This is the complete alphabetically sorted bibliography on Constructivity, Computability and Complexity
in Analysis with
1403 references, last updated Sat Feb 14 19:24:33 Europe/Berlin 2009
Oliver Aberth.
Analysis in the computable number field.
Journal of the Association for Computing Machinery, 15:275-299,
1968.
Oliver Aberth.
A chain of inclusion relations in computable analysis.
Proceedings of the American Mathematical Society, 22:539-548,
1969.
Oliver Aberth.
Computable analysis and differential equations.
In A. Kino, J. Myhill, and R.E. Vesley, editors, Intuitionism and Proof
Theory, Studies in Logic and the Foundations of Mathematics, pages
47-52, Amsterdam, 1970. North-Holland.
Proc. of the Summer Conf. at Buffalo N.Y. 1968.
Oliver Aberth.
The failure in computable analysis of a classical existence theorem for
differential equations.
Proceedings of the American Mathematical Society, 30:151-156,
1971.
Oliver Aberth.
Computable Analysis.
McGraw-Hill, New York, 1980.
Yohji Akama and Shinji
Iizuka.
Real number representations of graph-directed IFS attractors.
In Tanja Grubba, Peter Hertling, Hideki Tsuiki, and Klaus Weihrauch, editors,
Computability and Complexity in Analysis, volume 326 of
Informatik Berichte, pages 3-24. FernUniversität in Hagen,
July 2005.
Proccedings, Second International Conference, CCA 2005, Kyoto, Japan, August
25-29, 2005.
Klaus Ambos-Spies, Klaus
Weihrauch, and Xizhong Zheng.
Weakly computable real numbers.
Journal of Complexity, 16(4):676-690, 2000.
Klaus Ambos-Spies.
A note on recursively approximable real numbers.
Forschungsbericht Mathematische Logik 38, Universität Heidelberg, Heidelberg,
1998.
Valentin V. Andreev, Dale
Daniel, and Timothy H. McNicholl.
Technical report: Computation on the extended complex plane and conformal
mapping of multiply-connected domains.
In Vasco Brattka, Ruth Dillhage, Tanja Grubba, and Angela Klutsch, editors,
CCA 2008, Fifth International Conference on Computability and
Complexity in Analysis, volume 221 of Electronic Notes in
Theoretical Computer Science, pages 127-139. Elsevier, 2008.
CCA 2008, Fifth International Conference, Hagen, Germany, August 21-24,
2008.
Kalvis
Apsitis, Setsuo Arikawa, Rusins Freivalds, Eiju
Hirowatari, and Carl H. Smith.
On the inductive inference of recursive real-valued functions.
Theoretical Computer Science, 219:3-17, 1999.
Margaret Archibald, Vasco
Brattka, and Clemens Heuberger.
Randomness with respect to the signed-digit representation.
Fundamenta Informaticae, 83(1-2):1-19, 2008.
Jeremy Avigad and Ksenija
Simic.
Fundamental notions of analysis in subsystems of second-order arithmetic.
Annals of Pure and Applied Logic, 139:138-184, 2006.
Jeremy Avigad.
Weak theories of nonstandard arithmetic and analysis.
In Stephen Simpson, editor, Reverse Mathematics 2001, Lecture
Notes in Logic, pages 19-46, La Jolla, 2005. Association for Symbolic
Logic.
Serikzhan Badaev and
Dieter Spreen.
A note on partial numberings.
Mathematical Logic Quarterly, 51(2):129-136, 2005.
G. Baigger.
Die Nichtkonstruktivität des Brouwerschen Fixpunktsatzes.
Arch. Math. Logik Grundlag., 25:183-188, 1985.
R. Baire.
Sur les fonctions des variables reeles.
Annali di matematica pura ed applicata, 3:1-123, 1899.
Stefan Banach and
Stanislaw Mazur.
Sur les fonctions calculables.
Ann. Soc. Pol. de Math., 16:223, 1937.
George
Barmpalias and Antonio Montalbán.
A cappable almost everywhere dominating computably enumerable degree.
In Douglas Cenzer, Ruth Dillhage, Tanja Grubba, and Klaus Weihrauch, editors,
Proceedings of the Third International Conference on Computability and
Complexity in Analysis, volume 167 of Electronic Notes in
Theoretical Computer Science, pages 17-31, Amsterdam, 2007. Elsevier.
CCA 2006, Gainesville, Florida, USA, November 1-5, 2006.
George Barmpalias,
Douglas Cenzer, Jeffrey B. Remmel, and Rebecca Weber.
K-trivial closed sets and continuous functions.
In S. Barry Cooper, Benedikt Löwe, and Andrea Sorbi, editors,
Computation and Logic in the Real World, volume 4497 of
Lecture Notes in Computer Science, pages 135-145, Berlin, 2007.
Springer.
Third Conference on Computability in Europe, CiE 2007, Siena, Italy, June
18-23, 2007.
George Barmpalias, Paul
Brodhead, Douglas Cenzer, Jeffrey B. Remmel, and Rebecca Weber.
Algorithmic randomness of continuous functions.
Archive for Mathematical Logic, 46(7-8):533–--546, 2008.
George Barmpalias,
Douglas Cenzer, Jeffrey B. Remmel, and Rebecca Weber.
K-triviality of closed sets and continuous functions.
Journal of Logic and Computation, 19(1):3-16, 2009.
George Barmpalias.
On 0'-computable reals.
In Vasco Brattka, Matthias Schröder, and Klaus Weihrauch, editors,
CCA 2002 Computability and Complexity in Analysis, volume 66
of Electronic Notes in Theoretical Computer Science, Amsterdam,
2002. Elsevier.
5th International Workshop, CCA 2002, Málaga, Spain, July 12-13,
2002.
George Barmpalias.
The approximation structure of a computably approximable real.
The Journal of Symbolic Logic, 68(3):885-922, 2003.
George Barmpalias.
A transfinite hierarchy of reals.
Mathematical Logic Quarterly, 49(2):163-172, 2003.
George Barmpalias.
Approximation representations for delta 2 reals.
Archive for Mathematical Logic, 43(8):947-964, 2004.
George Barmpalias.
Approximation representations for reals and their wtt-degrees.
Mathematical Logic Quarterly, 50(4,5):370-380, 2004.
Georgios Barmpalias.
Computability and Applications to Analysis.
PhD thesis, University of Leeds, School of Mathematics, Leeds, 2004.
George Barmpalias.
Random non-cupping revisited.
Journal of Complexity, 22(6):850-857, 2006.
M. A. Baroni and D. S.
Bridges.
Continuity properties of preference relations.
In Ruth Dillhage, Tanja Grubba, Andrea Sorbi, Klaus Weihrauch, and Ning Zhong,
editors, Proceedings of the Fourth International Conference on
Computability and Complexity in Analysis (CCA 2007), volume 202 of
Electronic Notes in Theoretical Computer Science, pages 19-25.
Elsevier, 2008.
CCA 2007, Siena, Italy, June 16-18, 2007.
Marian A. Baroni and
Douglas S. Bridges.
Continuity properties of preference relations.
Mathematical Logic Quarterly, 54(5):454-459, 2008.
Marian Alexandru Baroni.
Constructive suprema.
Journal of Universal Computer Science, 11(12):1865-1877, 2005.
Prashant Batra.
Newton's method and the computational complexity of the fundamental theorem of
algebra.
In Ruth Dillhage, Tanja Grubba, Andrea Sorbi, Klaus Weihrauch, and Ning Zhong,
editors, Proceedings of the Fourth International Conference on
Computability and Complexity in Analysis (CCA 2007), volume 202 of
Electronic Notes in Theoretical Computer Science, pages
201-218. Elsevier, 2008.
CCA 2007, Siena, Italy, June 16-18, 2007.
Andrej Bauer and Iztok
Kavkler.
Implementing real numbers with RZ.
In Ruth Dillhage, Tanja Grubba, Andrea Sorbi, Klaus Weihrauch, and Ning Zhong,
editors, Proceedings of the Fourth International Conference on
Computability and Complexity in Analysis (CCA 2007), volume 202 of
Electronic Notes in Theoretical Computer Science, pages
365-384. Elsevier, 2008.
CCA 2007, Siena, Italy, June 16-18, 2007.
Andrej Bauer and Alex
Simpson.
Locally non-compact spaces and continuity principles.
In Vasco Brattka, Matthias Schröder, Klaus Weihrauch, and Ning Zhong,
editors, Computability and Complexity in Analysis, volume 302 of
Informatik Berichte, pages 103-116. FernUniversität in Hagen,
August 2003.
International Conference, CCA 2003, Cincinnati, USA, August 28-30, 2003.
Andrej Bauer and Alex
Simpson.
Two constructive embedding-extension theorems with applications to continuity
principles and to Banach-Mazur computability.
Mathematical Logic Quarterly, 50(4,5):351-369, 2004.
Andrej Bauer and
Christopher A. Stone.
RZ: A tool for bringing constructive and computable mathematics closer to
programming practice.
In S. Barry Cooper, Benedikt Löwe, and Andrea Sorbi, editors,
Computation and Logic in the Real World, volume 4497 of
Lecture Notes in Computer Science, pages 28-42, Berlin, 2007.
Springer.
Third Conference on Computability in Europe, CiE 2007, Siena, Italy, June
18-23, 2007.
Andrej Bauer and
Christopher A. Stone.
RZ: a tool for bringing constructive and computable mathematics closer to
programming practice.
Journal of Logic and Computation, 19(1):17-43, 2009.
Andrej Bauer and Paul
Taylor.
The Dedekind reals in abstract Stone duality.
In Tanja Grubba, Peter Hertling, Hideki Tsuiki, and Klaus Weihrauch, editors,
Computability and Complexity in Analysis, volume 326 of
Informatik Berichte, pages 25-64. FernUniversität in Hagen,
July 2005.
Proccedings, Second International Conference, CCA 2005, Kyoto, Japan, August
25-29, 2005.
Andrej Bauer,
Martín Hötzel Escardó, and Alex Simpson.
Comparing functional paradigms for exact real-number computation.
In Peter Widmayer, Francisco Triguero, Rafael Morales, Matthew Hennessy,
Stephan Eidenbenz, and Ricardo Conejo, editors, Automata, Languages and
Programming, volume 2380 of Lecture Notes in Computer
Science, pages 488-500, Berlin, 2002. Springer.
29th International Colloquium, ICALP, Málaga, Spain, July 8-13, 2002.
Andrej Bauer, Lars Birkedal,
and Dana S. Scott.
Equilogical spaces.
Theoretical Computer Science, 315:35-59, 2004.
Andrej Bauer.
The Realizability Approach to Computable Analysis and Topology.
PhD thesis, School of Computer Science, Carnegie Mellon University, Pittsburgh,
2000.
Andrej Bauer.
A relationship between equilogical spaces and type two effectivity.
In Stephen Brooks and Michael Mislove, editors, Seventeenth Conference on
the Mathematical Foundations of Programming Semantics, volume 45 of
Electronic Notes in Theoretical Computer Science, Amsterdam,
2001. Elsevier.
MFPS 2001, Aarhus, Denmark May 23-26, 2001.
Andrej Bauer.
A relationship between equilogical spaces and type two effectivity.
Mathematical Logic Quarterly, 48(Suppl. 1):1-15, 2002.
Verónica Becher and
Santiago Figueira.
An example of a computable absolutely normal number.
Theoretical Computer Science, 270:947-958, 2002.
Verónica Becher
and Serge Grigorieff.
Recursion and topology on 2 leq omega for possibly infinite computations.
Theoretical Computer Science, 322(1):85-136, 2004.
Verónica Becher
and Serge Grigorieff.
Random reals á la Chaitin with or without prefix-freeness.
Theoretical Computer Science, 385:193-201, 2007.
Verónica Becher,
Santiago Figueira, and Rafael Picchi.
Turing’s unpublished algorithm for normal numbers.
Theoretical Computer Science, 377(1-3):126-138, 2007.
Benjamín
René Callejas Bedregal and Benedito Melo Acióly.
Effectively given continuous domains: A computable interval analysis.
Electronic Journal on Mathematics of Computation, 0, 1999.
M.J. Beeson.
Problematic principles in constructive mathematics.
In Logic Colloquium '80, volume 108 of Studies in Logic and
the Foundations of Mathematics, pages 11-55, Amsterdam, 1980.
North-Holland.
Michael Beeson.
Constructivity, computability, and the continuum.
In Giandomenico Sica, editor, Essays on the Foundations of Mathematics
and Logic, volume 2 of Advanced Studies in Mathematics and
Logic, pages 9-37. Polimetrica, Milano, 2005.
Edwin J. Beggs and John V.
Tucker.
Can Newtonian systems, bounded in space, time, mass and energy compute all
functions?
Theoretical Computer Science, 371:4-19, 2007.
V. Benci, C. Bonanno,
S. Galatolo, G. Menconi, and M. Virgilio.
Dynamical systems and computable information.
Discrete and Continuous Dynamical Systems B, 4(4):935-960,
2004.
Josef Berger and
Douglas S. Bridges.
A bizarre property equivalent to the Pi 01--fan theorem.
Logic Journal of the IGPL, 14:867-871, 2006.
Josef Berger and
Douglas S. Bridges.
A fan-theoretic equivalent of the antithesis of Specker's theorem.
Indag. Math. N.S., 18(2):195-202, 2007.
Josef Berger and Douglas
Bridges.
The anti-Specker property, a Heine–Borel property.
Archive for Mathematical Logic, 46(7-8):583–--592, 2008.
Josef Berger and Hajime
Ishihara.
Brouwer's fan theorem and unique existence in constructive analysis.
Mathematical Logic Quarterly, 51(4):360-364, 2005.
Josef Berger, Douglas S.
Bridges, and Peter Schuster.
The fan theorem and unique existence of maxima.
The Journal of Symbolic Logic, 71(2):713-720, 2006.
Josef Berger.
Constructive equivalents of the uniform continuity theorem.
Journal of Universal Computer Science, 11(12):1878-1883, 2005.
Josef Berger.
Exact calculation of inverse functions.
Mathematical Logic Quarterly, 51(2):201-205, 2005.
Josef Berger.
The logical strength of the uniform continuity theorem.
In A. Beckmann, U. Berger, B. Löwe, and J.V. Tucker, editors, Logical
Approaches to Computational Barriers, volume 3988 of Lecture
Notes in Computer Science, pages 35-39, Berlin, 2006. Springer.
Second Conference on Computability in Europe, CiE 2006, Swansea, UK, June
30-July 5, 2006.
Yves Bertot.
Affine functions and series with co-inductive real numbers.
Mathematical Structures in Computer Science, 17:37-63, 2007.
Laurent Bienvenu and
Wolfgang Merkle.
Effective randomness for computable probability measures.
In Douglas Cenzer, Ruth Dillhage, Tanja Grubba, and Klaus Weihrauch, editors,
Proceedings of the Third International Conference on Computability and
Complexity in Analysis, volume 167 of Electronic Notes in
Theoretical Computer Science, pages 117-130, Amsterdam, 2007.
Elsevier.
CCA 2006, Gainesville, Florida, USA, November 1-5, 2006.
I. Binder, Mark Braverman, and
M. Yampolsky.
On computational complexity of Siegel Julia sets.
Comm. Math. Phys., 264(2):317-334, 2006.
Errett Bishop and
Douglas S. Bridges.
Constructive Analysis, volume 279 of Grundlehren der
Mathematischen Wissenschaften.
Springer, Berlin, 1985.
E. Bishop and H. Cheng.
Constructive Measure Theory.
American Mathematical Society, Providence, 1972.
Errett Bishop.
Constructive Methods in the Theory of Banach Algebras.
In F.T. Birtel, editor, Function Algebras, pages 343-345,
Chicago, 1966. Scott-Foresman.
Proc. Internat. Sympos. on Function Algebras, Tulane Univ., 1965.
Errett Bishop.
Foundations of Constructive Analysis.
McGraw-Hill, New York, 1967.
Errett Bishop.
A constructive ergodic theorem.
J. Math. Mech., 17:631-639, 1967/1968.
Errett Bishop.
The constructivization of abstract mathematical analysis.
Izdat. Mir, pages 308-313, 1968.
Proc. Internat. Congr. Math., Moscow, 1968.
Jens Blanck, Vasco Brattka,
and Peter Hertling, editors.
Computability and Complexity in Analysis, volume 2064 of
Lecture Notes in Computer Science, Berlin, 2001. Springer.
4th International Workshop, CCA 2000, Swansea, UK, September 17-19, 2000.
Selected Papers.
Jens Blanck, Viggo
Stoltenberg-Hansen, and John V. Tucker.
Domain representations of partial functions, with applications to spatial
objects and constructive volume geometry.
Theoretical Computer Science, 284(2):207-240, 2002.
Jens Blanck, Viggo
Stoltenberg-Hansen, and John V. Tucker.
Stability for effective algebras.
In Vasco Brattka, Ruth Dillhage, Tanja Grubba, and Angela Klutsch, editors,
CCA 2008, Fifth International Conference on Computability and
Complexity in Analysis, volume 221 of Electronic Notes in
Theoretical Computer Science, pages 3-15. Elsevier, 2008.
CCA 2008, Fifth International Conference, Hagen, Germany, August 21-24,
2008.
Jens Blanck.
Computability on topological spaces by effective domain
representations.
PhD thesis, Uppsala University, Department of Mathematics, Uppsala, Sweden,
1997.
Jens Blanck.
Domain representability of metric spaces.
Annals of Pure and Applied Logic, 83:225-247, 1997.
Jens Blanck.
Effective domain representations of H(X), the space of compact subsets.
Theoretical Computer Science, 219:19-48, 1999.
Jens Blanck.
Effectivity of regular spaces.
In Jens Blanck, Vasco Brattka, and Peter Hertling, editors, Computability
and Complexity in Analysis, volume 2064 of Lecture Notes in
Computer Science, pages 1-15, Berlin, 2001. Springer.
4th International Workshop, CCA 2000, Swansea, UK, September 2000.
Jens Blanck.
Exact real arithmetic systems: Results of competition.
In Jens Blanck, Vasco Brattka, and Peter Hertling, editors, Computability
and Complexity in Analysis, volume 2064 of Lecture Notes in
Computer Science, pages 389-393, Berlin, 2001. Springer.
4th International Workshop, CCA 2000, Swansea, UK, September 2000.
Jens Blanck.
Efficient exact computation of iterated maps.
The Journal of Logic and Algebraic Programming, 64:41-59,
2005.
Markus Bläser.
Uniform computational complexity of the derivatives of C^ infty -functions.
Theoretical Computer Science, 284(2):199-206, 2002.
Hans Boehm and Robert
Cartwright.
Exact real arithmetic, formulating real numbers as functions.
In D. Turner, editor, Research topics in functional programming,
pages 43-64. Addison-Wesley, 1990.
Hans-J. Boehm.
The constructive reals as a Java library.
The Journal of Logic and Algebraic Programming, 64:3-11, 2005.
Paolo Boldi and Sebastiano
Vigna.
delta -uniform BSS machines.
Journal of Complexity, 14(2):234-256, 1998.
Paolo Boldi and Sebastiano
Vigna.
Equality is a jump.
Theoretical Computer Science, 219:49-64, 1999.
Claudio Bonanno, Stefano
Galatolo, and Stefano Isola.
Recurrence and algorithmic information.
Nonlinearity, 17(3):1057-1074, 2004.
Volker Bosserhoff.
Computability of solutions of operator equations.
In Douglas Cenzer, Ruth Dillhage, Tanja Grubba, and Klaus Weihrauch, editors,
Proceedings of the Third International Conference on Computability and
Complexity in Analysis, volume 167 of Electronic Notes in
Theoretical Computer Science, pages 179-202, Amsterdam, 2007.
Elsevier.
CCA 2006, Gainesville, Florida, USA, November 1-5, 2006.
Volker Bosserhoff.
Computability of solutions of operator equations.
Mathematical Logic Quarterly, 53(4-5):326-344, 2007.
Volker Bosserhoff.
Are unbounded linear operators computable on the average for Gaussian
measures?
Journal of Complexity, 24(4):477-491, 2008.
Volker Bosserhoff.
Are unbounded linear operators computable on the average for Gaussian
measures?
Journal of Complexity, 24(4):477-491, 2008.
Volker Bosserhoff.
The bit-complexity of finding nearly optimal quadrature rules for weighted
integration.
Journal of Universal Computer Science, 14(6):938-955, 2008.
Volker Bosserhoff.
Notions of probabilistic computability on represented spaces.
In Ruth Dillhage, Tanja Grubba, Andrea Sorbi, Klaus Weihrauch, and Ning Zhong,
editors, Proceedings of the Fourth International Conference on
Computability and Complexity in Analysis (CCA 2007), volume 202 of
Electronic Notes in Theoretical Computer Science, pages
137-170. Elsevier, 2008.
CCA 2007, Siena, Italy, June 16-18, 2007.
Volker Bosserhoff.
Notions of probabilistic computability on represented spaces.
Journal of Universal Computer Science, 14(6):956-995, 2008.
Volker Bosserhoff.
On the effective existence of Schauder bases (extended abstract).
In Vasco Brattka, Ruth Dillhage, Tanja Grubba, and Angela Klutsch, editors,
CCA 2008, Fifth International Conference on Computability and
Complexity in Analysis, volume 221 of Electronic Notes in
Theoretical Computer Science, pages 17-21. Elsevier, 2008.
CCA 2008, Fifth International Conference, Hagen, Germany, August 21-24,
2008.
Olivier Bournez and
Emmanuel Hainry.
Elementarily computable functions over the real numbers and r-sub-recursive
functions.
Theoretical Computer Science, 348:130-147, 2005.
Olivier Bournez and
Emmanuel Hainry.
Recursive analysis characterized as a class of real recursive functions.
Fundamenta Mathematicae, 74(4):409-433, 2006.
Olivier Bournez, Manuel L.
Campagnolo, Daniel Graça, and Emmanuel S. Hainry.
Polynomial differential equations compute all real computable functions on
computable compact intervals.
Journal of Complexity, 23(3):317-335, 2007.
S.S. Brady and J.B. Remmel.
The undecidability of the lattice of r.e. closed subsets of an effective
topological space.
Annals of Pure and Applied Logic, 35:193-203, 1987.
Vasco Brattka and Ruth
Dillhage.
Computability of the spectrum of self-adjoint operators.
Journal of Universal Computer Science, 11(12):1884-1900, 2005.
Vasco Brattka and Ruth
Dillhage.
On computable compact operators on Banach spaces.
In Douglas Cenzer, Ruth Dillhage, Tanja Grubba, and Klaus Weihrauch, editors,
Proceedings of the Third International Conference on Computability and
Complexity in Analysis, volume 167 of Electronic Notes in
Theoretical Computer Science, pages 365-386, Amsterdam, 2007.
Elsevier.
CCA 2006, Gainesville, Florida, USA, November 1-5, 2006.
Vasco Brattka and Ruth
Dillhage.
On computable compact operators on computable Banach spaces with bases.
Mathematical Logic Quarterly, 53(4-5):345-364, 2007.
Vasco Brattka and Guido
Gherardi.
Borel complexity of topological operations on computable metric spaces.
In S. Barry Cooper, Benedikt Löwe, and Andrea Sorbi, editors,
Computation and Logic in the Real World, volume 4497 of
Lecture Notes in Computer Science, pages 83-97, Berlin, 2007.
Springer.
Third Conference on Computability in Europe, CiE 2007, Siena, Italy, June
18-23, 2007.
Vasco Brattka and Guido
Gherardi.
Borel complexity of topological operations on computable metric spaces.
Journal of Logic and Computation, 19(1):45-76, 2009.
Vasco Brattka and Peter
Hertling.
Continuity and computability of relations.
Informatik Berichte 164, FernUniversität Hagen, Hagen, September 1994.
Vasco Brattka and Peter
Hertling.
Feasible real random access machines.
Journal of Complexity, 14(4):490-526, 1998.
Vasco Brattka and Peter
Hertling.
Topological properties of real number representations.
Theoretical Computer Science, 284(2):241-257, 2002.
Vasco Brattka and Iraj
Kalantari.
A bibliography of recursive analysis and recursive topology.
In Yu. L. Ershov, S.S. Goncharov, A. Nerode, and J.B. Remmel, editors,
Handbook of Recursive Mathematics, volume 138 of Studies
in Logic and the Foundations of Mathematics, pages 583-620. Elsevier,
Amsterdam, 1998.
Volume 1, Recursive Model Theory.
Vasco Brattka and Gero
Presser.
Computability on subsets of metric spaces.
Theoretical Computer Science, 305:43-76, 2003.
Vasco Brattka and
Matthias Schröder.
Computing with sequences, weak topologies and the axiom of choice.
In Luke Ong, editor, Computer science logic, volume 3634 of
Lecture Notes in Computer Science, pages 462-476. Springer,
2005.
Vasco Brattka and Klaus
Weihrauch.
Computability on subsets of Euclidean space I: Closed and compact subsets.
Theoretical Computer Science, 219:65-93, 1999.
Vasco Brattka and
Atsushi Yoshikawa.
Towards computability of elliptic boundary value problems in variational
formulation.
Journal of Complexity, 22(6):858-880, 2006.
Vasco Brattka and Martin
Ziegler.
Computability of linear equations.
In Ricardo Baeza-Yates, Ugo Montanari, and Nicola Santoro, editors,
Foundations of Information Technology in the Era of Network and Mobile
Computing, volume 223 of IFIP International Federation for
Information Processing, pages 95-106, Dordrecht, 2002. Kluwer
Academic Publishers.
2nd IFIP International Conference on Theoretical Computer Science,
Montréal, Canada, August 25-30, 2002.
Vasco Brattka, Peter
Hertling, Mariko Yasugi, and Ning Zhong, editors.
Selected Papers of the Dagstuhl Seminar on Computability and Complexity
in Analysis 2001, volume 48 (Suppl. 1) of Mathematical Logic
Quarterly, Weinheim, 2002. Wiley-VCH.
Vasco Brattka, Matthias
Schröder, and Klaus Weihrauch, editors.
Computability and Complexity in Analysis, volume 66(1) of
Electronic Notes in Theoretical Computer Science, Amsterdam,
2002. Elsevier.
5th International Workshop, CCA 2002, Málaga, Spain, July 12-13,
2002.
Vasco Brattka, Matthias
Schröder, Klaus Weihrauch, and Ning Zhong.
Computability and complexity in analysis.
Informatik Berichte 302, FernUniversität in Hagen, Hagen, August 2003.
Proccedings, International Conference, CCA 2003, Cincinnati, USA, August
28-30, 2003.
Vasco Brattka, Peter
Hertling, Ker-I Ko, and Ning Zhong, editors.
Special Issue Computability and Complexity in Analysis, volume 50
of Mathematical Logic Quarterly, Weinheim, 2004. Wiley-VCH.
Selected Papers of the International Conference CCA 2003, held in Cincinnati,
Ohio, August 28-30, 2003.
Vasco Brattka, Ludwig
Staiger, and Klaus Weihrauch, editors.
Proceedings of the 6th Workshop on Computability and Complexity in
Analysis, volume 120 of Electronic Notes in Theoretical Computer
Science, Amsterdam, 2005. Elsevier.
6th International Workshop, CCA 2004, Wittenberg, Germany, August 16-20,
2004.
Vasco Brattka, Peter
Hertling, Ker-I Ko, and Hideki Tsuiki, editors.
Computability and Complexity in Analysis, volume 522 of
Journal of Complexity, Amsterdam, 2006. Elsevier.
Selected Papers of the International Conference CCA 2005, held in Kyoto, Japan,
August 25-29, 2005.
Vasco Brattka, Christiane
Frougny, and Norbert Müller, editors.
Real Numbers, volume 41 of Theoretical Informatics and
Applications, Les Ulis, 2007. EDP Sciences.
Selected Papers of the 6th conference on Real Numbers and Computers, Dagstuhl,
Germany, November 15-17, 2004.
Vasco Brattka, Ruth
Dillhage, Tanja Grubba, and Angela Klutsch, editors.
Proceedings of the Fifth International Conference on Computability and
Complexity in Analysis, volume 221 of Electronic Notes in
Theoretical Computer Science, Amsterdam, 2008. Elsevier.
CCA 2008, Hagen, Germany, August 21-24, 2008.
Vasco Brattka, Peter
Hertling, and Klaus Weihrauch.
A tutorial on computable analysis.
In S. Barry Cooper, Benedikt Löwe, and Andrea Sorbi, editors, New
Computational Paradigms: Changing Conceptions of What is Computable,
pages 425-491. Springer, New York, 2008.
Vasco Brattka, Hajime
Ishihara, Matthias Schröder, and Ning Zhong, editors.
Computability and Complexity in Analysis, volume 14 of
Journal of Universal Computer Science, Graz, 2008. Graz
University of Technology.
Selected Papers of the Fourth International Conference on Computability and
Complexity in Analysis, June 16-18, 2007, Siena, Italy.
Vasco Brattka, Hajime
Ishihara, Matthias Schröder, and Ning Zhong, editors.
Computability and Complexity in Analysis, volume 54 of
Mathematical Logic Quarterly, Weinheim, 2008. Wiley-VCH.
Selected Papers of the Fourth International Conference on Computability and
Complexity in Analysis, June 16-18, 2007, Siena, Italy.
Vasco Brattka.
Computable selection in analysis.
In Ker-I Ko and Klaus Weihrauch, editors, Computability and Complexity in
Analysis, volume 190 of Informatik Berichte, pages
125-138. FernUniversität Hagen, September 1995.
CCA Workshop, Hagen, August 19-20, 1995.
Vasco Brattka.
Recursive characterization of computable real-valued functions and relations.
Theoretical Computer Science, 162:45-77, 1996.
Vasco Brattka.
Order-free recursion on the real numbers.
Mathematical Logic Quarterly, 43:216-234, 1997.
Vasco Brattka.
Recursive and Computable Operations over Topological Structures.
PhD thesis, Fachbereich Informatik, FernUniversität Hagen, 1998.
Vasco Brattka.
A stability theorem for recursive analysis.
In Cristian S. Calude and Michael J. Dinneen, editors, Combinatorics,
Computation & Logic, Discrete Mathematics and Theoretical Computer
Science, pages 144-158, Singapore, 1999. Springer.
Proceedings of DMTCS'99 and CATS'99, Auckland, New Zealand, January 1999.
Vasco Brattka.
Realistic models of computability on the real numbers.
In Atsushi Yoshikawa, editor, Relevance and Feasibility of Mathematical
Analysis on the Computer, volume 1169 of
Surikaisekikenkyusho Kokyuroku, pages 62-75,
Kyoto, 2000. Research Institute for Mathematical Sciences.
Vasco Brattka.
Computability of Banach space principles.
Informatik Berichte 286, FernUniversität Hagen, Fachbereich Informatik,
Hagen, June 2001.
Vasco Brattka.
Computable versions of Baire's category theorem.
In Jirí Sgall, Ales Pultr, and Petr Kolman, editors,
Mathematical Foundations of Computer Science 2001, volume 2136
of Lecture Notes in Computer Science, pages 224-235, Berlin,
2001. Springer.
26th International Symposium, MFCS 2001, Mariánské
Lázne, Czech Republic, August 27-31, 2001.
Vasco Brattka.
Computing uniform bounds.
In Vasco Brattka, Matthias Schröder, and Klaus Weihrauch, editors,
CCA 2002 Computability and Complexity in Analysis, volume 66
of Electronic Notes in Theoretical Computer Science, Amsterdam,
2002. Elsevier.
5th International Workshop, CCA 2002, Málaga, Spain, July 12-13,
2002.
Vasco Brattka.
Random numbers and an incomplete immune recursive set.
In Peter Widmayer, Francisco Triguero, Rafael Morales, Matthew Hennessy,
Stephan Eidenbenz, and Ricardo Conejo, editors, Automata, Languages and
Programming, volume 2380 of Lecture Notes in Computer
Science, pages 950-961, Berlin, 2002. Springer.
29th International Colloquium, ICALP, Málaga, Spain, July 8-13, 2002.
Vasco Brattka.
Some notes on Fine computability.
Journal of Universal Computer Science, 8(3):382-395, 2002.
Vasco Brattka.
Computability on asymmetric spaces.
Informatik Berichte 305, FernUniversität in Hagen, Fachbereich Informatik,
Hagen, December 2003.
Vasco Brattka.
Computability over topological structures.
In S. Barry Cooper and Sergey S. Goncharov, editors, Computability and
Models, pages 93-136. Kluwer Academic Publishers, New York, 2003.
Vasco Brattka.
Effective representations of the space of linear bounded operators.
Applied General Topology, 4(1):115-131, 2003.
Vasco Brattka.
The emperor's new recursiveness: The epigraph of the exponential function in
two models of computability.
In Masami Ito and Teruo Imaoka, editors, Words, Languages &
Combinatorics III, pages 63-72, Singapore, 2003. World Scientific
Publishing.
ICWLC 2000, Kyoto, Japan, March 14-18, 2000.
Vasco Brattka.
The inversion problem for computable linear operators.
In Helmut Alt and Michel Habib, editors, STACS 2003, volume 2607
of Lecture Notes in Computer Science, pages 391-402, Berlin,
2003. Springer.
20th Annual Symposium on Theoretical Aspects of Computer Science, Berlin,
Germany, February 27-March 1, 2003.
Vasco Brattka.
Plottable real number functions and the computable graph theorem.
Informatik Berichte 300, FernUniversität in Hagen, Fachbereich Informatik,
Hagen, July 2003.
Vasco Brattka.
Du 13-ième problème de Hilbert à la théorie des réseaux
de neurones : aspects constructifs du théorème de superposition de
Kolmogorov.
In Éric Charpentier, Annick Lesne, and Nikolai Nikolski,
editors, L'héritage de Kolmogorov en mathématiques,
pages 241-268. Éditions Belin, Paris, 2004.
Vasco Brattka.
Computability on non-separable Banach spaces and Landau's theorem.
In Laura Crosilla and Peter Schuster, editors, From Sets and Types to
Topology and Analysis: Towards Practicable Foundations for Constructive
Mathematics, pages 316-333. Oxford University Press, 2005.
Vasco Brattka.
Effective Borel measurability and reducibility of functions.
Mathematical Logic Quarterly, 51(1):19-44, 2005.
Vasco Brattka.
On the Borel complexity of Hahn-Banach extensions.
In Vasco Brattka, Ludwig Staiger, and Klaus Weihrauch, editors,
Proceedings of the 6th Workshop on Computability and Complexity in
Analysis, volume 120 of Electronic Notes in Theoretical Computer
Science, pages 3-16, Amsterdam, 2005. Elsevier.
6th International Workshop, CCA 2004, Wittenberg, Germany, August 16-20,
2004.
Vasco Brattka.
Computable versions of the uniform boundedness theorem.
In Z. Chatzidakis, P. Koepke, and W. Pohlers, editors, Logic Colloquium
2002, volume 27 of Lecture Notes in Logic, pages
130-151, Urbana, 2006. Association for Symbolic Logic.
Vasco Brattka.
From Hilbert's 13th Problem to the theory of neural networks: constructive
aspects of Kolmogorov's Superposition Theorem.
In Éric Charpentier, Annick Lesne, and Nikolai Nikolski,
editors, Kolmogorov's Heritage in Mathematics, pages 253-280.
Springer, Berlin, 2007.
Vasco Brattka.
Borel complexity and computability of the Hahn-Banach Theorem.
Archive for Mathematical Logic, 46(7-8):547-564, 2008.
Vasco Brattka.
Plottable real number functions and the computable graph theorem.
SIAM Journal on Computing, 38(1):303-328, 2008.
Vasco Brattka.
A computable version of Banach's inverse mapping theorem.
Annals of Pure and Applied Logic, 157:85-96, 2009.
Mark Braverman and Stephen
Cook.
Computing over the reals: Foundations for scientific computing.
Notices of the AMS, 53(3):318-329, 2006.
Mark Braverman and
M. Yampolsky.
Non-computable Julia sets.
Journal of the American Mathematical Society, 19(3):551-578,
2006.
Mark Braverman.
Hyperbolic Julia sets are poly-time computable.
In Vasco Brattka, Ludwig Staiger, and Klaus Weihrauch, editors,
Proceedings of the 6th Workshop on Computability and Complexity in
Analysis, volume 120 of Electronic Notes in Theoretical Computer
Science, pages 17-30, Amsterdam, 2005. Elsevier.
6th International Workshop, CCA 2004, Wittenberg, Germany, August 16-20,
2004.
Mark Braverman.
Parabolic Julia sets are polynomial time computable.
Nonlinearity, 19(6):1383-1401, 2006.
Josef M. Breutzmann,
David W. Juedes, and Jack H. Lutz.
Baire category and nowhere differentiability for feasible real functions.
In Peter Eades and Tadao Takaoka, editors, Algorithms and
Computation, volume 2223 of Lecture Notes in Computer
Science, pages 219-230, Berlin, 2001. Springer.
12th International Symposium, ISAAC 2001, Christchurch, New Zealand, December
19-21, 2001.
Josef M. Breutzmann,
David W. Juedes, and Jack H. Lutz.
Baire category and nowhere differentiability for feasible real functions.
Mathematical Logic Quarterly, 50(4,5):460-472, 2004.
Douglas Bridges and
Luminita Dediu.
Paradise lost, or paradise regained?
Bulletin of the European Association for Theoretical Computer
Science, 63:141-155, 1997.
Douglas Bridges and
Luminita Dediu.
Weak continuity properties in constructive analysis.
Logic Journal of the IGPL. Interest Group in Pure and Applied
Logics, 7(3):277-281, 1999.
Douglas Bridges and
Luminita Dediu.
Weak-operator continuity and the existence of adjoints.
Mathematical Logic Quarterly, 45(2):203-206, 1999.
Douglas Bridges and
Luminita Dediu.
The weak-operator sequential continuity of left multiplication.
Indagationes Mathematicae, 11(1):39-42, 2000.
Douglas Bridges and Osvald
Demuth.
On the Lebesgue measurability of continuous functions in constructive
analysis.
BAMS, 24(2):259-276, 1991.
Douglas Bridges and
Hannes Diener.
A constructive treatment of Urysohn's Lemma in an apartness space.
Mathematical Logic Quarterly, 52(5):464-469, 2006.
D. S. Bridges and
N. F. Dudley Ward.
Constructing ultraweakly continuous functionals on B(H).
Proceedings of the American Mathematical Society,
126(11):3347-3353, 1998.
Douglas Bridges and Robin
Havea.
A constructive analysis of a proof that the numerical range is convex.
London Math. Soc. Journal of Mathematics and Computation,
3:191-206, 2000.
Douglas Bridges and Robin
Havea.
A constructive version of the spectral mapping theorem.
Mathematical Logic Quarterly, 47(3):299-304, 2001.
Douglas S. Bridges and
Robin Havea.
Powers of a Hermitian element.
New Zealand J. Math., 36:1-10, 2007.
Douglas Bridges and
Hajime Ishihara.
Linear mappings are fairly well-behaved.
Archiv der Mathematik. Archives of Mathematics. Archives
Mathématiques, 54(6):558-562, 1990.
Douglas Bridges and
Hajime Ishihara.
Locating the range of an operator on a Hilbert space.
The Bulletin of the London Mathematical Society, 24(6):599-605,
1992.
Douglas Bridges and
Hajime Ishihara.
Absolute continuity and the uniqueness of the constructive functional calculus.
Mathematical Logic Quarterly, 40(4):519-527, 1994.
Douglas S. Bridges and
Hajime Ishihara.
Complements of intersections in constructive mathematics.
Mathematical Logic Quarterly, 40(1):35-43, 1994.
Douglas S. Bridges and
Hajime Ishihara.
Erratum: ``Complements of intersections in constructive mathematics''.
Mathematical Logic Quarterly, 40(4):570, 1994.
Douglas Bridges and
Hajime Ishihara.
Spectra of selfadjoint operators in constructive analysis.
Indagationes Mathematicae, 7(1):11-35, 1996.
Douglas Bridges and
Hajime Ishihara.
A definite constructive open mapping theorem?
Mathematical Logic Quarterly, 44(4):545-552, 1998.
Douglas Bridges and
Hajime Ishihara.
Constructive closed range and open mapping theorems.
Indagationes Mathematicae, 11(4):509-516, 2001.
Douglas Bridges and
Hajime Ishihara.
Constructive unbounded operators.
In Peter Schuster, Ulrich Berger, and Horst Osswald, editors, Reuniting
the antipodes--constructive and nonstandard views of the continuum (Venice,
1999), volume 306 of Synthese Library, pages 25-37,
Dordrecht, 2001. Kluwer Acad. Publ.
Douglas Bridges and
Ayan Mahalanobis.
Sequential continuity of functions in constructive analysis.
Mathematical Logic Quarterly, 46(1):139-143, 2000.
Douglas Bridges and
Ayan Mahalanobis.
Bounded variation implies regulated: a constructive proof.
The Journal of Symbolic Logic, 66(4):1695-1700, 2001.
Douglas Bridges and
Ayan Mahalanobis.
Increasing, nondecreasing, and virtually continuous functions.
Journal of Automata, Languages and Combinatorics, 6(2):139-143,
2001.
D.S. Bridges and R. Mines.
What is constructive mathematics?
The Mathematical Intelligencer, 6(4):32-38, 1984.
Douglas Bridges and Ray
Mines.
Sequentially continuous linear mappings in constructive analysis.
The Journal of Symbolic Logic, 63(2):579-583, 1998.
Douglas Bridges and
Gabriela Popa.
Exact, continuous boundary crossings out of convex sets in rn.
The Quarterly Journal of Mathematics, 54(4):391-398, 2003.
Douglas Bridges and Steve
Reeves.
Constructive mathematics in theory and programming practice.
Philosophia Mathematica. Philosophy of Mathematics, its Learning, and its
Application. Series III, 7(1):65-104, 1999.
Mathematical proof.
Douglas Bridges and Fred
Richman.
Varieties of Constructive Mathematics, volume 97 of London
Mathematical Society Lecture Note Series.
Cambridge University Press, Cambridge, 1987.
Douglas S. Bridges and
Fred Richman.
A recursive counterexample to Debreu's theorem on the existence of a utility
function.
Mathematical Social Sciences, 21(2):179-182, 1991.
Douglas Bridges and
Peter Schuster.
A simple constructive proof of Kronecker's density theorem.
Elemente der Mathematik, 61:152-154, 2006.
Douglas Bridges and Karl
Svozil.
Constructive mathematics and quantum physics.
J. Theor. Physics, 39:501-513, 2000.
Douglas
Bridges and Luminita Vîta.
Constructing extensions of ultraweakly continuous linear functionals.
J. Functional Analysis, 178(2):421-434, 2000.
Douglas
Bridges and Luminita Vîta.
Characterising near continuity constructively.
Mathematical Logic Quarterly, 47(4):535-538, 2001.
Douglas
Bridges and Luminita Vîta.
Cauchy nets in the constructive theory of apartness spaces.
Scientiae Mathematicae Japonicae, 56(1):123-132, 2002.
Douglas
Bridges and Luminita Vîta.
Apartness spaces as a framework for constructive topology.
Annals of Pure and Applied Logic, 119(1-3):61-83, 2003.
Douglas
Bridges and Luminita Vîta.
Cauchy nets in uniform apartness spaces.
Revue Roumaine de Mathématiques Pures et Appliquées,
48(5-6):467-474, 2003.
Douglas
Bridges and Luminita Vîta.
A proof-technique in uniform space theory.
The Journal of Symbolic Logic, 68(3):795-802, 2003.
Douglas
Bridges and Luminita Vîta.
Separatedness in constructive topology.
Documenta Mathematica, 8:567-576, 2003.
Douglas
Bridges and Luminita Vîta.
Strong and uniform continuity--the uniform space case.
LMS Journal of Computation and Mathematics, 6:326-334, 2003.
Douglas
Bridges and Luminita Vîta.
Corrigendum to: ``A proof-technique in uniform space theory''.
The Journal of Symbolic Logic, 69(1):328, 2004.
Douglas
Bridges and Luminita Vîta.
An extension theorem for ultraweakly continuous linear functionals on b(x,y).
In Tanja Grubba, Peter Hertling, Hideki Tsuiki, and Klaus Weihrauch, editors,
Computability and Complexity in Analysis, volume 326 of
Informatik Berichte, pages 77-89. FernUniversität in Hagen,
July 2005.
Proccedings, Second International Conference, CCA 2005, Kyoto, Japan, August
25-29, 2005.
Douglas
Bridges and Luminita Vîta.
A general constructive proof technique.
In Vasco Brattka, Ludwig Staiger, and Klaus Weihrauch, editors,
Proceedings of the 6th Workshop on Computability and Complexity in
Analysis, volume 120 of Electronic Notes in Theoretical Computer
Science, pages 31-43, Amsterdam, 2005. Elsevier.
6th International Workshop, CCA 2004, Wittenberg, Germany, August 16-20,
2004.
Douglas
Bridges and Luminita Vîta.
Proximal connectedness.
In Tanja Grubba, Peter Hertling, Hideki Tsuiki, and Klaus Weihrauch, editors,
Computability and Complexity in Analysis, volume 326 of
Informatik Berichte, pages 91-101. FernUniversität in Hagen,
July 2005.
Proccedings, Second International Conference, CCA 2005, Kyoto, Japan, August
25-29, 2005.
Douglas
Bridges and Luminita Vîta.
Pre-apartness structures on spaces of functions.
Journal of Complexity, 22(6):881-893, 2006.
Douglas
Bridges and Luminita Vîta.
Techniques of Constructive Analysis.
Springer, New York, 2006.
Douglas
Bridges and Luminita Vîta.
Proximal connectedness.
Fundamenta Informaticae, 83(1-2):25-34, 2008.
Douglas Bridges and
Yuchuan Wang.
Constructing cutoff functions.
New Zealand Journal of Mathematics, 26(1):25-30, 1997.
Douglas Bridges and Yuchuan
Wang.
Constructive aspects of the Dirichlet problem.
Journal of Universal Computer Science, 3(11):1148-1161
(electronic), 1997.
Proceedings of the First Japan-New Zealand Workshop on Logic in Computer
Science (Auckland, 1997).
Douglas Bridges and
Yuchuan Wang.
Constructing best approximations on a Jordan curve.
Journal of Approximation Theory, 94(2):222-234, 1998.
Douglas Bridges and
Yuchuan Wang.
Constructive weak solutions of the Dirichlet problem.
The Journal of the London Mathematical Society. Second Series,
57(3):655-667, 1998.
Douglas Bridges and
Yuchuan Wang.
Weak solutions of the Dirichlet problem and the locatedness of H sp 1 sb
0( omega ).
New Zealand Journal of Mathematics, 27(1):1-5, 1998.
Douglas S. Bridges and
Nicholas Dudley Ward.
Kernels of seminorms in constructive analysis.
Theoretical Computer Science, 284(2):259-267, 2002.
Douglas Bridges, Allan
Calder, William Julian, Ray Mines, and Fred Richman.
Bounded linear mappings of finite rank.
Journal of Functional Analysis, 43(2):143-148, 1981.
Douglas Bridges, Allan
Calder, William Julian, Ray Mines, and Fred Richman.
Locating metric complements in Rn.
In F. Richman, editor, Constructive Mathematics, volume 873 of
Lecture Notes in Mathematics, pages 241-249, 1981.
Proc. New Mexico State Univ. Conf., Aug. 11-15, 1980, Las Cruces, NM.
Douglas Bridges, Allan
Calder, William Julian, Ray Mines, and Fred Richman.
Picard's theorem.
Trans. Amer. Math. Soc., 269(2):513-520, 1982.
Douglas Bridges, William
Julian, and Ray Mines.
A constructive treatment of open and unopen mapping theorems.
Zeitschrift für Mathematische Logik und Grundlagen der
Mathematik, 35(1):29-43, 1989.
D. S. Bridges, F. Richman,
W. H. Julian, and R. Mines.
Extensions and fixed points of contractive maps in r sp n.
Journal of Mathematical Analysis and Applications,
165(2):438-456, 1992.
D.S. Bridges, W.H. Julian,
F. Richman, and R. Mines.
Extensions and fixed points of contractive maps in Rn.
J. Math. Anal. Appl., 165:438-456, 1992.
Douglas Bridges, Fred
Richman, and Wang Yuchuan.
Sets, complements and boundaries.
Indagationes Mathematicae, 7(4):425-445, 1996.
D. Bridges, C. Calude,
B. Pavlov, and D. Stefanescu.
The constructive implicit function theorem and applications in mechanics.
Chaos, Solitons and Fractals, 10(6):927-934, 1999.
Douglas Bridges, Hajime
Ishihara, and Peter Schuster.
Sequential compactness in constructive analysis.
Österr. Akad. Wiss. Math.-Natur. Kl. Sitzungsber. II.,
208:159-163, 1999.
Douglas Bridges, Fred
Richman, and Peter Schuster.
Adjoints, absolute values, and polar decompositions.
J. Operator Theory, 44(2):243-254, 2000.
Douglas Bridges, Fred
Richman, and Peter Schuster.
Linear independence without choice.
Annals of Pure and Applied Logic, 101(1):95-102, 2000.
Douglas Bridges, Fred
Richman, and Peter Schuster.
A weak countable choice principle.
Proceedings of the American Mathematical Society,
128(9):2749-2752, 2000.
Douglas Bridges, Hajime
Ishihara, and Peter Schuster.
Compactness and continuity, constructively revisited.
In Julian Bradfield, editor, Computer science logic, volume 2471
of Lecture Notes in Computer Science, pages 89-102. Springer,
2002.
Douglas Bridges, Peter
Schuster, and Luminita Vîta.
Apartness, topology, and uniformity: a constructive view.
Mathematical Logic Quarterly, 48(Suppl. 1):16-28, 2002.
Douglas Bridges, Hajime
Ishihara, and Bas Spitters.
Locating the range of an operator with an adjoint.
Indagationes Mathematicae, 13(4):433-440, 2003.
Douglas Bridges, Dirk van
Dalen, and Hajime Ishihara.
Ishihara's proof technique in constructive analysis.
Indagationes Mathematicae, 14(2):163-168, 2003.
Douglas Bridges, Hajime
Ishihara, and Luminita Vîta.
Computing infima on convex sets, with applications in Hilbert spaces.
Proceedings of the American Mathematical Society,
132(9):2723-2732, 2004.
Douglas Bridges, Ray Mines,
Fred Richman, and Peter Schuster.
The polydisk Nullstellensatz.
Proceedings of the American Mathematical Society,
132(7):2133-2140, 2004.
Douglas Bridges, Robin
Havea, and Peter Schuster.
Constructive Banach algebra theory and the Nullstellensatz.
Publ. Math. Debrecen, 69(1,2):171-184, 2006.
Douglas Bridges, Robin
Havea, and Peter Schuster.
Ideals in constructive Banach algebra theory.
Journal of Complexity, 22(6):729-737, 2006.
Douglas Bridges, Hajime
Ishihara, and Luminita Vîta.
A new constructive version of Baire's theorem.
Hokkaido Math. Journal, 35(1):107-118, 2006.
Douglas Bridges, Hajime
Ishihara, Ray Mines, Fred Richman, Peter M. Schuster, and Luminita
Vîta.
Almost locatedness in uniform spaces.
Czechoslovak Math. J., 57(1):1-12, 2007.
Douglas S. Bridges.
Some notes on continuity in constructive analysis.
Bull. London Math. Soc., 8(2):179-182, 1976.
Douglas S. Bridges.
A constructive look at orthonormal bases in Hilbert space.
Amer. Math. Monthly, 84(3):189-191, 1977.
Douglas S. Bridges.
The constructive Radon-Nikodym theorem.
Pacific J. Math., 70(1):51-65, 1977.
D. S. Bridges.
More on the connectivity of convex sets.
Proceedings of the American Mathematical Society, 68(2):214-216,
1978.
Douglas S. Bridges.
A note on Morse's lambda-notation in set theory.
Zeitschrift für Mathematische Logik und Grundlagen der
Mathematik, 24(2):113-114, 1978.
Douglas S. Bridges.
On continuous mappings between locally compact metric spaces.
The Bulletin of the London Mathematical Society, 10(2):201-208,
1978.
Douglas S. Bridges.
On the connectivity of convex sets.
The Bulletin of the London Mathematical Society, 10(1):86-90,
1978.
Douglas S. Bridges.
On weak operator compactness of the unit ball of L(H).
Zeitschrift für Mathematische Logik und Grundlagen der
Mathematik, 24(6):493-494, 1978.
Douglas S. Bridges.
Connectivity properties of metric spaces.
Pacific Journal of Mathematics, 80(2):325-331, 1979.
Douglas S. Bridges.
Constructive Functional Analysis.
Pitman, London, 1979.
Douglas S. Bridges.
A criterion for compactness in metric spaces?
Zeitschrift für Mathematische Logik und Grundlagen der
Mathematik, 25(2):97-98, 1979.
Douglas S. Bridges.
Geometric intuition and elementary constructive analysis.
Zeitschrift für Mathematische Logik und Grundlagen der
Mathematik, 25(6):521-523, 1979.
Douglas S. Bridges.
On the constructive convergence of series of independent functions.
Zeitschrift für Mathematische Logik und Grundlagen der
Mathematik, 25(1):93-96, 1979.
Douglas S. Bridges.
A constructive development of Chebyshev approximation theory.
Journal of Approximation Theory, 30(2):99-120, 1980.
Douglas S. Bridges.
On the foundations of best-approximation theory.
Journal of Approximation Theory, 28(3):273-292, 1980.
Douglas S. Bridges.
A constructive analysis of the Remes algorithm.
Journal of Approximation Theory, 32(4):257-270, 1981.
Douglas S. Bridges.
A constructive look at positive linear functionals on l(H).
Pacific Journal of Mathematics, 95(1):11-25, 1981.
Douglas S. Bridges.
A constructive proximinality property of finite-dimensional linear subspaces.
The Rocky Mountain Journal of Mathematics, 11(4):491-497,
1981.
Douglas S. Bridges.
Correction to: ``On the isolation of zeroes of an analytic function'' [Pacific J. Math. 96 (1981), no. 1, 13-22; MR 82k:03095].
Pacific Journal of Mathematics, 97(2):487-488, 1981.
Douglas S. Bridges.
On Montel's proof of the great Picard theorem.
The American Mathematical Monthly, 88(1):45-47, 1981.
Douglas S. Bridges.
On the isolation of zeroes of an analytic function.
Pacific Journal of Mathematics, 96(1):13-22, 1981.
Douglas S. Bridges.
Towards a constructive foundation for quantum mechanics.
In F. Richman, editor, Constructive Mathematics, volume 873 of
Lecture Notes in Mathematics, pages 260-273, 1981.
Proc. New Mexico State Univ. Conf., Aug. 11-15, 1980, Las Cruces, NM.
Douglas S. Bridges.
Lipschitz constants and moduli of continuity for the Chebyshev projection.
Proceedings of the American Mathematical Society, 85(4):557-561,
1982.
Douglas S. Bridges.
Preference and utility: a constructive development.
Journal of Mathematical Economics, 9(1-2):165-185, 1982.
Douglas S. Bridges.
Recent progress in constructive approximation theory.
In The L. E. J. Brouwer Centenary Symposium (Noordwijkerhout,
1981), pages 41-50. North-Holland, Amsterdam, 1982.
Douglas S. Bridges.
Numerical representation of intransitive preferences on a countable set.
Journal of Economic Theory, 30(1):213-217, 1983.
Douglas S. Bridges.
A numerical representation of preferences with intransitive indifference.
Journal of Mathematical Economics, 11(1):25-42, 1983.
Douglas S. Bridges.
Operator ranges, integrable sets, and the functional calculus.
Houston Journal of Mathematics, 11(1):31-44, 1985.
Douglas S. Bridges.
Representing interval orders by a single real-valued function.
Journal of Economic Theory, 36(1):149-155, 1985.
Douglas S. Bridges.
Numerical representation of interval orders on a topological space.
Journal of Economic Theory, 38(1):160-166, 1986.
Douglas S. Bridges.
A constructive Morse theory of sets.
In Mathematical logic and its applications (Druzhba, 1986), pages
61-79. Plenum, New York, 1987.
Douglas S. Bridges.
The Euclidean distance construction of order homomorphisms.
Mathematical Social Sciences, 15(2):179-188, 1988.
Douglas S. Bridges.
Locatedness, convexity, and lebesque measurability.
Quart. J. Math. Oxford Ser. 2, 39:411-421, 1988.
Douglas S. Bridges.
Approximate interpolation by functions in a Haar space.
Journal of Approximation Theory, 57(1):35-39, 1989.
Douglas S. Bridges.
The constructive theory of preference relations on a locally compact space.
Indagationes Mathematicae, 51(2):141-165, 1989.
Douglas S. Bridges.
A general constructive intermediate value theorem.
Zeitschrift für Mathematische Logik und Grundlagen der
Mathematik, 35:433-435, 1989.
Douglas S. Bridges.
Order isomorphisms--a constructive measure-theoretic view.
In Mathematical logic, pages 243-255. Plenum, New York, 1990.
Douglas S. Bridges.
Preference, indifference, and Markov's principle.
Mathematical Social Sciences, 20(2):131-145, 1990.
Douglas S. Bridges.
The constructive inequivalence of various notions of preference ordering.
Mathematical Social Sciences, 21(2):169-176, 1991.
Douglas S. Bridges.
Constructive notions of strict convexity.
Mathematical Logic Quarterly, 39(3):295-300, 1993.
Douglas S. Bridges.
Sequential, pointwise, and uniform continuity: a constructive note.
Mathematical Logic Quarterly, 39(1):55-61, 1993.
Douglas S. Bridges.
A constructive look at the real number line.
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of the 80th anniversary of Kurt Gödel's birth, held September 24-October
4, 1986 in Druzhba, Bulgaria.
Osvald Demuth and
V. Kmínek.
Properties of indefinite constructive Lebesgue-Stieltjes integrals
(Russian).
Commentationes Mathematicae Universitatis Carolinae,
21(4):629-644, 1980.
Osvald Demuth and
A. Kucera.
Remarks on constructive mathematical analysis.
In Logic Colloquium '78 (Mons, 1978), pages 81-129.
North-Holland, Amsterdam, 1979.
Osvald Demuth and
A. Kucera.
Remarks on 1-genericity, semigenericity and related concepts.
Commentationes Mathematicae Universitatis Carolinae, 28(1):85-94,
1987.
Osvald Demuth and
L. Nemeckova.
The constructive analogue of the property (T sb 1) (Russian).
Comment. Math. Univ. Carolinae, 14:421-439, 1973.
Osvald Demuth and L. Nemecková.
The constructive analogues of the properties (N) and (S) (Russian).
Comment. Math. Univ. Carolinae, 14:565-582, 1973.
Osvald Demuth and
I. Polivka.
The representation of linear functionals in the space of codes of constructive
functions that are uniformly continuous on the segment 0 triangle 1
(Russian).
Commentationes Mathematicae Universitatis Carolinae,
20(4):765-780, 1979.
Osvald Demuth, R. Kryl, and
A. Kucera.
The use of the theory of functions that are partial recursive relative to
numerical sets in constructive mathematics (Russian).
Acta Universitatis Carolinae. Mathematica et Physica,
19(1):15-60, 1978.
Osvald Demuth.
On Lebesgue integration in constructive analysis (Russian).
Dokl. Akad. Nauk SSSR, 160:1239-1241, 1965.
Osvald Demuth.
The Lebesgue integral in constructive analysis (Russian).
Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov., 4:30-43,
1967.
[translation in: A.O. Slisenko (ed.), Studies in constructive mathematics and
mathematical logic, Part II, Consultants Bureau, New York, 1970].
Osvald Demuth.
A necessary and sufficient condition for the Riemann integrability of
constructive functions.
Dokl. Akad. Nauk SSSR, 176:757-758, 1967.
Osvald Demuth.
The connection between Riemann and Lebesgue integrability of constructive
functions (Russian).
Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov., 8:29-31,
1968.
[translation in: A.O. Slisenko (ed.), Studies in constructive mathematics and
mathematical logic, Part II, Consultants Bureau, New York, 1970].
Osvald Demuth.
Fubini's theorem for the Riemann integral in constructive mathematics.
(Russian).
Comment. Math. Univ. Carolinae, 9:677-686, 1968.
Osvald Demuth.
The Lebesgue integral and the concept of measurability of functions in
constructive analysis (Russian).
Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov., 8:21-28,
1968.
[translation in: A.O. Slisenko (ed.), Studies in constructive mathematics and
mathematical logic, Part II, Consultants Bureau, New York, 1970].
Osvald Demuth.
The differentiability of constructive functions (Russian).
Comment. Math. Univ. Carolinae, 10:167-175, 1969.
Osvald Demuth.
The Lebesgue measurability of sets in constructive mathematic (Russian).
Comment. Math. Univ. Carolinae, 10:463-492, 1969.
Osvald Demuth.
Linear functionals in the constructive spaces L sb r (Russian).
Comment. Math. Univ. Carolinae, 10:357-390, 1969.
Osvald Demuth.
Note on the paper: ``Fubini's theorem for the Riemann integral in
constructive mathematics'' (Russian).
Comment. Math. Univ. Carolinae, 10:115-120, 1969.
Osvald Demuth.
The spaces L sb n and S in constructive mathematics (Russian).
Comment. Math. Univ. Carolinae, 10:261-284, 1969.
Osvald Demuth.
The integrability of derivatives of constructive functions (Russian).
Comment. Math. Univ. Carolinae, 11:667-691, 1970.
Osvald Demuth.
Mean value theorems for the constructive Lebesgue integral (Russian).
Comment. Math. Univ. Carolinae, 11:249-269, 1970.
Osvald Demuth.
Necessary and sufficient conditions for the absolute continuity of constructive
functions (Russian).
Comment. Math. Univ. Carolinae, 11:705-726, 1970.
Osvald Demuth.
The representability of constructive functions of weakly bounded variation
(Russian).
Comment. Math. Univ. Carolinae, 11:421-434, 1970.
Osvald Demuth.
The representability of constructive functions of weakly bounded variation
(Russian).
Comment. Math. Univ. Carolinae, 11:421-434, 1970.
Osvald Demuth.
A certain condition for the differentiability of constructive functions of
bounded variation (Russian).
Comment. Math. Univ. Carolinae, 12:687-711, 1971.
Osvald Demuth.
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 (Russian).
Comment. Math. Univ. Carolinae, 12:587-610, 1971.
Osvald Demuth.
The superpositions of absolutely continuous constructive functions (Russian).
Comment. Math. Univ. Carolinae, 12:423-451, 1971.
Osvald Demuth.
A necessary and sufficient condition for the representability of constructive
functions in the form of a superposition of absolutely continuous functions
(Russian).
Comment. Math. Univ. Carolinae, 13:227-251, 1972.
Osvald Demuth.
A sufficient condition for the representability of constructive functions in
the form of the sum of two superpositions of absolutely continuous functions
(Russian).
Comment. Math. Univ. Carolinae, 13:265-282, 1972.
Osvald Demuth.
The constructive analogue of the connection between the Lebesgue
measurability of sets and of functions (Russian).
Comment. Math. Univ. Carolinae, 14:377-396, 1973.
Osvald Demuth.
The representability of uniformly continuous constructive functions
(Russian).
Comment. Math. Univ. Carolinae, 14:7-25, 1973.
Osvald Demuth.
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 (Russian).
Comment. Math. Univ. Carolinae, 15:195-210, 1974.
Osvald Demuth.
The representability of constructive functions possessing the properties ( rm
s) and ( rm t sb 1) in the form of superpositions (Russian).
Comment. Math. Univ. Carolinae, 15:49-64, 1974.
Osvald Demuth.
The differentiability of constructive functions of weakly bounded variation on
pseudo numbers (Russian).
Comment. Math. Univ. Carolinae, 16(3):583-599, 1975.
Osvald Demuth.
The constructive analogue of the Denjoy-Young theorem on derived numbers
(Russian).
Comment. Math. Univ. Carolinae, 17(1):111-126, 1976.
Osvald Demuth.
The domains of definition of effective operators over general recursive
functions and of constructive functions of a real variable (Russian).
Comment. Math. Univ. Carolinae, 17(4):633-646, 1976.
Osvald Demuth.
A constructive analogue of the functions of the nth Baire class
(Russian).
Comment. Math. Univ. Carolinae, 18(2):231-245, 1977.
Osvald Demuth.
A generalization of the constructive Lebesgue integral (Russian).
Comment. Math. Univ. Carolinae, 18(3):499-514, 1977.
Osvald Demuth.
Constructive analogues of generalized absolutely continuous functions of
generalized bounded variation (Russian).
Commentationes Mathematicae Universitatis Carolinae,
19(3):471-487, 1978.
Osvald Demuth.
The pseudodifferentiability of uniformly continuous constructive functions on
constructive real numbers (Russian).
Comment. Math. Univ. Carolin., 19(2):319-333, 1978.
Osvald Demuth.
Some questions of the theory of constructive functions of a real variable
(Russian).
Acta Universitatis Carolinae. Mathematica et Physica,
19(1):61-96, 1978.
Osvald Demuth.
The use of the Riemann-Stieltjes integral in the theory of the constructive
Lebesgue integral, and its generalizations (Russian).
Commentationes Mathematicae Universitatis Carolinae,
20(4):781-793, 1979.
Osvald Demuth.
A constructive analogue of K. M. Garg's theorem on derivative numbers
(Russian).
Commentationes Mathematicae Universitatis Carolinae,
21(3):457-472, 1980.
Osvald Demuth.
On the constructive Perron integral (Russian).
Acta Universitatis Carolinae. Mathematica et Physica, 21(1):3-57,
1980.
Osvald Demuth.
Pseudodifferentiability of constructive functions on constructive real numbers
(Russian).
Commentationes Mathematicae Universitatis Carolinae,
21(3):489-505, 1980.
Osvald Demuth.
A generalization of a constructive analogue of K. M. Garg's theorem
(Russian).
Commentationes Mathematicae Universitatis Carolinae,
22(3):607-620, 1981.
Osvald Demuth.
On the pseudodifferentiability of uniformly continuous constructive functions
from functions of the same type (Russian).
Commentationes Mathematicae Universitatis Carolinae,
22(3):497-512, 1981.
Osvald Demuth.
Borel types of some classes of arithmetical real numbers (Russian).
Commentationes Mathematicae Universitatis Carolinae,
23(3):593-606, 1982.
Osvald Demuth.
Some classes of arithmetical real numbers (Russian).
Commentationes Mathematicae Universitatis Carolinae,
23(3):453-465, 1982.
Osvald Demuth.
Arithmetic complexity of differentiation in constructive mathematics
(Russian).
Commentationes Mathematicae Universitatis Carolinae,
24(2):301-316, 1983.
Osvald Demuth.
On the pseudodifferentiability of pseudo-uniformly continuous constructive
functions from functions of the same type (Russian).
Commentationes Mathematicae Universitatis Carolinae,
24(3):391-406, 1983.
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An example of the construction of pseudonumbers by the methods of recursion
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In R.N. Tonoyan, editor, Applied mathematics, No. 5 (Russian),
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A notion of semigenericity.
Commentationes Mathematicae Universitatis Carolinae, 28(1):71-84,
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Osvald Demuth.
Reducibilities of sets based on constructive functions of a real variable.
Commentationes Mathematicae Universitatis Carolinae,
29(1):143-156, 1988.
Osvald Demuth.
Remarks on the structure of tt-degrees based on constructive measure theory.
Commentationes Mathematicae Universitatis Carolinae,
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Remarks on Denjoy sets.
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A Functional Approach to Computability on Real Numbers.
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An abstract data type for real numbers.
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WoLLIC 2006, 13th Workshop on Logic, Language, Information and Computation,
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Proof interpretations and the computational content of proofs in mathematics.
Bulletin of the EATCS, 93:143-173, 2007.
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Effective bounds from proofs in abstract functional analysis.
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On the principle of tertium non datur (Russian).
Mat. Sb., 32:646-667, 1925.
[translated in: From Frege to Gödel: A Source Book in Logic, 1879-1931, J.
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PhD thesis, School of Computer Science, University of Birmingham, Birmingham,
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Real functions incrementally computable by finite automata.
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Proceedings of the 12th International Workshop (CSL '98) (7th Annual Conference
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Proceedings of the Kazan Workshop, Kazan, Russia, July 14-19, 1997.
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In Jens Blanck, Vasco Brattka, and Peter Hertling, editors, Computability
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Margarita V. Korovina
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In Laurent Fribourg, editor, Computer Science Logic, volume 2142
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Oleg Kudinov.
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In Barry S. Cooper, Benedikt Löwe, and Leen Torenvliet, editors, New
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First Conference on Computability in Europe, CiE 2005, Amsterdam, The
Netherlands, June 2005.
Margarita Korovina and
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The uniformity principle for Sigma -definability with applications to
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In S. Barry Cooper, Benedikt Löwe, and Andrea Sorbi, editors,
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Third Conference on Computability in Europe, CiE 2007, Siena, Italy, June
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Margarita Korovina and
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Towards computability over effectively enumerable topological spaces.
In Vasco Brattka, Ruth Dillhage, Tanja Grubba, and Angela Klutsch, editors,
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CCA 2008, Fifth International Conference, Hagen, Germany, August 21-24,
2008.
Margarita Korovina and
Oleg Kudinov.
The uniformity principle for Sigma -definability.
Journal of Logic and Computation, 19(1):159-174, 2009.
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Generalized computability of real functions.
Siberian Advances in Mathematics, 2(4):85-103, 1992.
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Fixed points on the real numbers without the equality test.
In Vasco Brattka, Matthias Schröder, and Klaus Weihrauch, editors,
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5th International Workshop, CCA 2002, Málaga, Spain, July 12-13,
2002.
Vladik Kreinovich
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Computational complexity and feasibility of data processing and interval
computations, with extension to cases when we have partial information about
probabilities.
In Vasco Brattka, Matthias Schröder, Klaus Weihrauch, and Ning Zhong,
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computable initial data such that its unique solution' (1981).
The Journal of Symbolic Logic, 47:900-902, 1982.
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the problem of foundations of mathematics, florence, 1981.
Synthese Lib., 62:139-151, 1985.
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6th GI-Conference, Dortmund, January 5-7, 1983.
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A unified approach to constructive and recursive analysis.
In M.M. Richter, E. Börger, W. Oberschelp, B. Schinzel, and W. Thomas,
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Proceedings of the Logic Colloquium, Aachen, July 18-23, 1983, Part II.
Christoph Kreitz and
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Theory of representations.
Theoretical Computer Science, 38:35-53, 1985.
Christoph Kreitz and
Klaus Weihrauch.
Compactness in constructive analysis revisited.
Annals of Pure and Applied Logic, 36:29-38, 1987.
Christoph Kreitz.
Theorie der Darstellungen und ihre Anwendungen in der konstruktiven
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PhD thesis, Fachbereich Mathematik und Informatik, FernUniversität Hagen,
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Effective simultaneous approximability of reals.
Theoretical Computer Science, 284(2):397-417, 2002.
Marko Krznaric.
Computing a required absolute precision from a stream of linear fractional
transformations.
In Jens Blanck, Vasco Brattka, and Peter Hertling, editors, Computability
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4th International Workshop, CCA 2000, Swansea, UK, September 2000.
Martin Kummer and Marcus
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Computability of convex sets.
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12th Annual STACS, Munich.
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Some examples of non-metrizable spaces allowing a simple type-2 complexity
theory.
In Vasco Brattka, Ludwig Staiger, and Klaus Weihrauch, editors,
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Computability on spaces of integrable functions.
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Defining type-2 computability structures on analytical spaces.
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Type-2 computability on spaces of integrable functions.
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Riemann integration in constructive analysis (Russian).
Dokl. Akad. Nauk SSSR, 156:255-257, 1964.
[translated in: Soviet Math.-Dokl., 5 (1964) 628-630].
Boris Abramovich Kusner.
Constructive theory of the Riemann integral (Russian).
Dokl. Akad. Nauk SSSR, 165:1238-1240, 1965.
[translated in: Soviet Math.-Dokl. 6 (1965) 1584-1587].
Boris Abramovich
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The existence of unbounded constructive analytic functions (Russian).
Dokl. Akad. Nauk SSSR, 160:29-31, 1965.
[translated in: Soviet Math.-Dokl., 6 (1965) 26-28].
Boris Abramovich Kusner.
A remark on the domains of definition of constructive analytic functions
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Zap. Naucn. Sem. Leningrad. Otdel. Inst. Steklov., 8:103-106,
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Boris Abramovich Kusner.
Some mass problems connected with the integration of constructive functions
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Trudy Mat. Inst. Steklov., 113:39-72, 1970.
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Boris Abramovich Kusner.
Computationally complex real numbers (Russian).
Zeitschrift für Mathematische Logik und Grundlagen der
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Boris Abramovich
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Continuity theorems for some types of computable operators (Russian).
Dokl. Akad. Nauk SSSR, 208:1031-1034, 1973.
[translated in: Soviet Math. - Dokl., 14 (1973) 221-225].
Boris Abramovich
Kusner.
Lectures on Constructive Mathematical Analysis (Russian).
Izdat. Nauka, 1973.
translated: by Mendelson, E., and edited by Leifman, L.J., Transl. Math.
Monographs, 60 (1984).
Boris Abramovich
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the sense of Markov, Grzegorczyk and Lacombe (Russian).
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Dokl. Akad. Nauk SSSR, 215:259-262, 1974.
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Boris Abramovich Kusner.
The computation of isolated roots of constructive functions (Russian).
Zeitschrift für Mathematische Logik und Grundlagen der
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Boris Abramovich
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On Grzegorczyk's theorem on the computability of an isolated extremum
(Russian).
In A.A. Markov and B.A. Kusner, editors, Studies in the Theory of
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(Vycisl. Centr Akad. Nauk SSSR).
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In A.A. Markov and V.I. Homic, editors, Studies in the Theory of
Algorithms and Mathematical Logic, pages 62-69, 133. Nauka, 1979.
Boris Abramovich Kusner.
Behavior of the general term of a Specker series (Russian).
In M. Gladkii, editor, Mathematical Logic and Mathematical
Linguistics, pages 112-116. Kalinin. Gos. Univ., 1981.
Boris Abramovich
Kusner.
On some topological properties of constructive plane curves (Russian).
Dokl. Akad. Nauk SSSR, 260:281-283, 1981.
[translated in: Soviet Math. - Dokl., 24 (1981) 258-261].
Boris Abramovich Kusner.
Some extensions of Markov's constructive continuum and their applications to
the theory of constructive functions.
In A.S. Troelstra and D. van Dalen, editors, The L.E.J. Brouwer Centenary
Symposium (Noordwijkerhout, June 8-13,1981), volume 110 of
Studies in Logic and the Foundations of Mathematics, pages
261-273, Amsterdam, 1982. North-Holland.
Boris Abramovich Kusner.
A class of Specker sequences (Russian).
In M. Gladlii, editor, Mathematical Logic, Mathematical Linguistics
and Theory of Algorithms, pages 62-65. Kalinin. Gos. Univ., 1983.
Boris Abramovich Kusner.
Lectures on Constructive Mathematical Analysis, volume 60 of
Translations of Mathematical Monographs.
American Mathematical Society, Providence, 1984.
Boris Abramovich Kusner.
Differentiability and uniform continuity of constructive functions (Russian).
Doklady Akademii Nauk, 281:1314-1316, 1985.
[translated in: Soviet Math. - Dokl., 31 (1985) 433-435].
Boris Abramovich Kusner.
The principle of bar-induction in Brouwer's theory of the continuum
(Russian).
In M.I. Panov, editor, Patterns in the Development of Modern Mathematics,
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Effective meaning of a theorem on uniform limit transition (Russian).
In N.M. Nagornyi, editor, Problems in Mathematical Logic and in the
Theory of Algorithms, pages 3-10. Akad. Nauk SSSR, Vycisl.
Centr., 1988.
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In P.P. Petkov, editor, Mathematical Logic, pages 53-58. Plenum,
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(Proc. Heyting '88 Summer School, Chaika, Sept. 13-23, 1988).
Boris Abramovich Kusner.
The constructive mathematics of A.A. Markov: some reflections
(Russian).
Modern Logic, 3:119-144, 1993.
Boris Abramovich
Kusner.
Markov and Bishop: an essay in memory of A.A. Markov (1903-1979) and
E. Bishop (1928-1983).
In S. Zdrovkovska and P.L. Duren, editors, Golden Years of Moscow
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1993.
Boris Abramovich Kusner.
Kurt Gödel and the constructive mathematics of A.A. Markov.
In P. Hájek, editor, Gödel '96, volume 6 of Lecture
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Proc. Conf, Brno, August 1996.
Boris Abramovich Kusner.
Markov's constructive analysis; a participant's view.
Theoretical Computer Science, 219:267-285, 1999.
Boris Abramovich Kusner.
The centenary of A.A. Markov, jr.; His personality, his constructive
mathematics.
In Vasco Brattka, Matthias Schröder, Klaus Weihrauch, and Ning Zhong,
editors, Computability and Complexity in Analysis, volume 302 of
Informatik Berichte, pages 55-79. FernUniversität in Hagen,
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International Conference, CCA 2003, Cincinnati, USA, August 28-30, 2003.
A. Kucera, , and
B. Kusner.
A type of recursive isomorphism of certain concepts of constructive analysis
(Russian).
Comment. Math. Univ. Carolinæ, 19:97-105, 1978.
Salah Labhalla and
Henri Lombardi.
Comparaison des complexites des nombres reels dans differentes representations
(a la cauchy, a la dedekind, par fractions continues).
Comptes Rendus Académie des Sciences Paris, 310:483-488,
1990.
Salah Labhalla and
Henri Lombardi.
Comparaison des differentes representations des nombres reels du point de vue
des fonctionnelles recursives.
Comptes Rendus Académie des Sciences Paris, 311:229-234,
1990.
Salah Labhalla and
Henri Lombardi.
Real numbers, continued fractions, and complexity classes.
Annals of Pure and Applied Logic, 50:1-28, 1990.
Salah Labhalla and
Henri Lombardi.
Complexite du calcul du developpement d'un nombre reel en fractions continues.
Theoretical Computer Science, 83:219-235, 1991.
Salah Labhalla and
Henri Lombardi.
Analyse de complexité pour un théorème de Hall sur les fractions
continues.
Mathematical Logic Quarterly, 42:134-144, 1996.
S. Labhalla, H. Lombardi,
and E. Moutai.
Espaces métriques rationnellement présentés et complexité, le cas de
l'espace des fonctions réelles uniformément continues sur un intervalle
compact.
Theoretical Computer Science, 250:265-332, 2001.
A.H. Lachlan.
Recursive real numbers.
The Journal of Symbolic Logic, 28:1-16, 1963.
Daniel Lacombe.
Classes récursivement fermés et fonctions majorantes.
Comptes Rendus Académie des Sciences Paris, 240:716-718, June
1955.
Théorie des fonctions.
Daniel Lacombe.
Extension de la notion de fonction récursive aux fonctions d'une ou
plusieurs variables réelles I.
Comptes Rendus Académie des Sciences Paris, 240:2478-2480,
June 1955.
Théorie des fonctions.
Daniel Lacombe.
Extension de la notion de fonction récursive aux fonctions d'une ou
plusieurs variables réelles II.
Comptes Rendus Académie des Sciences Paris, 241:13-14, July
1955.
Théorie des fonctions.
Daniel Lacombe.
Extension de la notion de fonction récursive aux fonctions d'une ou
plusieurs variables réelles III.
Comptes Rendus Académie des Sciences Paris, 241:151-153, July
1955.
Théorie des fonctions.
Daniel Lacombe.
Remarques sur les opérateurs récursifs et sur les fonctions
récursives d'une variable réelle.
Comptes Rendus Académie des Sciences Paris, 241:1250-1252,
November 1955.
Théorie des fonctions.
Daniel Lacombe.
Les ensembles récursivement ouverts ou fermés, et leurs applications
à l'Analyse récursive.
Comptes Rendus Académie des Sciences Paris, 245:1040-1043,
1957.
Logique.
Daniel Lacombe.
Quelques propriétés d'analyse récursive.
Comptes Rendus Académie des Sciences Paris,
244:838-840,996-997, 1957.
Daniel Lacombe.
Les ensembles récursivement ouverts ou fermés, et leurs applications
à l'Analyse récursive.
Comptes Rendus Académie des Sciences Paris, 246:28-31, 1958.
Logique.
Daniel Lacombe.
Sur les possibilites d'extension de la notion de fonction récursive aux
fonctions d'une ou plusieurs variables réelles.
In Le raisonnement en mathematiques et en sciences, pages 67-75,
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In A. Heyting, editor, Constructivity in mathematics, pages
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Colloquium at Amsterdam, 1957.
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A two-layer approach to the computability and complexity of real functions.
In Vasco Brattka, Matthias Schröder, Klaus Weihrauch, and Ning Zhong,
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Informatik Berichte, pages 303-324. FernUniversität in Hagen,
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International Conference, CCA 2003, Cincinnati, USA, August 28-30, 2003.
Branimir Lambov.
Rates of convergence of recursively defined sequences.
In Vasco Brattka, Ludwig Staiger, and Klaus Weihrauch, editors,
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Analysis, volume 120 of Electronic Notes in Theoretical Computer
Science, pages 125-133, Amsterdam, 2005. Elsevier.
6th International Workshop, CCA 2004, Wittenberg, Germany, August 16-20,
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Branimir Lambov.
RealLib: an efficient implementation of exact real arithmetic.
In Tanja Grubba, Peter Hertling, Hideki Tsuiki, and Klaus Weihrauch, editors,
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Informatik Berichte, pages 169-175. FernUniversität in Hagen,
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Proccedings, Second International Conference, CCA 2005, Kyoto, Japan, August
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Branimir Lambov.
Topics in the Theory and Practice of Computable Analysis.
PhD thesis, Department of Computer Science, University of Aarhus, Denmark,
Aarhus, 2005.
Branimir Lambov.
The basic feasible functionals in computable analysis.
Journal of Complexity, 22(6):909-917, 2006.
Branimir Lambov.
RealLib: An efficient implementation of exact real arithmetic.
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Simon Langley and
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What can we do with a solution?
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5th International Workshop, CCA 2002, Málaga, Spain, July 12-13,
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Jimmie D. Lawson and Bin Lu.
Riemann and Edalat integration on domains.
Theoretical Computer Science, 305:259-275, 2003.
Stéphane Le Roux and
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Singular coverings and non-uniform notions of closed set computability.
In Ruth Dillhage, Tanja Grubba, Andrea Sorbi, Klaus Weihrauch, and Ning Zhong,
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Elsevier, 2008.
CCA 2007, Siena, Italy, June 16-18, 2007.
Stéphane Le Roux and
Martin Ziegler.
Singular coverings and non-uniform notions of closed set computability.
Mathematical Logic Quarterly, 54(5):545-560, 2008.
R.S. Lehman.
On primitive recursive real numbers.
Fundamenta Mathematicae, 49:105-118, 1961.
Davorin Lesnik.
Constructive Urysohn’s universal metric space.
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David Lester, Scott Chambers,
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A constructive algorithm for finding the exact roots of polynomials with
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Theoretical Computer Science, 279:51-64, 2002.
Laurentiu
Leustean.
Proof mining in R-trees and hyperbolic spaces.
In Grigori Mints and Ruy de Queiroz, editors, Logic, Language,
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Elsevier.
WoLLIC 2006, 13th Workshop on Logic, Language, Information and Computation,
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7th Annual International Conference, COCOON 2001, Guilin, China, August 20-23,
2001.
Klaus Weihrauch and
Ning Zhong.
Is wave propagation computable or can wave computers beat the Turing machine?
Proceedings of the London Mathematical Society, 85(2):312-332,
2002.
Klaus Weihrauch and Ning
Zhong.
The solution operator of the Korteweg-de Vries equation is computable.
In Vasco Brattka, Matthias Schröder, and Klaus Weihrauch, editors,
CCA 2002 Computability and Complexity in Analysis, volume 66
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2002. Elsevier.
5th International Workshop, CCA 2002, Málaga, Spain, July 12-13,
2002.
Klaus Weihrauch and
Ning Zhong.
The solution operator of the Korteweg-de Vries equation is computable.
Informatik Berichte 293, FernUniversität Hagen, Hagen, June 2002.
Klaus Weihrauch and Ning
Zhong.
An algorithm for computing fundamental solutions.
In Vasco Brattka, Ludwig Staiger, and Klaus Weihrauch, editors,
Proceedings of the 6th Workshop on Computability and Complexity in
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Science, pages 201-215, Amsterdam, 2005. Elsevier.
6th International Workshop, CCA 2004, Wittenberg, Germany, August 16-20,
2004.
Klaus Weihrauch and
Ning Zhong.
Computing the solution of the Korteweg-de Vries equation with arbitrary
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Theoretical Computer Science, 332(1-3):337-366, 2005.
Klaus Weihrauch and Ning
Zhong.
An algorithm for computing fundamental solutions.
SIAM Journal on Computing, 35(6):1283-1294, 2006.
Klaus Weihrauch and
Ning Zhong.
Computing Schrödinger propagators on Type-2 Turing machines.
Journal of Complexity, 22(6):918-935, 2006.
Klaus Weihrauch and Ning
Zhong.
Computable analysis of the abstract Cauchy problem in a Banach space and
its applications (I).
In Douglas Cenzer, Ruth Dillhage, Tanja Grubba, and Klaus Weihrauch, editors,
Proceedings of the Third International Conference on Computability and
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Theoretical Computer Science, pages 33-59, Amsterdam, 2007. Elsevier.
CCA 2006, Gainesville, Florida, USA, November 1-5, 2006.
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Computable analysis of the abstract Cauchy problem in a Banach space and
its applications I.
Mathematical Logic Quarterly, 53(4-5):511-531, 2007.
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A generalized computability thesis.
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Proceedings of the 1977 International FCT-Conference, Poznan-Kornik, Poland,
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Computability on metric spaces.
Informatik Berichte 21, FernUniversität Hagen, Hagen, September 1981.
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Recursion and complexity theory on cpo-s.
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5th GI-Conference, Karlsruhe, March 23-25, 1981.
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On natural numberings and representations.
Informatik Berichte 29, FernUniversität Hagen, Hagen, December 1982.
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Type 2 recursion theory.
Theoretical Computer Science, 38:17-33, 1985.
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Computability, volume 9 of EATCS Monographs on Theoretical
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The lowest Wadge-degrees of subsets of the Cantor space.
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On the complexity of online computations of real functions.
Journal of Complexity, 7:380-394, 1991.
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The degrees of discontinuity of some translators between representations of the
real numbers.
Technical Report TR-92-050, International Computer Science Institute, Berkeley,
July 1992.
Klaus Weihrauch.
The degrees of discontinuity of some translators between representations of the
real numbers.
Informatik Berichte 129, FernUniversität Hagen, Hagen, July 1992.
Klaus Weihrauch.
The TTE-interpretation of three hierarchies of omniscience principles.
Informatik Berichte 130, FernUniversität Hagen, Hagen, September 1992.
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Computability on computable metric spaces.
Theoretical Computer Science, 113:191-210, 1993.
Fundamental Study.
Klaus Weihrauch.
A simple introduction to computable analysis.
Informatik Berichte 171, FernUniversität Hagen, Hagen, July 1995.
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A foundation for computable analysis.
In Douglas S. Bridges, Cristian S. Calude, Jeremy Gibbons, Steve Reeves, and
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Discrete Mathematics and Theoretical Computer Science, pages 66-89,
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Proceedings of DMTCS'96.
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Random real numbers.
Informatik Berichte 219, FernUniversität Hagen, Hagen, June 1997.
Klaus Weihrauch.
A refined model of computation for continuous problems.
Journal of Complexity, 14:102-121, 1998.
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Computability on the probability measures on the Borel sets of the unit
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Theoretical Computer Science, 219:421-437, 1999.
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Computable Analysis.
Springer, Berlin, 2000.
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On computable metric spaces Tietze-Urysohn extension is computable.
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4th International Workshop, CCA 2000, Swansea, UK, September 2000.
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Computational complexity on computable metric spaces.
Mathematical Logic Quarterly, 49(1):3-21, 2003.
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Continuity in computable analysis (abstract).
In Vasco Brattka, Matthias Schröder, Klaus Weihrauch, and Ning Zhong,
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Informatik Berichte, pages 99-100. FernUniversität in Hagen,
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International Conference, CCA 2003, Cincinnati, USA, August 28-30, 2003.
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Multi-functions on multi-represented sets are closed under flowchart
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Informatik Berichte, pages 267-300. FernUniversität in Hagen,
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Proccedings, Second International Conference, CCA 2005, Kyoto, Japan, August
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The computable multi-functions on multi-represented sets are closed under
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Journal of Universal Computer Science, 14(6):801-844, 2008.
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Computers, Rigidity, and Moduli: The Large-Scale Fractal Geometry of
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Relativistic computers and non-uniform complexity theory.
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Yongcheng Wu and Decheng Ding.
Computability of measurable sets via effective topologies.
Archive for Mathematical Logic, 45(3):365-379, 2006.
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Mathematical Logic Quarterly, 51(2):157-170, 2005.
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Theory of Computing Systems, 38:701-729, 2005.
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Theoretical Computer Science, 284(2):499-518, 2002.
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Mathematical Logic Quarterly, 48(Suppl. 1):131-156, 2002.
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Theoretical Informatics and Applications, 41(1):3-25, 2007.
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Finitely bounded effective computability.
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Computability theory of generalized functions.
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Computability theory of generalized functions.
Journal of the Association for Computing Machinery,
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Computability structure of the Sobolev spaces and its applications.
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PhD thesis, Fachbereich Mathematik/Informatik, Universität Paderborn,
Paderborn, 2002.
Martin Ziegler.
Computable operators on regular sets.
In Vasco Brattka, Matthias Schröder, Klaus Weihrauch, and Ning Zhong,
editors, Computability and Complexity in Analysis, volume 302 of
Informatik Berichte, pages 389-406. FernUniversität in Hagen,
August 2003.
International Conference, CCA 2003, Cincinnati, USA, August 28-30, 2003.
Martin Ziegler.
Stability versus speed in a computable algebraic model.
In Marc et al. Daumas, editor, RNC'5 Real Numbers and Computers,
pages 47-64. INRIA, Institut National de Recherche en Informatique et en
Automatique, 2003.
Lyon, September 3-5, 2003.
Martin Ziegler.
Computable operators on regular sets.
Mathematical Logic Quarterly, 50(4,5):392-404, 2004.
Martin Ziegler.
Computability and continuity on the real arithmetic hierarchy and the power of
type-2 nondeterminism.
In Barry S. Cooper, Benedikt Löwe, and Leen Torenvliet, editors, New
Computational Paradigms, volume 3526 of Lecture Notes in
Computer Science, pages 562-571, Berlin, 2005. Springer.
First Conference on Computability in Europe, CiE 2005, Amsterdam, The
Netherlands, June 2005.
Martin Ziegler.
Effectively open real functions.
Journal of Complexity, 22(6):827-849, 2006.
Martin Ziegler.
Stability versus speed in a computable algebraic model.
Theoretical Computer Science, 351(1):14-26, 2006.
Martin Ziegler.
Real hypercomputation and continuity.
Theory of Computing Systems, 41(1):177-206, 2007.
Martin Ziegler.
Revising type-2 computation and degrees of discontinuity.
In Douglas Cenzer, Ruth Dillhage, Tanja Grubba, and Klaus Weihrauch, editors,
Proceedings of the Third International Conference on Computability and
Complexity in Analysis, volume 167 of Electronic Notes in
Theoretical Computer Science, pages 255-274, Amsterdam, 2007.
Elsevier.
CCA 2006, Gainesville, Florida, USA, November 1-5, 2006.
Martin Ziegler.
(Short) survey of real hypercomputation.
In S. Barry Cooper, Benedikt Löwe, and Andrea Sorbi, editors,
Computation and Logic in the Real World, volume 4497 of
Lecture Notes in Computer Science, pages 809-824, Berlin, 2007.
Springer.
Third Conference on Computability in Europe, CiE 2007, Siena, Italy, June
18-23, 2007.
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