher = {Research Institute for Mathematical Sciences},
address = {Kyoto},
year = {2022},
pages = {168--185},
}
@inproceedings{Yu07,
author = {Yu, Fuxiang},
title = {On the complexity of the pancake problem},
editor = {Cenzer, Douglas and Dillhage, Ruth and Grubba, Tanja and Weihrauch, Klaus},
booktitle = {Proceedings of the Third International Conference on Computability and Complexity in Analysis},
series = {Electronic Notes in Theoretical Computer Science},
volume = {167},
publisher = {Elsevier},
address = {Amsterdam},
year = {2007},
pages = {95--115},
note = {{CCA} 2006, Gainesville, Florida, USA, November 1--5, 2006},
}
@article{Yu07a,
author = {Yu, Fuxiang},
title = {On the complexity of the pancake problem},
journal = {Mathematical Logic Quarterly},
volume = {53},
number = {4--5},
year = {2007},
pages = {532--546},
}
@article{Yu20,
author = {Yu, Liang},
title = {An Application of Recursion Theory to Analysis},
journal = {The Bulletin of Symbolic Logic},
volume = {26},
number = {1},
year = {2020},
pages = {15--25},
doi = {10.1017/bsl.2020.19},
}
@article{Yu94,
author = {Yu, Xiaokang},
title = {Lebesgue convergence theorems and reverse mathematics},
journal = {Mathematical Logic Quarterly},
volume = {40},
number = {1},
year = {1994},
pages = {1--13},
doi = {10.1002/malq.19940400102},
}
@inproceedings{Yue21,
author = {Yuen, Henry},
title = {Einstein Meets {T}uring: The Computability of Nonlocal Games},
editor = {De Mol, Liesbeth and Weiermann, Andreas and Manea, Florin and Fern{\'a}ndez-Duque, David},
booktitle = {Connecting with Computability},
publisher = {Springer},
address = {Cham},
year = {2021},
pages = {483--493},
doi = {10.1007/978-3-030-80049-9_47},
}
@inproceedings{YW03,
author = {Yasugi, Mariko and Washihara, Masako},
title = {A note on {R}ademacher Functions and Computability},
editor = {Ito, Masami and Imaoka, Teruo},
booktitle = {Words, Languages \& Combinatorics III},
publisher = {World Scientific Publishing},
address = {Singapore},
year = {2003},
pages = {466--475},
note = {ICWLC 2000, Kyoto, Japan, March 14--18, 2000},
}
@article{YW10,
author = {Yasugi, Mariko and Washihara, Masako},
title = {Sequential computability of a function---limiting recursion versus effective uniformity---to the memory of {M}arian {B}oykan {P}our-{E}l},
journal = {Sci. Math. Jpn.},
volume = {71},
number = {3},
year = {2010},
pages = {331--341},
}
@book{Zah78,
author = {Zahn, Peter},
title = {Ein konstruktiver {W}eg zur {M}a{\ss}theorie und {F}unktionalanalysis},
publisher = {Wissenschaftliche Buchgesellschaft},
address = {Darmstadt},
year = {1978},
}
@article{Zah85,
author = {Zahn, Peter},
title = {Gilt das {L}emma von {K}{\"{o}}nig ``konstruktiv''?},
journal = {Archiv f\"ur Mathematische Logik und Grundlagenforschung},
volume = {25},
year = {1985},
pages = {33--35},
}
@article{Zas55,
author = {Zaslavski{\u{i}}, Igor D.},
title = {Disproof of some theorems of classical analysis in constructive analysis ({R}ussian)},
journal = {Usp.\ Mat.\ Nauk},
volume = {10},
number = {4},
year = {1955},
pages = {209--210},
}
@article{Zas62,
author = {Zaslavski{\u{i}}, Igor D.},
title = {Some properties of constructive real numbers and constructive functions ({R}ussian)},
journal = {Tr.\ Mat.\ Inst.\ Steklov},
volume = {67},
number = {4},
year = {1962},
pages = {385--457},
note = {(English translation in: Amer.\ Math.\ Soc.\ Translations 2 57,1--84(1966))},
}
@article{Zas64,
author = {Zaslavski{\u{i}}, Igor D.},
title = {On the differentiation and integration of constructive functions ({R}ussian)},
journal = {Doklady Akademii Nauk},
volume = {156},
year = {1964},
pages = {25--27},
}
@article{Zas67,
author = {Zaslavski{\u{i}}, Igor D.},
title = {Rectifiability of constructive plane curves ({R}ussian)},
journal = {Izv. Akad. Nauk Armjan. SSR Ser. Mat.},
volume = {2},
year = {1967},
pages = {69--82},
}
@inproceedings{ZB00,
author = {Ziegler, Martin and Brattka, Vasco},
title = {Computing the Dimension of Linear Subspaces},
editor = {Hlav{\'{a}}{\v{c}}, V{\'{a}}clav and Jeffery, Keith G. and Wiedermann, Ji{\v{r}}{\'{\i}}},
booktitle = {SOFSEM 2000: Theory and Practice of Informatics},
series = {Lecture Notes in Computer Science},
volume = {1963},
publisher = {Springer},
address = {Berlin},
year = {2000},
pages = {450--458},
note = {27th Conference on Current Trends in Theory and Practice of Informatics, Milovy, Czech Republic, November 25--December 2, 2000},
}
@inproceedings{ZB01,
author = {Ziegler, Martin and Brattka, Vasco},
title = {A Computable Spectral Theorem},
editor = {Blanck, Jens and Brattka, Vasco and Hertling, Peter},
booktitle = {Computability and Complexity in Analysis},
series = {Lecture Notes in Computer Science},
volume = {2064},
publisher = {Springer},
address = {Berlin},
year = {2001},
pages = {378--388},
note = {4th International Workshop, CCA 2000, Swansea, UK, September 2000},
}
@inproceedings{ZB01a,
author = {Ziegler, Martin and Brattka, Vasco},
title = {Turing Computability of (Non-)Linear Optimization},
editor = {Therese Biedl},
booktitle = {Thirteenth Canadian Conference on Computational Geometry},
publisher = {University of Waterloo},
year = {2001},
pages = {181--184},
note = {CCCG 2001, August 13--15, 2001},
}
@inproceedings{ZB03,
author = {Zheng, Xizhong and Barmpalias, George},
title = {On the Monotonic Computability of Semi-computable Real Numbers},
editor = {Calude, Cristian S. and Dinneen, Michael J. and Vajnovszki, Vincent},
booktitle = {Discrete Mathematics and Theoretical Computer Science},
series = {Lecture Notes in Computer Science},
volume = {2731},
publisher = {Springer},
address = {Berlin},
year = {2003},
pages = {290--300},
note = {DMTCS 2003, 4th International Conference, July 7--12, 2003, Dijon},
}
@article{ZB04,
author = {Ziegler, Martin and Brattka, Vasco},
title = {Computability in Linear Algebra},
journal = {Theoretical Computer Science},
volume = {326},
number = {1--3},
year = {2004},
pages = {187--211},
}
@article{ZBW99,
author = {Zheng, Xizhong and Brattka, Vasco and Weihrauch, Klaus},
title = {Approaches to Effective Semi-Continuity of Real Functions},
journal = {Mathematical Logic Quarterly},
volume = {45},
number = {4},
year = {1999},
pages = {481--496},
doi = {10.1002/malq.19990450407},
}
@article{ZH05,
author = {Zhou, Qing and Hu, Weihao},
title = {Decidability in Analysis},
journal = {Computing},
volume = {75},
year = {2005},
pages = {319--336},
}
@article{Zhe02,
author = {Zheng, Xizhong},
title = {The closure properties on real numbers under limits and computable operators},
journal = {Theoretical Computer Science},
volume = {284},
number = {2},
year = {2002},
pages = {499--518},
}
@article{Zhe02a,
author = {Zheng, Xizhong},
title = {Recursive Approximability of Real Numbers},
journal = {Mathematical Logic Quarterly},
volume = {48},
number = {Suppl. 1},
year = {2002},
pages = {131--156},
}
@article{Zhe03,
author = {Zheng, Xizhong},
title = {On the {T}uring degrees of weakly computable real numbers},
journal = {Journal of Logic and Computation},
volume = {13},
number = {2},
year = {2003},
pages = {159--172},
}
@inproceedings{Zhe03a,
author = {Zheng, Xizhong},
title = {On the divergence bounded computable real numbers},
editor = {Warnow, Tandy and Zhu, Binhai},
booktitle = {Computing and Combinatorics},
series = {Lecture Notes in Computer Science},
volume = {2697},
publisher = {Springer},
address = {Berlin},
year = {2003},
pages = {102--111},
note = {{COCOON} 2003, 9th Annual International Conference, July 25-28, 2003, Big Sky, MT, USA},
}
@inproceedings{Zhe04,
author = {Zheng, Xizhong},
title = {On the hierarchy of $\Delta^0_2$--real numbers},
editor = {Frougny, Christiane and Brattka, Vasco and M{\"{u}}ller, Norbert},
booktitle = {RNC'6 Real Numbers and Computers},
year = {2004},
pages = {192--216},
note = {Dagstuhl, Germany, November 15--17, 2004},
}
@inproceedings{Zhe07,
author = {Zheng, Xizhong},
title = {Classification of the computable approximations by divergence boundings},
editor = {Cenzer, Douglas and Dillhage, Ruth and Grubba, Tanja and Weihrauch, Klaus},
booktitle = {Proceedings of the Third International Conference on Computability and Complexity in Analysis},
series = {Electronic Notes in Theoretical Computer Science},
volume = {167},
publisher = {Elsevier},
address = {Amsterdam},
year = {2007},
pages = {325--344},
note = {{CCA} 2006, Gainesville, Florida, USA, November 1--5, 2006},
}
@article{Zhe07a,
author = {Zheng, Xizhong},
title = {On the Hierarchies of {$\Delta^0_2$}--Real Numbers},
journal = {Theoretical Informatics and Applications},
volume = {41},
number = {1},
year = {2007},
pages = {3--25},
}
@inproceedings{Zhe07b,
author = {Zheng, Xizhong},
title = {Bounded computable enumerability and hierarchy of computably enumerable reals},
booktitle = {Computing and combinatorics},
series = {Lecture Notes in Comput. Sci.},
volume = {4598},
publisher = {Springer},
address = {Berlin},
year = {2007},
pages = {327--337},
doi = {10.1007/978-3-540-73545-8_33},
}
@inproceedings{Zhe08,
author = {Zheng, Xizhong},
title = {Finitely Bounded Effective Computability},
editor = {Dillhage, Ruth and Grubba, Tanja and Sorbi, Andrea and Weihrauch, Klaus and Zhong, Ning},
booktitle = {Proceedings of the Fourth International Conference on Computability and Complexity in Analysis ({CCA} 2007)},
series = {Electronic Notes in Theoretical Computer Science},
volume = {202},
publisher = {Elsevier},
year = {2008},
pages = {255--265},
note = {{CCA} 2007, Siena, Italy, June 16--18, 2007},
}
@article{Zhe08a,
author = {Zheng, Xizhong},
title = {A hierarchy of computably enumerable reals},
journal = {Fundamenta Informaticae},
volume = {83},
number = {1-2},
year = {2008},
pages = {219--230},
}
@article{Zhe08b,
author = {Zheng, Xizhong},
title = {Classification of computably approximable real numbers},
journal = {Theory of Computing Systems},
volume = {43},
number = {3-4},
year = {2008},
pages = {603--624},
doi = {10.1007/s00224-007-9026-5},
}
@phdthesis{Zhe98a,
author = {Zheng, Xizhong},
title = {Weak Computability and Semi-Computability in Analysis},
school = {Fachbereich Informatik},
address = {FernUniversit\"{a}t Hagen},
year = {1998},
}
@inproceedings{Zhe99,
author = {Zheng, Xizhong},
title = {Binary Enumerability of Real Numbers},
editor = {Asana, Takao and Imai, Hiroshi and Lee, D.T. and Nakano, Shin-ichi and Tokuyama, Takeshi},
booktitle = {Computing and Combinatorics},
series = {Lecture Notes in Computer Science},
volume = {1627},
publisher = {Springer},
address = {Berlin},
year = {1999},
pages = {300--309},
note = {5th Annual Conference, COCOON'99, Tokyo, Japan, July 1999},
}
@article{Zho00,
author = {Zhou, Qing},
title = {Grzegorczyk's hierarchy of computable analysis},
journal = {Theoretical Computer Science},
volume = {243},
year = {2000},
pages = {449--466},
}
@article{Zho01,
author = {Zhou, Qing},
title = {Relatively computable functions of real variables},
journal = {Computing},
volume = {67},
number = {2},
year = {2001},
pages = {167--181},
}
@inproceedings{Zho05,
author = {Zhong, Ning},
title = {Computable Analysis of a Non-homogeneous Boundary-Value Problem for the {K}orteweg-de {V}ries Equation},
editor = {Cooper, S. Barry and L{\"o}we, Benedikt and Torenvliet, Leen},
booktitle = {New Computational Paradigms},
series = {Lecture Notes in Computer Science},
volume = {3526},
publisher = {Springer},
address = {Berlin},
year = {2005},
pages = {552--561},
note = {{F}irst Conference on Computability in Europe, CiE 2005, Amsterdam, The Netherlands, June 2005},
}
@inproceedings{Zho06,
author = {Zheng, Xizhong},
title = {A Computability Theory of Real Numbers},
editor = {Beckmann, A. and Berger, U. and L{\"o}we, B. and Tucker, J.V.},
booktitle = {Logical Approaches to Computational Barriers},
series = {Lecture Notes in Computer Science},
volume = {3988},
publisher = {Springer},
address = {Berlin},
year = {2006},
pages = {584--594},
note = {Second Conference on Computability in Europe, CiE 2006, Swansea, UK, June 30-July 5, 2006},
}
@article{Zho07,
author = {Zhong, Ning},
title = {Computable Analysis of a Boundary-Value Problem for the {K}orteweg-de {V}ries Equation},
journal = {Theory of Computing Systems},
volume = {41},
number = {1},
year = {2007},
pages = {155--175},
}
@article{Zho09,
author = {Zhong, Ning},
title = {Computational unsolvability of domains of attraction of nonlinear systems},
journal = {Proc. Amer. Math. Soc.},
volume = {137},
number = {8},
year = {2009},
pages = {2773--2783},
doi = {10.1090/S0002-9939-09-09851-7},
}
@phdthesis{Zho92,
author = {Zhou, Qing},
title = {Computability on open and closed subsets of {E}uclidean space},
school = {University of Minnesota},
address = {Minneapolis},
year = {1992},
}
@article{Zho96,
author = {Zhou, Qing},
title = {Computable real-valued functions on recursive open and closed subsets of {E}uclidean space},
journal = {Mathematical Logic Quarterly},
volume = {42},
year = {1996},
pages = {379--409},
}
@article{Zho96a,
author = {Zhong, Ning},
title = {Effective Separation Axioms},
journal = {Questions and Answers in General Topology},
volume = {14},
number = {2},
year = {1996},
pages = {177--185},
}
@inproceedings{Zho97,
author = {Zhou, Qing},
title = {Subclasses of Computable Real Valued Functions},
editor = {Jiang, Tao and Lee, D.T.},
booktitle = {Computing and Combinatorics},
series = {Lecture Notes in Computer Science},
volume = {1276},
publisher = {Springer},
address = {Berlin},
year = {1997},
pages = {156--165},
note = {Third Annual Conference, COCOON'97, Shanghai, China, August 1997},
}
@article{Zho97a,
author = {Zhong, Ning},
title = {Effective collectionwise {H}ausdorff and normal axioms},
journal = {Questions and Answers in General Topology},
volume = {15},
number = {2},
year = {1997},
pages = {225--230},
}
@article{Zho98,
author = {Zhong, Ning},
title = {Recursively Enumerable Subsets of ${R}^q$ In Two Computing Models: {B}lum-{S}hub-{S}male Machine and {T}uring Machine},
journal = {Theoretical Computer Science},
volume = {197},
year = {1998},
pages = {79--94},
}
@article{Zho98a,
author = {Zhong, Ning},
title = {Derivatives of computable functions},
journal = {Mathematical Logic Quarterly},
volume = {44},
year = {1998},
pages = {304--316},
}
@article{Zho99,
author = {Zhong, Ning},
title = {Computability structure of the {S}obolev spaces and its applications},
journal = {Theoretical Computer Science},
volume = {219},
year = {1999},
pages = {487--510},
}
@article{Zie02,
author = {Ziegler, Martin},
title = {Computability on Regular Subsets of {E}uclidean Space},
journal = {Mathematical Logic Quarterly},
volume = {48},
number = {Suppl. 1},
year = {2002},
pages = {157--181},
}
@phdthesis{Zie02a,
author = {Ziegler, Martin},
title = {Zur Berechenbarkeit reeller geometrischer Probleme},
school = {Fachbereich Mathematik/Informatik, Universit\"at Paderborn},
address = {Paderborn},
year = {2002},
}
@inproceedings{Zie03,
author = {Ziegler, Martin},
title = {Computable operators on regular sets},
editor = {Brattka, Vasco and Schr{\"{o}}der, Matthias and Weihrauch, Klaus and Zhong, Ning},
booktitle = {Computability and Complexity in Analysis},
series = {Informatik Berichte},
volume = {302},
publisher = {FernUniversit\"at in Hagen},
year = {2003},
month = aug,
pages = {389--406},
note = {International Conference, CCA 2003, Cincinnati, USA, August 28--30, 2003},
}
@inproceedings{Zie03a,
author = {Ziegler, Martin},
title = {Stability versus Speed in a Computable Algebraic Model},
editor = {Daumas, Marc et al.},
booktitle = {RNC'5 Real Numbers and Computers},
year = {2003},
pages = {47--64},
note = {Lyon, September 3--5, 2003},
}
@article{Zie04,
author = {Ziegler, Martin},
title = {Computable operators on regular sets},
journal = {Mathematical Logic Quarterly},
volume = {50},
number = {4,5},
year = {2004},
pages = {392--404},
}
@inproceedings{Zie05,
author = {Ziegler, Martin},
title = {Computability and Continuity on the Real Arithmetic Hierarchy and the Power of Type-2 Nondeterminism},
editor = {Cooper, Barry S. and L{\"o}we, Benedikt and Torenvliet, Leen},
booktitle = {New Computational Paradigms},
series = {Lecture Notes in Computer Science},
volume = {3526},
publisher = {Springer},
address = {Berlin},
year = {2005},
pages = {562--571},
note = {First Conference on Computability in Europe, CiE 2005, Amsterdam, The Netherlands, June 2005},
}
@article{Zie05b,
author = {Ziegler, Martin},
title = {Computational Power of Infinite Quantum Parallelism},
journal = {International Journal of Theoretical Physics},
volume = {44},
number = {11},
year = {2005},
pages = {2059--2071},
doi = {10.1007/s10773-005-8984-0},
}
@article{Zie06,
author = {Ziegler, Martin},
title = {Stability versus speed in a computable algebraic model},
journal = {Theoretical Computer Science},
volume = {351},
number = {1},
year = {2006},
pages = {14--26},
}
@article{Zie06b,
author = {Ziegler, Martin},
title = {Effectively open real functions},
journal = {Journal of Complexity},
volume = {22},
number = {6},
year = {2006},
pages = {827--849},
}
@inproceedings{Zie07,
author = {Ziegler, Martin},
title = {Revising type-2 computation and degrees of discontinuity},
editor = {Cenzer, Douglas and Dillhage, Ruth and Grubba, Tanja and Weihrauch, Klaus},
booktitle = {Proceedings of the Third International Conference on Computability and Complexity in Analysis},
series = {Electronic Notes in Theoretical Computer Science},
volume = {167},
publisher = {Elsevier},
address = {Amsterdam},
year = {2007},
pages = {255--274},
note = {{CCA} 2006, Gainesville, Florida, USA, November 1--5, 2006},
}
@article{Zie07a,
author = {Ziegler, Martin},
title = {Real Hypercomputation and Continuity},
journal = {Theory of Computing Systems},
volume = {41},
number = {1},
year = {2007},
pages = {177--206},
}
@inproceedings{Zie07b,
author = {Ziegler, Martin},
title = {({S}hort) Survey of Real Hypercomputation},
editor = {Cooper, S. Barry and L{\"o}we, Benedikt and Sorbi, Andrea},
booktitle = {Computation and Logic in the Real World},
series = {Lecture Notes in Computer Science},
volume = {4497},
publisher = {Springer},
address = {Berlin},
year = {2007},
pages = {809--824},
note = {Third Conference on Computability in Europe, CiE 2007, Siena, Italy, June 18-23, 2007},
}
@phdthesis{Zie07c,
author = {Ziegler, Martin},
title = {Real Computability and Hypercomputation},
school = {Department of Computer Science, University of Paderborn},
address = {Paderborn, Germany},
year = {2007},
note = {Habilitation Thesis},
}
@article{Zie09,
author = {Ziegler, Martin},
title = {Physically-relativized {C}hurch-{T}uring {H}ypotheses: physical foundations of computing and complexity theory of computational physics},
journal = {Appl. Math. Comput.},
volume = {215},
number = {4},
year = {2009},
pages = {1431--1447},
doi = {10.1016/j.amc.2009.04.062},
}
@article{Zie12,
author = {Ziegler, Martin},
title = {Real computation with least discrete advice: a complexity theory of nonuniform computability with applications to effective linear algebra},
journal = {Ann. Pure Appl. Logic},
volume = {163},
number = {8},
year = {2012},
pages = {1108--1139},
doi = {10.1016/j.apal.2011.12.030},
}
@article{ZLB06,
author = {Zheng, Xizhong and Lub, Dianchen and Bao, Kejin},
title = {Divergence bounded computable real numbers},
journal = {Theoretical Computer Science},
volume = {351},
number = {1},
year = {2006},
pages = {27--38},
}
@inproceedings{ZM08,
author = {Zhao, Xishun and M\"uller, Norbert},
title = {Complexity of Operators on Compact Sets},
editor = {Dillhage, Ruth and Grubba, Tanja and Sorbi, Andrea and Weihrauch, Klaus and Zhong, Ning},
booktitle = {Proceedings of the Fourth International Conference on Computability and Complexity in Analysis ({CCA} 2007)},
series = {Electronic Notes in Theoretical Computer Science},
volume = {202},
publisher = {Elsevier},
year = {2008},
pages = {101--119},
note = {{CCA} 2007, Siena, Italy, June 16--18, 2007},
}
@article{ZM68,
author = {Zaslavski\u{\i}, I. D. and Manukjan, S. N.},
title = {Partitionings of the plane by constructive curves},
journal = {Trudy Vy\v{c}isl. Centra Akad. Nauk Armjan. SSR i Erevan. Gos. Univ.},
volume = {5},
year = {1968},
pages = {26--138},
}
@inproceedings{ZR03,
author = {Zheng, Xizhong and Rettinger, Robert},
title = {$h$--{M}onotonically computable real numbers},
editor = {Brattka, Vasco and Schr{\"{o}}der, Matthias and Weihrauch, Klaus and Zhong, Ning},
booktitle = {Computability and Complexity in Analysis},
series = {Informatik Berichte},
volume = {302},
publisher = {FernUniversit\"at in Hagen},
year = {2003},
month = aug,
pages = {375--388},
note = {International Conference, CCA 2003, Cincinnati, USA, August 28--30, 2003},
}
@article{ZR04,
author = {Zheng, Xizhong and Rettinger, Robert},
title = {Weak computability and representation of reals},
journal = {Mathematical Logic Quarterly},
volume = {50},
number = {4,5},
year = {2004},
pages = {431--442},
}
@inproceedings{ZR04b,
author = {Zheng, Xizhong and Rettinger, Robert},
title = {On the extensions of {S}olovay Reducibility},
editor = {Chwa, Kyung-Yong and Munro, J. Ian},
booktitle = {Computing and Combinatorics},
series = {Lecture Notes in Computer Science},
volume = {3106},
publisher = {Springer},
address = {Berlin},
year = {2005},
pages = {360--369},
note = {10th Annual International Conference, {COCOON} 2004, Jeju Island, Korea, August 17--20, 2004},
}
@inproceedings{ZR05,
author = {Zheng, Xizhong and Rettinger, Robert},
title = {A Note On the {T}uring Degrees of Divergence Bounded Computable Reals},
editor = {Brattka, Vasco and Staiger, Ludwig and Weihrauch, Klaus},
booktitle = {Proceedings of the 6th Workshop on Computability and Complexity in Analysis},
series = {Electronic Notes in Theoretical Computer Science},
volume = {120},
publisher = {Elsevier},
address = {Amsterdam},
year = {2005},
pages = {231--237},
note = {6th International Workshop, {CCA} 2004, Wittenberg, Germany, August 16--20, 2004},
}
@article{ZR05a,
author = {Zheng, Xizhong and Rettinger, Robert},
title = {Effective {J}ordan decomposition},
journal = {Theory of Computing Systems},
volume = {38},
number = {2},
year = {2005},
pages = {189--209},
}
@article{ZR12,
author = {Zheng, Xizhong and Rettinger, Robert},
title = {Point-separable classes of simple computable planar curves},
journal = {Log. Methods Comput. Sci.},
volume = {8},
number = {3},
year = {2012},
pages = {3:15, 19},
}
@inproceedings{ZRB02,
author = {Zheng, Xizhong and Rettinger, Robert and von Braunm\"uhl, Burchard},
title = {Effectively Absolute Continuity and Effective {J}ordan Decomposability},
editor = {Brattka, Vasco and Schr{\"{o}}der, Matthias and Weihrauch, Klaus},
booktitle = {{CCA} 2002 Computability and Complexity in Analysis},
series = {Electronic Notes in Theoretical Computer Science},
volume = {66},
publisher = {Elsevier},
address = {Amsterdam},
year = {2002},
note = {5th International Workshop, {CCA} 2002, M{\'{a}}laga, Spain, July 12--13, 2002},
}
@inproceedings{ZRB03,
author = {Zheng, Xizhong and Rettinger, Robert and von Braunm\"uhl, Burchard},
title = {On the Effective {J}ordan Decomposability},
editor = {Alt, Helmut and Habib, Michel},
booktitle = {STACS 2003},
series = {Lecture Notes in Computer Science},
volume = {2607},
publisher = {Springer},
address = {Berlin},
year = {2003},
pages = {167--178},
note = {20th Annual Symposium on Theoretical Aspects of Computer Science, Berlin, Germany, February 27--March 1, 2003},
}
@article{ZRB05,
author = {Zheng, Xizhong and Rettinger, Robert and Barmpalias, George},
title = {h-monotonically computable real numbers},
journal = {Mathematical Logic Quarterly},
volume = {51},
number = {2},
year = {2005},
pages = {157--170},
doi = {10.1002/malq.200410016},
}
@inproceedings{ZRG03,
author = {Zheng, Xizhong and Rettinger, Robert and Gengler, Romain},
title = {Ershov's hierarchy of real numbers},
editor = {Rovan, B. and Vojtas, P.},
booktitle = {Mathematical Foundations of Computer Science 2003},
series = {Lecture Notes in Computer Science},
volume = {2747},
publisher = {Springer},
address = {Berlin},
year = {2003},
pages = {681--690},
note = {MFCS 2003, August 25--29, 2003, Bratislava, Slovakia},
}
@article{ZRG05,
author = {Zheng, Xizhong and Rettinger, Robert and Gengler, Romain},
title = {Closure properties of real number classes under {CBV} functions},
journal = {Theory of Computing Systems},
volume = {38},
year = {2005},
pages = {701--729},
}
@article{ZW01,
author = {Zheng, Xizhong and Weihrauch, Klaus},
title = {The Arithmetical Hierarchy of Real Numbers},
journal = {Mathematical Logic Quarterly},
volume = {47},
number = {1},
year = {2001},
pages = {51--65},
}
@article{ZW03,
author = {Zhong, Ning and Weihrauch, Klaus},
title = {Computability theory of generalized functions},
journal = {Journal of the Association for Computing Machinery},
volume = {50},
number = {4},
year = {2003},
pages = {469--505},
}
@inproceedings{ZW99,
author = {Zheng, Xizhong and Weihrauch, Klaus},
title = {The Arithmetical Hierarchy of Real Numbers},
editor = {Kuty{\l}owski, Miros{\l}aw and Pacholski, Leszek and Wierzbicki, Tomasz},
booktitle = {Mathematical Foundations of Computer Science 1999},
series = {Lecture Notes in Computer Science},
volume = {1672},
publisher = {Springer},
address = {Berlin},
year = {1999},
pages = {23--33},
note = {24th International Symposium, MFCS'99, Szklarska Por\c{e}ba, Poland, September, 1999},
}
@article{ZZ99,
author = {Zhong, Ning and Zhang, Bing-Yu},
title = {{$L^p$}-Computability},
journal = {Mathematical Logic Quarterly},
volume = {45},
number = {4},
year = {1999},
pages = {449--456},
}
%
% This bibliography has 2527 entries
%