Classified Bibliography

• Computability and Complexity in Analysis (based on classical logic),
• Intuitionistic and Constructive Analysis (Brouwer's and Bishop's school),
• Russian Constructive Analysis (Markov's school),
• Books on Related Topics.

• 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.

• Yohji Akama. Limiting partial combinatory algebras. Theoretical Computer Science, 311:199-220, 2004.

• 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.

• 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.

• J.C. Baez. Recursivity in quantum mechanics. Trans. Amer. Math. Soc., 280:339-350, 1983.

• 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. 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.

• 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 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.

• 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.

• 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.

• 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. 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. Domain representations of topological spaces. Theoretical Computer Science, 247:229-255, 2000.

• 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. 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.

• 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 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, 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. 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. Computable invariance. Theoretical Computer Science, 210:3-20, 1999.

• 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. Recursive quasi-metric spaces. Theoretical Computer Science, 305:17-42, 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.

• 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.

• Eyvind Briseid. A rate of convergence for asymptotic contractions. J. Math. Anal. Appl., 330:364-376, 2007.

• Eyvind Briseid. Some results on Kirk's asymptotic contractions. Fixed Point Theory, 8:17-27, 2007.

• Paul Brodhead and Douglas Cenzer. Effectively closed sets and enumerations. Archive for Mathematical Logic, 46(7-8):565–--582, 2008.

• Paul Brodhead, Douglas Cenzer, and Seyyed Dashti. Random closed sets. 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 55-64, Berlin, 2006. Springer. Second Conference on Computability in Europe, CiE 2006, Swansea, UK, June 30-July 5, 2006.

• Paul Brodhead, Douglas Cenzer, and Jeffrey B. Remmel. Random continuous functions. 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, Amsterdam, 2007. Elsevier. CCA 2006, Gainesville, Florida, USA, November 1-5, 2006.

• Paul Brodhead. Enumerations of Pi ⁰₁ classes: acceptability and decidable classes. 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 289-301, Amsterdam, 2007. Elsevier. CCA 2006, Gainesville, Florida, USA, November 1-5, 2006.

• Ashley Burrows and David Lester. Exact arithmetic and the Korteweg-de Vries equation. In Jens Blanck, Vasco Brattka, Peter Hertling, and Klaus Weihrauch, editors, Computability and Complexity in Analysis, volume 272 of Informatik Berichte, pages 23-41. FernUniversität Hagen, September 2000. CCA 2000 Workshop, Swansea, Wales, September 17-19, 2000.

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