%
% CCA Bibliography on
% Constructivity, Computability and Complexity in Analysis
%
% http://cca-net.de/
%
% Last updated on 1 December 2022
%
% (c) 2000-2022 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},
}
@incollection{AH22a,
author = {Amir, Djamel Eddine and Hoyrup, Mathieu},
title = {Computability of finite simplicial complexes},
booktitle = {49th {EATCS} {I}nternational {C}onference on {A}utomata, {L}anguages, and {P}rogramming},
series = {LIPIcs. Leibniz Int. Proc. Inform.},
volume = {229},
publisher = {Schloss Dagstuhl. Leibniz-Zent. Inform., Wadern},
year = {2022},
pages = {Art. No. 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{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},
}
@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},
}
@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},
}
@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},
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year = {2014},
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author = {Bridges, Douglas S. and Dent, James and McKubre-Jordens, Maarten},
title = {{Z}-stability in Constructive Analysis},
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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},
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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},
}
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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},
}
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title = {A domain-theoretic approach to {B}rownian motion and general continuous stochastic processes},
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pages = {10--26},
doi = {10.1016/j.tcs.2017.07.016},
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publisher = {Springer},
address = {Heidelberg},
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pages = {35--45},
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author = {Beeson, Michael},
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publisher = {Polimetrica},
address = {Milano},
year = {2005},
pages = {9--37},
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publisher = {North-Holland},
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author = {Beeson, Michael J.},
title = {Foundations of {C}onstructive {M}athematics},
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author = {Berger, Josef},
title = {Exact calculation of inverse functions},
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year = {2005},
pages = {201--205},
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@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},
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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},
}
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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},
}
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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},
}
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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},
}
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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},
}
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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},
}
@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},
}
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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},
}
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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},
volume = {accepted for publication},
year = {2022},
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},
}
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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},
}
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author = {Binder, Ilia and Rojas, Cristobal and Yampolsky, Michael},
title = {Carath\'{e}odory convergence and harmonic measure},
journal = {Potential Analysis},
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number = {4},
year = {2019},
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doi = {10.1007/s11118-018-9721-7},
}
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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},
}
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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},
}
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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,
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title = {Constructing non-computable {J}ulia sets},
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author = {Braverman, Mark and Yampolsky, Michael},
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author = {Braverman, Mark and Yampolsky, Michael},
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author = {Calude, Cristian S.},
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address = {Lisbon},
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series = {Lecture Notes in Computer Science},
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year = {2002},
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note = {Third International Conference, UMC 2002, Kobe, Japan, October 15-19, 2002},
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author = {Carroy, Rapha{\"e}l},
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address = {Amsterdam},
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title = {Certified Reasoning on Real Numbers and Objects in Co-inductive Type Theory},
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year = {2003},
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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{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},
year = {2022},
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 = {Hannes Diener},
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},
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note = {4th International Workshop, CCA 2000, Swansea, UK, September 2000},
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booktitle = {{CCA} 2002 Computability and Complexity in Analysis},
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volume = {66},
publisher = {Elsevier},
address = {Amsterdam},
year = {2002},
note = {5th International Workshop, {CCA} 2002, M{\'{a}}laga, Spain, July 12--13, 2002},
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author = {Hertling, Peter},
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booktitle = {Automata, Languages and Programming},
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year = {2003},
month = aug,
pages = {13},
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booktitle = {Computability and Complexity: Essays Dedicated to Rodney G. Downey on the Occasion of His 60th Birthday},
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booktitle = {29th {I}nternational {S}ymposium on {T}heoretical {A}spects of {C}omputer {S}cience},
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booktitle = {31st International Symposium on Theoretical Aspects of Computer Science (STACS 2014)},
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@inproceedings{Hoy16,
author = {Hoyrup, Mathieu},
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doi = {10.1007/978-3-319-40189-8_12},
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@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.},
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publisher = {Schloss Dagstuhl. Leibniz-Zent. Inform., Wadern},
year = {2016},
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@inproceedings{Hoy18,
author = {Hoyrup, Mathieu},
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volume = {10936},
publisher = {Springer},
address = {Cham},
year = {2018},
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author = {Hoyrup, Mathieu},
title = {Descriptive Complexity on Non-{P}olish Spaces {II}},
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booktitle = {47th International Colloquium on Automata, Languages, and Programming ({ICALP} 2020)},
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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},
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@incollection{Hoy20a,
author = {Hoyrup, Mathieu},
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journal = {Journal of Complexity},
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year = {1986},
pages = {95--120},
}
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author = {Ko, Ker-I},
title = {On the continued fraction representation of computable real numbers},
journal = {Theoretical Computer Science},
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year = {1986},
pages = {299--313},
note = {corr. ibid., Vol. 54 (1987), Pages 341--343},
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author = {Ko, Ker-I},
title = {Corrigenda: ``{O}n the continued fraction representation of computable real numbers''},
journal = {Theoretical Computer Science},
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number = {2-3},
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pages = {341--343},
doi = {10.1016/0304-3975(87)90139-3},
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author = {Ko, Ker-I},
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booktitle = {Feasible Mathematics},
journal = {Progr. Comput. Sci. Appl. Logic},
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pages = {239--257},
note = {(Proc. Workshop, June 16--18, 1989, Cornell Univ. Ithaca, NY)},
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author = {Ko, Ker-I},
title = {Complexity Theory of Real Functions},
series = {Progress in Theoretical Computer Science},
publisher = {Birkh\"auser},
address = {Boston},
year = {1991},
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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},
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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},
}
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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},
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author = {Ko, Ker-I},
title = {Computational complexity of fixed points and intersection points},
journal = {Journal of Complexity},
volume = {11},
year = {1995},
pages = {265--292},
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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},
}
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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},
}
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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},
}
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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},
}
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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},
}
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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},
}
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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},
}
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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},
}
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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},
}
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author = {Kohlenbach, Ulrich},
title = {On the Disjunctive {M}arkov Principle},
journal = {Studia Logica},
volume = {103},
number = {6},
year = {2015},
pages = {1313--1317},
}
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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},
}
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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},
}
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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},
}
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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},
}
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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},
}
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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},
}
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author = {Kohlenbach, Ulrich},
title = {Proof theory and computational analysis},
journal = {Electronic Notes in Theoretical Computer Science},
volume = {13},
year = {1998},
pages = {1--34},
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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},
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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]},
}
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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},
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author = {Kone{\v{c}}n{\'{y}}, Michal},
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author = {Kone{\v{c}}n{\'{y}}, Michal},
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author = {Kihara, Takayuki and Pauly, Arno},
title = {Dividing by Zero - How Bad Is It, Really?},
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booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
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publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
year = {2016},
pages = {58:1--58:14},
doi = {10.4230/LIPIcs.MFCS.2016.58},
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@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},
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author = {Kihara, Takayuki and Pauly, Arno},
title = {Finite choice, convex choice and sorting},
editor = {Gopal, T.V. and Watada, Junzo},
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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},
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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},
}
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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},
}
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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},
}
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author = {Lorenzen, Paul},
title = {Mass und {I}ntegral in der konstruktiven {A}nalysis},
journal = {Mathematische Zeitschrift},
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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},
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author = {Lorenzen, Paul},
title = {Konstruktive {A}nalysis und das geometrische {K}ontinuum},
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year = {1978},
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@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},
}
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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},
}
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author = {Luckhardt, Horst},
title = {A fundamental effect in computations on real numbers},
journal = {Theoretical Computer Science},
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number = {3},
year = {1977},
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}
@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},
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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},
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author = {Manukjan, S. N.},
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@article{Man71a,
author = {Manukjan, S. N.},
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publisher = {American Mathematical Society (AMS), Providence, RI},
year = {1971},
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@article{Man73,
author = {Manukjan, S. N.},
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@article{Man73a,
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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},
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@article{Man75,
author = {Manukjan, S. N.},
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volume = {220},
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pages = {1267--1270},
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@article{Man75a,
author = {Manukjan, S. N.},
title = {Some properties of partitionings of the plane by nondegenerate constructive curves},
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volume = {8},
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author = {Manukjan, S. N.},
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publisher = {American Mathematical Society (AMS), Providence, RI},
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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.},
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author = {Mandelkern, Mark},
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@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},
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booktitle = {6th International Conference on Computability and Complexity in Analysis (CCA'09)},
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}
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author = {Pauly, Arno},
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author = {Pauly, Arno},
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number = {5},
year = {2010},
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@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},
}
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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},
}
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author = {Pauly, Arno},
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number = {2},
year = {2016},
pages = {159--180},
doi = {10.3233/COM-150049},
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doi = {10.1017/S0960129515000262},
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booktitle = {Sailing Routes in the World of Computation},
publisher = {Springer},
address = {Cham},
year = {2018},
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doi = {10.1007/978-3-319-94418-0_33},
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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},
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author = {P{\'e}gny, Ma{\"e}l},
title = {Sur les limites empiriques du calcul -- Calculabilit{\'e}, complexit{\'e} et physique},
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author = {P{\'e}gny, Ma{\"e}l},
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author = {Pequignot, Yann},
title = {Better-quasi-order: ideals and spaces},
school = {University of Lausanne and University Paris 7},
year = {2015},
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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},
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author = {Petrakis, Iosif},
title = {A Direct Constructive Proof of a {S}tone-{W}eierstrass Theorem for Metric Spaces},
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series = {Lecture Notes in Computer Science},
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publisher = {Springer},
address = {Switzerland},
year = {2016},
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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},
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author = {Petrakis, Iosif},
title = {A constructive function-theoretic approach to topological compactness},
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address = {New York},
year = {2016},
pages = {10},
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author = {Petrakis, Iosif},
title = {The {U}rysohn extension theorem for {B}ishop spaces},
booktitle = {Logical foundations of computer science},
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volume = {9537},
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address = {Cham},
year = {2016},
pages = {299--316},
doi = {10.1007/978-3-319-27683-0_21},
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author = {Petrakis, Iosif},
title = {{McShane}-{W}hitney Pairs},
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booktitle = {Unveiling Dynamics and Complexity},
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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},
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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.},
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year = {2017},
pages = {484--498},
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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},
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series = {Lecture Notes in Computer Science},
volume = {11558},
publisher = {Springer},
address = {Cham},
year = {2019},
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note = {15th Conference on Computability in Europe, CiE 2019, Durham, UK, July 15-19, 2019},
doi = {10.1007/978-3-030-22996-2_21},
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author = {Petrakis, Iosif},
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author = {Pauly, Arno and Fouch{\'{e}}, Willem and Davie, George},
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author = {Porter, Christopher P.},
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series = {Lecture Notes in Computer Science},
volume = {4497},
publisher = {Springer},
address = {Berlin},
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pages = {638--647},
note = {Third Conference on Computability in Europe, CiE 2007, Siena, Italy, June 18-23, 2007},
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author = {Rettinger, Robert},
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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},
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publisher = {Elsevier},
year = {2008},
pages = {315--322},
note = {{CCA} 2007, Siena, Italy, June 16--18, 2007},
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booktitle = {{CCA} 2008, Fifth International Conference on Computability and Complexity in Analysis},
series = {Electronic Notes in Theoretical Computer Science},
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publisher = {Elsevier},
year = {2008},
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note = {{CCA} 2008, Fifth International Conference, Hagen, Germany, August 21--24, 2008},
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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},
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number = {8},
publisher = {Cambridge University Press},
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pages = {1495--1520},
doi = {10.1017/S0960129516000153},
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note = {4th International Workshop, CCA 2000, Swansea, UK, September 2000},
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author = {Rojas, Crist{\'o}bal and Yampolsky, Michael},
title = {Computable Geometric Complex Analysis and Complex Dynamics},
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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},
}
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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},
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doi = {10.4204/EPTCS.213.3},
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@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},
}
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author = {{\v{S}}anin, N.A.},
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author = {{\v{S}}anin, N.A.},
title = {Constructive Real Numbers and Constructive Function Spaces},
series = {Translations of Mathematical Monographs},
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publisher = {American Mathematical Society},
address = {Providence},
year = {1968},
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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},
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author = {{\v{S}}anin, N.A.},
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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},
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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},
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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}},
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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},
}
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author = {Sella, Lorenzo and Collins, Pieter},
title = {Computation of symbolic dynamics for one-dimensional maps},
journal = {J. Comput. Appl. Math.},
volume = {234},
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year = {2010},
pages = {418--436},
doi = {10.1016/j.cam.2009.12.034},
}
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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},
}
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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},
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author = {Scarpellini, Bruno},
title = {A model for barrecursion of higher types},
journal = {Compositio Mathematica},
volume = {23},
year = {1971},
pages = {123--153},
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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},
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@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},
}
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year = {2000},
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author = {van Lambalgen, Michiel},
title = {Random sequences},
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year = {1987},
note = {{Ph.D.} thesis},
}
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author = {Va{\u\i}nberg, Ju. R. and Nogina, Elena Ju.},
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author = {Waaldijk, Frank},
title = {Modern Intuitionistic Topology},
school = {Radboud University Nijmegen},
year = {1996},
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author = {Wang, Hao},
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journal = {Monograph. Enseign. Math.},
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publisher = {Univ. Geneva},
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@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},
}
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@book{Wei00,
author = {Weihrauch, Klaus},
title = {Computable Analysis},
publisher = {Springer},
address = {Berlin},
year = {2000},
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@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},
}
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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},
}
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author = {Welch, P.D.},
title = {The extent of computation in {M}alament-{H}ogarth spacetimes},
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volume = {59},
number = {4},
year = {2008},
pages = {659--674},
}
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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},
}
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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},
}
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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},
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author = {Weyl, H.},
title = {Das {K}ontinuum},
publisher = {Veit},
address = {Leipzig},
year = {1978},
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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},
}
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author = {Whyman, Richard Arthur James},
title = {Characterising Computational Devices with Logical Systems},
school = {School of Mathematics, University of Leeds},
year = {2018},
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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},
}
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title = {Computing with infinite objects},
journal = {Theoretical Computer Science},
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year = {1980},
pages = {133--155},
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author = {Weihrauch, Klaus and Kreitz, Christoph},
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volume = {35},
year = {1987},
pages = {247--260},
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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},
}
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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},
}
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year = {1996},
pages = {564--568},
}
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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},
}
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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},
}
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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},
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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},
}
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