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.

• Dmitry Buy. Some remarks about fixpoint theorems. In Jens Blanck, Vasco Brattka, Peter Hertling, and Klaus Weihrauch, editors, Computability and Complexity in Analysis, volume 272 of Informatik Berichte, pages 43-52. FernUniversität Hagen, September 2000. CCA 2000 Workshop, Swansea, Wales, September 17-19, 2000.

• Benoit Cagnard and Pierre Simonnet. Automata, Borel functions and real numbers in Pisot base. Theoretical Informatics and Applications, 41(1):27-44, 2007.

• J. Caldwell and Marian Boykan Pour-El. On a simple definition of computable functions of a real variable - with applications to functions of a complex variable. Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, 21:1-19, 1975.

• Cristian S. Calude and Peter Hertling. Computable approximations of reals: An information-theoretic analysis. Fundamenta Informaticae, 33(2):105-120, 1998.

• Cristian Calude and Helmut Jürgensen. Randomness as an invariant for number representations. In H. Maurer, J. Karhumäki, and G. Rozenberg, editors, Results and Trends in Theoretical Computer Science, pages 44-66, Berlin, 1994. Springer.

• Cristian S. Calude and Ludwig Staiger. Generalisations of disjunctive sequences. Mathematical Logic Quarterly, 51(2):120-128, 2005.

• Cristian S. Calude, Peter Hertling, and Bakhadyr Khoussainov. Do the zeros of Riemann's Zeta-function form a random sequence? Bulletin of the European Association for Theoretical Computer Science, 62:199-207, 1997.

• Cristian S. Calude, Peter Hertling, Bakhadyr Khoussainov, and Yongge Wang. Recursively enumerable reals and Chaitin omega numbers. In Michel et al. Morvan, editor, STACS'98, volume 1373 of Lecture Notes in Computer Science, pages 596-606, Berlin, 1998. Springer. 15th Annual Symposium on Theoretical Aspects of Computer Science. Paris, France, February 25-27, 1998.

• C. S. Calude, R. Coles, P. H. Hertling, and B. Khoussainov. Degree theoretic aspects of computably enumerable reals. In S. B. Cooper and J. K. Truss, editors, Models and Computability, volume 259 of London Math. Society Lecture Note Series, pages 23-39, Cambridge, 1999. Cambridge University Press. Invited Papers from Logic Colloquium 1997, Leeds.

• Cristian S. Calude, Peter H. Hertling, Bakhadyr Khoussainov, and Yongge Wang. Recursively enumerable reals and Chaitin omega numbers. Theoretical Computer Science, 255:125-149, 2001.

• C.S. Calude, P. Hertling, H. Jürgensen, and K. Weihrauch. Randomness on full shift spaces. Chaos, Solitons & Fractals, 12(3):491-503, 2001.

• Cristian S. Calude. Chaitin omega numbers, Solovay machines, and Gödel incompleteness. Theoretical Computer Science, 284(2):269-277, 2002.

• Cristian S. Calude. A characterization of c.e. random reals. Theoretical Computer Science, 271:3-14, 2002.

• Manuel Lameiras Campagnolo and Cristopher Moore. Upper and lower bounds on continuous-time computation. In I. Antoniou, C.S. Calude, and M.J. Dinneen, editors, Unconventional Models of Computation, UMC2'K, Discrete Mathematics and Theoretical Computer Science, pages 135-153, London, 2001. Springer. Second International Conference, UMC 2000, Brussels, Belgium.

• Manuel L. Campagnolo and Kerry Ojakian. The methods of approximation and lifting in real computation. 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 387-423, Amsterdam, 2007. Elsevier. CCA 2006, Gainesville, Florida, USA, November 1-5, 2006.

• Manuel L. Campagnolo and Kerry Ojakian. The elementary computable functions over the real numbers: applying two new techniques. Archive for Mathematical Logic, 46(7-8):593–--627, 2008.

• Manuel Lameiras Campagnolo, Cristopher Moore, and José Félix Costa. Iteration, inequalities, and differentiability in analog computers. Journal of Complexity, 16(4):642-660, 2001.

• Manuel Lameiras Campagnolo, Cristopher Moore, and José Félix Costa. An analog characterization of the Grzegorczyk hierarchy. Journal of Complexity, 18(4):977-1000, 2002.

• Manuel Lameiras Campagnolo. Computational Complexity of Real Valued Recursive Functions and Analog Circuits. PhD thesis, Instituto Superior Técnico, Universidade Técnica de Lisboa, Lisbon, 2001.

• Manuel Lameiras Campagnolo. The complexity of real recursive functions. In C.S. Calude, M.J. Dinneen, and F. Peper, editors, Unconventional Models of Computation, volume 2509 of Lecture Notes in Computer Science, pages 1-14, Berlin, 2002. Springer. Third International Conference, UMC 2002, Kobe, Japan, October 15-19, 2002.

• Douglas Cenzer and Peter G. Hinman. Medvedev degrees of generalized r.e. separating 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 203-223, Amsterdam, 2007. Elsevier. CCA 2006, Gainesville, Florida, USA, November 1-5, 2006.

• Douglas Cenzer and Jeffrey B. Remmel. Index sets in computable analysis. Theoretical Computer Science, 219:111-150, 1999.

• Douglas Cenzer and Jeffrey B. Remmel. Effectively closed sets and graphs of computable real functions. Theoretical Computer Science, 284(2):279-318, 2002.

• Douglas Cenzer and Jeffrey B. Remmel. Index sets for computable real functions. In Vasco Brattka, Matthias Schröder, Klaus Weihrauch, and Ning Zhong, editors, Computability and Complexity in Analysis, volume 302 of Informatik Berichte, pages 164-182. FernUniversität in Hagen, August 2003. International Conference, CCA 2003, Cincinnati, USA, August 28-30, 2003.

• Douglas Cenzer and Jeffrey B. Remmel. Index sets for omega --languages. Mathematical Logic Quarterly, 49(1):22-33, 2003.

• Douglas Cenzer and Jeffrey B. Remmel. Index sets for computable differential equations. Mathematical Logic Quarterly, 50(4,5):329-344, 2004.

• 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.

• Douglas Cenzer, S. Ali Dashti, and Jonathan L. F. King. Effective symbolic dynamics. 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 89-99. Elsevier, 2008. CCA 2007, Siena, Italy, June 16-18, 2007.

• Douglas Cenzer. Effective real dynamics. In John N. Crossley, Jefferey B. Remmel, Richard A. Shore, and Moss E. Sweedler, editors, Logical Methods in Honor of Anil Nerode's Sixtieth Birthday, volume 12 of Progress in Computer Science and Applied Logic, pages 162-177, Boston, 1993. Birkhäuser.

• Thomas Chadzelek and Günter Hotz. Analytic machines. Theoretical Computer Science, 219:151-167, 1999.

• Thomas Chadzelek. Analytische Maschinen. PhD thesis, Technische Fakultät der Universität des Saarlandes, Saarbrücken, 1998.

• G.J. Chaitin. Incompleteness theorems for random reals. Adv. in Appl. Math., 8:119-146, 1987.

• Qingliang Chen, Kaile Su, and Xizhong Zheng. Primitive recursive real numbers. Mathematical Logic Quarterly, 53(4-5):365-380, 2007.

• Qingliang Chen, Kaile Su, and Xizhong Zheng. Primitive recursiveness of real numbers under different representation. 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 303-324, Amsterdam, 2007. Elsevier. CCA 2006, Gainesville, Florida, USA, November 1-5, 2006.

• A.V. Chernavskya and V.P. Leksineb. Unrecognizability of manifolds. Annals of Pure and Applied Logic, 141(3):447-455, 2006.

• Arthur Chou and Ker-I Ko. Computational complexity of two-dimensional regions. SIAM Journal on Computing, 24:923-947, 1995.

• Arthur W. Chou and Ker-I Ko. On the complexity of finding paths in a two-dimensional domain I: Shortest paths. Mathematical Logic Quarterly, 50(6):551-572, 2004.

• Arthur W. Chou and Ker-I Ko. The computational complexity of distance functions of two-dimensional domains. Theoretical Computer Science, 337:360-369, 2005.

• Arthur W. Chou and Ker-I Ko. On the complexity of finding paths in a two-dimensional domain II: Picewise straight-line paths. 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 45-57, Amsterdam, 2005. Elsevier. 6th International Workshop, CCA 2004, Wittenberg, Germany, August 16-20, 2004.

• Arthur W. Chou. Some complexity issues in complex analysis. In Ker-I Ko and Klaus Weihrauch, editors, Computability and Complexity in Analysis, volume 190 of Informatik Berichte, pages 91-98. FernUniversität Hagen, September 1995. CCA Workshop, Hagen, August 19-20, 1995.

• Alberto Ciaffaglione and Pietro Di Gianantonio. A co-inductive approach to real numbers. In Thierry Coquand, Peter Dybjer, Bengt Nordström, and Jan Smith, editors, Types for Proofs and Programs, volume 1956 of Lecture Notes in Computer Science, pages 114-130, Berlin, 2000. Springer. International Workshop, TYPES'99, Lökeberg, Sweden, June 12-16, 1999.

• Alberto Ciaffaglione and Pietro Di Gianantonio. A certified, corecursive implementation of exact real numbers. Theoretical Computer Science, 351(1):39-51, 2006.

• J.P. Cleave. The primitive recursive analysis of ordinary differential equations and the complexity of their solutions. Journal of Computer and Systems Sciences, 3:447-455, 1969.

• W. Collins and P. Young. Discountinuities of provably correct operators on the provably recursive real numbers. The Journal of Symbolic Logic, 48:913-920, 1983.

• W. Collins. Provably recursive real numbers. Notre Dame J. Formal Logic, 19:513-522, 1978.

• Pieter Collins. Continuity and computability on reachable sets. Theoretical Computer Science, 341:162-195, 2005.

• Pieter Collins. Effective computation for nonlinear systems. 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 169-178, Berlin, 2007. Springer. Third Conference on Computability in Europe, CiE 2007, Siena, Italy, June 18-23, 2007.

• Pieter Collins. Optimal semicomputable approximations to reachable and invariant sets. Theory of Computing Systems, 41(1):33-48, 2007.

• Stephen A. Cook. Computability and complexity of higher type functions. In Y.N. Moschovakis, editor, Logic from computer science, volume 21 of Mathematical Sciences Research Institute Publications, pages 51-72, New York, 1992. Springer. Proceedings of the workshop held in Berkeley, California, November 13-17, 1989.

• José Félix Costa, Bruno Loff, and Jerzy Mycka. The new promise of analog computation. 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 189-195, Berlin, 2007. Springer. Third Conference on Computability in Europe, CiE 2007, Siena, Italy, June 18-23, 2007.

• Fredrik Dahlgren. Computability and continuity in metric partial algebras equipped with computability structures. Mathematical Logic Quarterly, 50(4,5):486-500, 2004.

• Fredrik Dahlgren. Partial continuous functions and admissible domain representations. 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 94-104, Berlin, 2006. Springer. Second Conference on Computability in Europe, CiE 2006, Swansea, UK, June 30-July 5, 2006.

• Frédéric De Jaeger, Martín Escardó, and Gabriele Santini. On the computational content of the Lawson topology. Theoretical Computer Science, 357(1-3):230-240, 2006.

• Gregorio de Miguel Casado, Juan Manuel García Chamizo, and María Teresa Signes Pont. Algebraic model of an arithmetic unit for TTE-computable normalized rational numbers. 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 218-227, Berlin, 2007. Springer. Third Conference on Computability in Europe, CiE 2007, Siena, Italy, June 18-23, 2007.

• Thomas Deil. Darstellungen und Berechenbarkeit reeller Zahlen. PhD thesis, Fachbereich Mathematik und Informatik, FernUniversität Hagen, 1984.

• H.J. Dettki, H. Schuster, and K. Weihrauch. Type 2 recursion theory. In J. Demetrovics, G. Katona, and A. Salomaa, editors, Algebra, Combinatorics and Logic in Computer Science, Vol. 1, volume 42 of Coll. Math. Soc. János Bolyai, pages 355-361, 1986. Papers from Colloq., Sept. 12-16, 1983, Györ.

• Hans Joachim Dettki. Untersuchungen zur Darstellungsberechenbarkeit von Ordinalzahlfunktionen. PhD thesis, Fachbereich Mathematik und Informatik, FernUniversität Hagen, 1985.

• Pietro Di Gianantonio. A Functional Approach to Computability on Real Numbers. Dottorato di ricerca in informatica, Università di Pisa-Genova-Udine, Udine, June 1993.

• Pietro Di Gianantonio. Real number computation and domain theory. Information and Computation, 127:11-25, 1996.

• Pietro Di Gianantonio. An abstract data type for real numbers. Theoretical Computer Science, 221:295-326, 1999.

• 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, Amsterdam, 2008. CCA 2007, Siena, Italy, June 16-18, 2007.

• Ruth Dillhage. Computability of the spectrum of self-adjoint operators and the computable operational calculus. 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.

• Decheng Ding, Klaus Weihrauch, and Yongcheng Wu. Absolutely non-effective predicates and functions in computable analysis. In Jin-Yi Cai, S. Barry Cooper, and Hong Zhou, editors, Theory and Applications of Models of Computation, volume 4484 of Lecture Notes in Computer Science, pages 595-604, 2007.

• Rod G. Downey and Evan J. Griffiths. Schnorr randomness. 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.

• Rod Downey and Iraj Kalantari. Effective extensions of linear forms on a recursive vector space over a recursive field. Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, 31(3):193-200, 1985.

• Rodney G. Downey and Geoffrey L. LaForte. Presentations of computably enumerable reals. Theoretical Computer Science, 284(2):539-555, 2002.

• Rod Downey and Sebastiaan Terwijn. Computably enumerable reals and uniformly presentable ideals. Mathematical Logic Quarterly, 48(Suppl. 1):29-40, 2002.

• Rod G. Downey, Denis R. Hirschfeldt, and Geoffrey L. LaForte. Randomness and reducibility. In Jirí Sgall, Ales Pultr, and Petr Kolman, editors, Mathematical Foundations of Computer Science 2001, volume 2136 of Lecture Notes in Computer Science, pages 316-327, Berlin, 2001. Springer. 26th International Symposium, MFCS 2001, Mariánské Lázne, Czech Republic, August 27-31, 2001.

• Rod G. Downey, Denis R. Hirschfeldt, André Nies, and Frank Stephan. Trivial 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.

• Rod G. Downey, Denis R. Hirschfeldt, André Nies, and Frank Stephan. Trivial reals. In Rod Downey, Ding Decheng, Tung Shih Ping, Qiu Yu Hui, and Mariko Yasugi, editors, Proceedings of the 7th and 8th Asian Logic Conferences, pages 63-102, Singapore, 2003. World Scientific. 7th Conference: Hsi-Tou, Taiwan, June 6-10, 1999; 8th Conference: Chongqing, China, August 29 -- September 2, 2002.

• Rod Downey, Guohua Wu, and Xizhong Zheng. Degrees of d.c.e. reals. Mathematical Logic Quarterly, 50(4,5):345-350, 2004.

• Rod G. Downey, Evan J. Griffiths, and Geoffrey L. LaForte. On Schnorr and computable randomness, martingales, and machines. Mathematical Logic Quarterly, 50(6):613-627, 2004.

• Rodney Downey, Wolfgang Merkle, and Jan Reimann. Schnorr dimension. Mathematical Structures in Computer Science, 16(5):789-811, 2006.

• Rodney G. Downey. Presentations of reals (abstract). In Vasco Brattka, Matthias Schröder, Klaus Weihrauch, and Ning Zhong, editors, Computability and Complexity in Analysis, volume 302 of Informatik Berichte, pages 11-12. FernUniversität in Hagen, August 2003. International Conference, CCA 2003, Cincinnati, USA, August 28-30, 2003.

• D. Du and Ker-I Ko. Computational complexity of integration and differentiation of convex functions. System Sci. and Math. Sci., 2:70-79, 1989.

• D. Du and Ker-I Ko. A note on best fractions of a computable real number. Journal of Complexity, 8:216-229, 1992.

• Zilin Du, Maria Eleftheriou, José E. Moreira, and Chee Yap. Hypergeometric functions in exact geometric computation. 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.

• Anthony J. Dunlop and Marian Boykan Pour-El. The degree of unsolvability of a real number. In Jens Blanck, Vasco Brattka, and Peter Hertling, editors, Computability and Complexity in Analysis, volume 2064 of Lecture Notes in Computer Science, pages 16-29, Berlin, 2001. Springer. 4th International Workshop, CCA 2000, Swansea, UK, September 2000.

• Abbas Edalat and Martín Hötzel Escardó. Integration in real PCF. Information and Computation, 160:128-166, 2001.

• Abbas Edalat and Reinhold Heckmann. A computational model for metric spaces. Theoretical Computer Science, 193:53-73, 1998.

• Abbas Edalat and Marko Krznaric. Numerical integration with exact real arithmetic. In Jirí Wiedermann, Peter van Emde Boas, and Mogens Nielsen, editors, Automata, Languages and Programming, volume 1644 of Lecture Notes in Computer Science, pages 90-104, Berlin, 1999. Springer. 26th International Colloquium, ICALP'99, Prague, Czech Republic, July, 1999.

• Abbas Edalat and André Lieutier. Domain of differentiable functions. In Jens Blanck, Vasco Brattka, Peter Hertling, and Klaus Weihrauch, editors, Computability and Complexity in Analysis, volume 272 of Informatik Berichte, page 79. FernUniversität Hagen, September 2000. CCA 2000 Workshop, Swansea, Wales, September 17-19, 2000.

• Abbas Edalat and André Lieutier. Foundation of a computable solid modelling. Theoretical Computer Science, 284(2):319-345, 2002.

• Abbas Edalat and Dirk Pattinson. Initial value problems in domain theory. In Vasco Brattka, Matthias Schröder, Klaus Weihrauch, and Ning Zhong, editors, Computability and Complexity in Analysis, volume 302 of Informatik Berichte, pages 211-227. FernUniversität in Hagen, August 2003. International Conference, CCA 2003, Cincinnati, USA, August 28-30, 2003.

• Abbas Edalat and Dirk Pattinson. A domain-theoretic account of Picard's theorem. LMS Journal of Computation and Mathematics, 10:83-118, 2007.

• Abbas Edalat and Peter John Potts. A new representation for exact real numbers. Electronical Notes in Theoretical Computer Science, 6:14 pp., 1997. Mathematical foundations of programming semantics (Pittsburgh, PA, 1997).

• Abbas Edalat and Fabien Rico. Root finding in exact real arithmetic using linear fractional transformations. In J.-M. Chesneaux, F. Jézéquel, J.-L. Lamotte, and J. Vignes, editors, Third Real Numbers and Computers Conference, pages 27-43. Université Pierre et Marie Curie, Paris, 1998. Paris, France, April 27-29, 1998.

• Abbas Edalat and Philipp Sünderhauf. Computable Banach spaces via domain theory. Theoretical Computer Science, 219:169-184, 1999.

• Abbas Edalat and Philipp Sünderhauf. A domain-theoretic approach to computability on the real line. Theoretical Computer Science, 210:73-98, 1999.

• Abbas Edalat, Elham Kashefi, and André Lieutier. The convex hull is computable! In Jens Blanck, Vasco Brattka, Peter Hertling, and Klaus Weihrauch, editors, Computability and Complexity in Analysis, volume 272 of Informatik Berichte, pages 75-77. FernUniversität Hagen, September 2000. CCA 2000 Workshop, Swansea, Wales, September 17-19, 2000.

• Abbas Edalat, Ali A. Khanban, and André Lieutier. Computability in computational geometry. In Barry S. Cooper, Benedikt Löwe, and Leen Torenvliet, editors, New Computational Paradigms, volume 3526 of Lecture Notes in Computer Science, pages 117-127, Berlin, 2005. Springer. First Conference on Computability in Europe, CiE 2005, Amsterdam, The Netherlands, June 2005.

• Abbas Edalat. Domain theory and integration. Theoretical Computer Science, 151:163-193, 1995.

• Abbas Edalat. Dynamical systems, measures, and fractals via domain theory. Information and Computation, 120(1):32-48, 1995.

• Abbas Edalat. Power domains and iterated function systems. Information and Computation, 124(2):182-197, 1996.

• Abbas Edalat. Domains for computation in mathematics, physics and exact real arithmetic. Bulletin of Symbolic Logic, 3(4):401-452, 1997.

• Abbas Edalat. A continuous derivative for real-valued 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 248-257, Berlin, 2007. Springer. Third Conference on Computability in Europe, CiE 2007, Siena, Italy, June 18-23, 2007.

• Ju. L. Ersov. Computable functionals of finite type. Algebra and Logic, 11(4):203-242, 1972.

• Henri-Alex Esblin. Rudimentary computable reals. In Ker-I Ko, Anil Nerode, Marian B. Pour-El, Klaus Weihrauch, and Jirí Wiedermann, editors, Computability and Complexity in Analysis, volume 235 of Informatik Berichte, pages 21-30. FernUniversität Hagen, August 1998. CCA Workshop, Brno, Czech Republic, August, 1998.

• Martín H. Escardó and J. Raymundo Marcial-Romero. Semantics of a sequential language for exact real-number computation. Theoretical Computer Science, 379:120-141, 2007.

• Martín Hötzel Escardó and Thomas Streicher. Induction and recursion on the partial real line with applications to real PCF. Theoretical Computer Science, 210:121-157, 1999.

• Martín Hötzel Escardó and Thomas Streicher. In domain realizability not all functionals on c[-1,1] are continuous. Mathematical Logic Quarterly, 48(Suppl. 1):41-44, 2002.

• Martín Hötzel Escardó. PCF extended with real numbers. Theoretical Computer Science, 162:79-115, 1996.

• Martín Hötzel Escardó. PCF extended with real numbers: a domain-theoretic approach to higher-order exact real number computation. PhD thesis, Imperial College, University of London, London, Great Britain, 1997.

• Mirko Degli Esposti and Stefano Galatolo. Recurrence near given sets and the complexity of the Casati-Prosen map. Chaos Solitons Fractals, 23(4):1275-1284, 2005.

• Gábor Etesi and István Németi. Non-Turing computations via Malament-Hogarth space-times. International Journal of Theoretical Physics, 41(2):341-370, 2002.

• Amin Farjudian. SHRAD: A language for sequential real number computation. Theory of Computing Systems, 41(1):49-105, 2007.

• Fernando Ferreira and Gilda Ferreira. Counting as integration in feasible analysis. Mathematical Logic Quarterly, 52(3):315-320, 2006.

• Fernando Ferreira and Gilda Ferreira. The Riemann integral in weak systems of analysis. Journal of Universal Computer Science, 14(6):908-937, 2008.

• Fernando Ferreira and Paulo Oliva. Bounded functional interpretation and feasible analysis. Annals of Pure and Applied Logic, 145(2):115-129, 2007.

• Santiago Figueira, Frank Stephan, and Guohua Wu. Randomness and universal machines. Journal of Complexity, 22(6):738-751, 2006.

• Willem Fouché. Arithmetical representation of Brownian motion I. The Journal of Symbolic Logic, 65:421-442, 2000.

• Willem Fouché. The descriptive complexity of Brownian motion. Advances in Mathematics, 155:317-343, 2000.

• Willem Fouché. Dynamics of a generic Brownian motion: Recursive aspects. Theoretical Computer Science, 394:175-186, 2008.

• Johanna N.Y. Franklin. Schnorr trivial reals: a construction. 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 79-93, Amsterdam, 2007. Elsevier. CCA 2006, Gainesville, Florida, USA, November 1-5, 2006.

• Johanna N.Y. Franklin. Schnorr trivial reals: a construction. Archive for Mathematical Logic, 46(7-8):665–--678, 2008.

• Rudolf Freund and Ludwig Staiger. Numbers defined via Turing machines. In Ker-I Ko and Klaus Weihrauch, editors, Computability and Complexity in Analysis, volume 190 of Informatik Berichte, pages 119-124. FernUniversität Hagen, September 1995. CCA Workshop, Hagen, August 19-20, 1995.

• Rudolf Freund and Ludwig Staiger. Numbers defined by Turing machines. Collegium Logicum, Annals of the Kurt-Gödel-Society, 2:118-137, 1996.

• Rudolf Freund. Real functions and numbers defined by Turing machines. Theoretical Computer Science, 23:287-304, 1983.

• Harvey Friedman. On the computational complexity of maximization and integration. Advances in Mathematics, 53:80-98, 1984.

• Peter Gács. Uniform test of algorithmic randomness over a general space. Theoretical Computer Science, 341:91-137, 2005.

• Stefano Galatolo. Pointwise information entropy for metric spaces. Nonlinearity, 12:1289-1298, 1999.

• Stefano Galatolo. Orbit computability by computable structures. Nonlinearity, 13:1531-1546, 2000.

• Stefano Galatolo. Complexity, initial condition sensitivity, dimension and weak chaos in dynamical systems. Nonlinearity, 16(4):1219-1238, 2003.

• Stefano Galatolo. Global and local complexity in weakly chaotic dynamical systems. Discrete and Continuous Dynamical Systems, 9(6):1607-1624, 2003.

• Tobias Gärtner and Günter Hotz. Recursive analytic functions of a complex variable. In Jens Blanck, Vasco Brattka, Peter Hertling, and Klaus Weihrauch, editors, Computability and Complexity in Analysis, volume 272 of Informatik Berichte, pages 81-97. FernUniversität Hagen, September 2000. CCA 2000 Workshop, Swansea, Wales, September 17-19, 2000.

• William Gay, Bing-Yu Zhang, and Ning Zhong. Computability of solutions of the Korteweg-de Vries equation. Mathematical Logic Quarterly, 47(1):93-110, 2001.

• Xiaolin Ge and Anil Nerode. On extreme points of convex compact Turing located sets. In Anil Nerode and Yu. V. Matiyasevich, editors, Logical Foundations of Computer Science, volume 813 of Lecture Notes in Computer Science, pages 114-128, Berlin, 1994. Springer. Third International Symposium, LFCS'94, St. Petersburg, Russia, July 11-14, 1994.

• Xiaolin Ge and Anil Nerode. Effective content of the calculus of variations I: semi-continuity and the chattering lemma. Annals of Pure and Applied Logic, 78:127-146, 1996.

• Xiaolin Ge and J. Ian Richards. Computability in unitary representations of compact groups. In John N. Crossley, Jefferey B. Remmel, Richard A. Shore, and Moss E. Sweedler, editors, Logical Methods in Honor of Anil Nerode's Sixtieth Birthday, volume 12 of Progress in Computer Science and Applied Logic, pages 386-421, Boston, 1993. Birkhäuser.

• Xiaolin Ge. Some Algorithms in Euclidean Space and Group Representations. Thesis, University of Minnesota, Minneapolis, May 1993.

• Philipp Gerhardy. Applications of Proof Interpretations. PhD thesis, Department of Computer Science, University of Aarhus, Denmark, Aarhus, 2006.

• Philipp Gerhardy. A quantitative version of Kirk's fixed point theorem for asymptotic contractions. J. Math. Anal. Appl., 316:339-345, 2006.

• Herman Geuvers, Milad Niqui, Bas Spitters, and Freek Wiedijk. Constructive analysis, types and exact real numbers. Mathematical Structures in Computer Science, 17:3-36, 2007.

• Guido Gherardi. An analysis of the lemmas of Urysohn and Urysohn-Tietze according to effective Borel measurability. 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 199-208, Berlin, 2006. Springer. Second Conference on Computability in Europe, CiE 2006, Swansea, UK, June 30-July 5, 2006.

• Guido Gherardi. Effective Borel degrees of some topological functions. Mathematical Logic Quarterly, 52(6):625-642, 2006.

• Guido Gherardi. Some Results in Computable Analysis and Effective Borel Measurability. PhD thesis, University of Siena, Department of Mathematics and Computer Science, Siena, 2006.

• Guido Gherardi. Internal computability. 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 348-357, Berlin, 2007. Springer. Third Conference on Computability in Europe, CiE 2007, Siena, Italy, June 18-23, 2007.

• R.L. Goodstein and J. Hooley. On recursive transcendence. Notre Dame J. Formal Logic, 1:127-137, 1960.

• R.L. Goodstein. Missing value theorems. Math. Gaz., 33:19-25, 1949.

• R.L. Goodstein. Mean value theorems in recursive function theory I. Differential mean value theorems. Proc. London Math. Soc., 52:81-106, 1950.

• R.L. Goodstein. The recursive irrationality of pi . The Journal of Symbolic Logic, 19:267-274, 1954.

• R.L. Goodstein. On non-constructive theorems of analysis and the decision problem. Math. Scand., 3:261-263, 1956.

• R.L. Goodstein. Recursive analysis. In A. Heyting, editor, Constructivity in Mathematics, Studies in Logic and the Foundations of Mathematics, pages 37-42, Amsterdam, 1959. North-Holland. Proc. Colloq., Amsterdam, Aug. 26-31, 1957.

• R.L. Goodstein. Recursive Analysis. Studies in Logic and the Foundations of Mathematics. North-Holland, Amsterdam, 1961.

• R.L. Goodstein. Existence in mathematics. Compositio Math., 20:70-82, 1968.

• R.L. Goodstein. A constructive form for the second Gauss proof of the fundamental theorem of algebra. In Constructive Aspects of the Fundamental Theorem of Algebra, pages 69-76, NY, 1969. Willey-Interscience. Proc. Sympos. Zürich-Rüschlikon, June 5-7, 1967.

• R.L. Goodstein. Polynomials with computable coefficients. Notre Dame J. Formal Logic, 11:447-448, 1970.

• Dan Gordon and Eliahu Shamir. Computation of recursive functionals using minimal initial segments. Theoretical Computer Science, 23:305-315, 1983.

• Marco Gori and Klaus Meer. A step towards a complexity theory for analog systems. Mathematical Logic Quarterly, 48(Suppl. 1):45-58, 2002.

• Paul Gowland and David Lester. A survey of exact arithmetic implementations. In Jens Blanck, Vasco Brattka, and Peter Hertling, editors, Computability and Complexity in Analysis, volume 2064 of Lecture Notes in Computer Science, pages 30-47, Berlin, 2001. Springer. 4th International Workshop, CCA 2000, Swansea, UK, September 2000.

• Daniel Silva Graça and José Félix Costa. Analog computers and recursive functions over the reals. Journal of Complexity, 19(5):644-664, 2003.

• Daniel Silva Graça, Manuel L. Campagnolo, and Jorge Buescu. Robust simulations of Turing machines with analytic maps and flows. In Barry S. Cooper, Benedikt Löwe, and Leen Torenvliet, editors, New Computational Paradigms, volume 3526 of Lecture Notes in Computer Science, pages 169-179, Berlin, 2005. Springer. First Conference on Computability in Europe, CiE 2005, Amsterdam, The Netherlands, June 2005.

• Daniel Silva Graça. Computability via analog circuits. In Vasco Brattka, Matthias Schröder, Klaus Weihrauch, and Ning Zhong, editors, Computability and Complexity in Analysis, volume 302 of Informatik Berichte, pages 229-240. FernUniversität in Hagen, August 2003. International Conference, CCA 2003, Cincinnati, USA, August 28-30, 2003.

• Daniel Silva Graça. Some recent developments on Shannon's general purpose analog computer. Mathematical Logic Quarterly, 50(4,5):473-485, 2004.

• Daniel S. Graça, Jorge Boescu, and Manuel L. Campagnolo. Boundedness of the domain of definition is undecidable for polynomial ODEs. 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 49-57. Elsevier, 2008. CCA 2007, Siena, Italy, June 16-18, 2007.

• Tanja Grubba and Klaus Weihrauch. A computable version of Dini's theorem for topological spaces. In Pinar Yolum, Tunga Güngör, Fikret Gürgen, and Can Özturan, editors, Computer and Information Sciences - ISCIS 2005, volume 3733 of Lecture Notes in Computer Science, pages 927-936, Berlin, 2005. Springer. 20th International Symposium, ISCIS, Istanbul, Turkey, October 2005.

• Tanja Grubba and Klaus Weihrauch. On computable metrization. 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 345-364, Amsterdam, 2007. Elsevier. CCA 2006, Gainesville, Florida, USA, November 1-5, 2006.

• Tanja Grubba, Peter Hertling, Hideki Tsuiki, and Klaus Weihrauch. Computability and complexity in analysis. Informatik Berichte 326, FernUniversität Hagen, Hagen, July 2005. Proccedings, Second International Conference, CCA 2005, Kyoto, Japan, August 25-29, 2005.

• Tanja Grubba, Matthias Schröder, and Klaus Weihrauch. Computable metrization. Mathematical Logic Quarterly, 53(4-5):381-395, 2007.

• Tanja Grubba, Klaus Weihrauch, and Yatao Xu. Effectivity on continuous functions in topological 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 237-254. Elsevier, 2008. CCA 2007, Siena, Italy, June 16-18, 2007.

• Andrzej Grzegorczyk. Undecidability of some topological theories. Fund. Math., 38:137-152, 1951.

• Andrzej Grzegorczyk. Computable functionals. Fundamenta Mathematicae, 42:168-202, 1955.

• Andrzej Grzegorczyk. On the definition of computable functionals. Fundamenta Mathematicae, 42:232-239, 1955.

• Andrzej Grzegorczyk. On the definitions of computable real continuous functions. Fundamenta Mathematicae, 44:61-71, 1957.

• Andrzej Grzegorczyk. Some approaches to constructive analysis. In A. Heyting, editor, Constructivity in mathematics, Studies in Logic and the Foundations of Mathematics, pages 43-61, Amsterdam, 1959. North-Holland. Colloquium at Amsterdam, 1957.

• Andrzej Grzegorczyk. Mathematical and empirical verifiability. In Twenty-five Years of logic. Methodol. in Poland, pages 165-169, 1977.

• Xiaoyang Gu, Jack H. Lutz, and Elvira Mayordomo. Points on computable curves. In 47th Annual IEEE Symposium on Foundations of Computer Science, pages 469-474. IEEE Computer Society Press, 2006. Proceedings of FOCS 2006, Berkeley, CA, October 22-24, 2006.

• Jürgen Hauck. Ein Kriterium für die Annahme des Maximums in der Berechenbaren Analysis. Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, 17:193-196, 1971.

• Jürgen Hauck. Zur Präzisierung des Begriffes berechenbare reelle Funktion. Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, 17:295-300, 1971.

• Jürgen Hauck. Berechenbare gleichmäßige Finitheit rekursiver funktionale. Wissenschaftliche Zeitschrift der Humboldt-Universität zu Berlin, Math.-Nat. R. XXI(5):527-529, 1972.

• Jürgen Hauck. Berechenbare gleichmäßige Stetigkeit in der konstruktiven Analysis von Klaua. Wissenschaftliche Zeitschrift der Humboldt-Universität zu Berlin, Math.-Nat. R. XXI(5):523-526, 1972.

• Jürgen Hauck. Funktional-Rekursion. Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, 18:31-36, 1972.

• Jürgen Hauck. Berechenbare reelle Funktionen. Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, 19:121-140, 1973.

• Jürgen Hauck. Iterationsverfahren in der konstruktiven Analysis. Wissenschaftliche Zeitschrift der Humboldt-Universität zu Berlin, Math.-Nat. R. XXIV(6):799-800, 1975.

• Jürgen Hauck. Turingmaschinen und berechenbare reelle Funktionen. Wissenschaftliche Zeitschrift der Humboldt-Universität zu Berlin, Math.-Nat. R. XXIV(6):797-798, 1975.

• Jürgen Hauck. Berechenbare reelle Funktionenfolgen. Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, 22:265-282, 1976.

• Jürgen Hauck. Rekursive Funktionale und der Fixpunksatz von Banach. Wissenschaftliche Zeitschrift der Humboldt-Universität zu Berlin, Math.-Nat. R. XXVI(5):635-636, 1977.

• Jürgen Hauck. Zum Zwischenwertsatz in der konstruktiven Analysis. Wissenschaftliche Zeitschrift der Humboldt-Universität zu Berlin, Math.-Nat. R. XXVI(5):623-627, 1977.

• Jürgen Hauck. Konstruktive Darstellungen reeller Zahlen und Folgen. Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, 24:365-374, 1978.

• Jürgen Hauck. Konstruktive Darstellungen in topologischen Räumen mit rekursiver Basis. Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, 26:565-576, 1980.

• Jürgen Hauck. Stetigkeitseigenschaften berechenbarer reeller Funktionen. Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, 26:69-76, 1980.

• Jürgen Hauck. Berechenbarkeit in topologischen Räumen mit rekursiver Basis. Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, 27:473-480, 1981.

• Jürgen Hauck. Stetigkeitseigenschaften berechenbarer Funktionale. Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, 28:377-383, 1982.

• Jürgen Hauck. Konstruktive reelle Funktionale und Operatoren. Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, 29:213-218, 1983.

• Jürgen Hauck. Eine neue Definition berechenbarer reeller Funktionen. Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, 30:259-268, 1984.

• Jürgen Hauck. Zur Wellengleichung mit konstruktiven Randbedingungen. Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, 30:561-566, 1984.

• Jürgen Hauck. Ein Kriterium für die konstruktive Lösbarkeit der Differentialgleichung y'=f(x,y). Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, 31:357-362, 1985.

• Jürgen Hauck. Eine berechenbare Funktion mit rationalen Werten, die nicht rekursiv ist. Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, 33:255-256, 1987.

• Susumu Hayashi. Mathematics based on incremental learning-excluded middle and inductive inference. Theoretical Computer Science, 350:125-139, 2006.

• Reinhold Heckmann. Contractivity of linear fractional transformations. Theoretical Computer Science, 279:65-82, 2002.

• Gerhard Heindl, Vladik Kreinovich, and Maria Rifqi. In case of interval (or more general) uncertainty, no algorithm can choose the simplest representative. Reliable Computing, 8:213-227, 2002.

• Armin Hemmerling. On the time complexity of partial real functions. In Ker-I Ko, Anil Nerode, Marian B. Pour-El, Klaus Weihrauch, and Jirí Wiedermann, editors, Computability and Complexity in Analysis, volume 235 of Informatik Berichte, pages 31-40. FernUniversität Hagen, August 1998. CCA Workshop, Brno, Czech Republic, August, 1998.

• Armin Hemmerling. On approximative and algebraic computability over the real numbers. Theoretical Computer Science, 219:185-223, 1999.

• Armin Hemmerling. Berechenbarkeit über den reellen Zahlen, der approximative und der algebraische Zugang. In Jürgen Flachsmeyer, Rudolph Fritsch, and Hans-Christian Reichel, editors, Mathematik-interdisziplinär, pages 167-176, Aachen, 2000. Shaker Verlag.

• Armin Hemmerling. On the time complexity of partial real functions. Journal of Complexity, 16:363-376, 2000.

• Armin Hemmerling. Standard representations of effective metric spaces. In Jens Blanck, Vasco Brattka, and Peter Hertling, editors, Computability and Complexity in Analysis, volume 2064 of Lecture Notes in Computer Science, pages 48-68, Berlin, 2001. Springer. 4th International Workshop, CCA 2000, Swansea, UK, September 2000.

• Armin Hemmerling. Effective metric spaces and representations of the reals. Theoretical Computer Science, 284(2):347-372, 2002.

• Armin Hemmerling. Approximate decidability in Euclidean spaces. Mathematical Logic Quarterly, 49(1):34-56, 2003.

• Armin Hemmerling. Characterizations of the class delta ₂^ta over Euclidean spaces. In Vasco Brattka, Matthias Schröder, Klaus Weihrauch, and Ning Zhong, editors, Computability and Complexity in Analysis, volume 302 of Informatik Berichte, pages 241-254. FernUniversität in Hagen, August 2003. International Conference, CCA 2003, Cincinnati, USA, August 28-30, 2003.

• Armin Hemmerling. The discrete parts of approximately decidable sets in Euclidean spaces. Mathematical Logic Quarterly, 49(4):428-432, 2003.

• Armin Hemmerling. Characterizations of the class Delta ₂^ta over Euclidean spaces. Mathematical Logic Quarterly, 50(4,5):507-519, 2004.

• Armin Hemmerling. Hierarchies of function classes defined by the first-value operator (extended abstract). 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 59-72, Amsterdam, 2005. Elsevier. 6th International Workshop, CCA 2004, Wittenberg, Germany, August 16-20, 2004.

• Armin Hemmerling. The Hausdorff-Ershov hierarchy in Euclidean spaces. Archive for Mathematical Logic, 45:323-350, 2006.

• Peter Hertling and Klaus Weihrauch. Levels of degeneracy and exact lower complexity bounds for geometric algorithms. In Proceedings of the Sixth Canadian Conference on Computational Geometry, pages 237-242. University of Saskatchewan, 1994. Saskatoon, Saskatchewan, August 2-6, 1994.

• Peter Hertling and Klaus Weihrauch. On the topological classification of degeneracies. Informatik Berichte 154, FernUniversität Hagen, Hagen, February 1994.

• Peter Hertling and Klaus Weihrauch. Randomness spaces. In Kim G. Larsen, Sven Skyum, and Glynn Winskel, editors, Automata, Languages and Programming, volume 1443 of Lecture Notes in Computer Science, pages 796-807, Berlin, 1998. Springer. 25th International Colloquium, ICALP'98, Aalborg, Denmark, July 1998.

• Peter Hertling and Klaus Weihrauch. Random elements in effective topological spaces with measure. Information and Computation, 181(1):32-56, 2003.

• Peter Hertling. Stetige Reduzierbarkeit auf Sigma ^ omega von Funktionen mit zweielementigem Bild und von zweistetigen Funktionen mit diskretem Bild. Informatik Berichte 153, FernUniversität Hagen, Hagen, December 1993.

• Peter Hertling. Topologische Komplexitätsgrade von Funktionen mit endlichem Bild. Informatik Berichte 152, FernUniversität Hagen, Hagen, December 1993.

• Peter Hertling. Disjunctive omega -words and real numbers. Informatik Berichte 180, FernUniversität Hagen, Hagen, May 1995.

• Peter Hertling. Disjunctive omega-words und real numbers. Journal of Universal Computer Science, 2(7):549-568, 1996.

• Peter Hertling. Topological complexity with continuous operations. Journal of Complexity, 12:315-338, 1996.

• Peter Hertling. Unstetigkeitsgrade von Funktionen in der effektiven Analysis. PhD thesis, Fachbereich Informatik, FernUniversität Hagen, 1996.

• Peter Hertling. Effectivity and effective continuity of functions between computable metric spaces. In Douglas S. Bridges, Cristian S. Calude, Jeremy Gibbons, Steve Reeves, and Ian H. Witten, editors, Combinatorics, Complexity, and Logic, Discrete Mathematics and Theoretical Computer Science, pages 264-275, Singapore, 1997. Springer. Proceedings of DMTCS'96.

• Peter Hertling. The real number structure is effectively categorical. CDMTCS Research Report Series 057, University of Auckland, Auckland, September 1997.

• Peter Hertling. Surjective functions on computably growing Cantor sets. Journal of Universal Computer Science, 3(11):1226-1240, 1997.

• Peter Hertling. An effective Riemann Mapping Theorem. Theoretical Computer Science, 219:225-265, 1999.

• Peter Hertling. A real number structure that is effectively categorical. Mathematical Logic Quarterly, 45(2):147-182, 1999.

• Peter Hertling. Standard representations of real numbers. Chaos, Solitons & Fractals, 10(6):1087-1101, 1999.

• Peter Hertling. Banach-Mazur computable functions on metric spaces. In Jens Blanck, Vasco Brattka, and Peter Hertling, editors, Computability and Complexity in Analysis, volume 2064 of Lecture Notes in Computer Science, pages 69-81, Berlin, 2001. Springer. 4th International Workshop, CCA 2000, Swansea, UK, September 2000.

• Peter Hertling. Random sets versus random sequences. Informatik Berichte 288, FernUniversität Hagen, Hagen, September 2001.

• Peter Hertling. A Banach-Mazur computable but not Markov computable function on the computable real numbers. 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 962-972, Berlin, 2002. Springer. 29th International Colloquium, ICALP, Málaga, Spain, July 8-13, 2002.

• Peter Hertling. A comparison of certain representations of regularly closed sets. 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.

• Peter Hertling. Topological complexity of zero finding with algebraic operations. Journal of Complexity, 18(4):912-942, 2002.

• Peter Hertling. Topological complexity of zero finding for continuous functions (abstract). In Vasco Brattka, Matthias Schröder, Klaus Weihrauch, and Ning Zhong, editors, Computability and Complexity in Analysis, volume 302 of Informatik Berichte, page 13. FernUniversität in Hagen, August 2003. International Conference, CCA 2003, Cincinnati, USA, August 28-30, 2003.

• Peter Hertling. A Banach-Mazur computable but not Markov computable function on the computable real numbers. Annals of Pure and Applied Logic, 132(2-3):227-246, 2005.

• Peter Hertling. Is the Mandelbrot set computable? Mathematical Logic Quarterly, 51(1):5-18, 2005.

• Peter Hertling. A sequentially computable function that is not effectively continuous at any point. Journal of Complexity, 22(6):752-767, 2006.

• Eiju Hirowatari and Setsuo Arikawa. A comparison of identification criteria for inductive inference of recursive real-valued functions. Theoretical Computer Science, 268:351-366, 2001.

• John M. Hitchcock and Jack H. Lutz. Why computational complexity requires stricter martingales. 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 549-560, Berlin, 2002. Springer. 29th International Colloquium, ICALP, Málaga, Spain, July 8-13, 2002.

• John M. Hitchcock. Correspondence principles for effective dimensions. 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 561-572, Berlin, 2002. Springer. 29th International Colloquium, ICALP, Málaga, Spain, July 8-13, 2002.

• Chun-Kuen Ho. Beyond recursive real functions. Technical Report 1994-06, University of Chicago, Department of Computer Science, 1994.

• Chun-Kuen Ho. Relatively recursive reals and real functions. Technical Report 1994-02, University of Chicago, Department of Computer Science, 1994.

• Chun-Kuen Ho. Beyond recursive real functions. Information and Computation, 124(2):113-126, 1996.

• Chun-Kuen Ho. Relatively recursive reals and real functions. Theoretical Computer Science, 210(1):99-120, 1999.

• Mark L. Hogarth. Predictability, Computability, and Spacetime. Phd thesis, University of Cambridge, UK, 2000.

• H. James Hoover. Feasible Constructive Analysis. Ph.d. dissertation, Dept. of Computer Science, University of Toronto, Toronto, Canada, 1987.

• H. James Hoover. Why integration is hard. In Erich Kaltofen and Stephen M. Watt, editors, Computers and mathematics, pages 172-181. Springer, 1989. Conference held at the Massachusetts Institute of Technology, Cambridge, Massachusetts, June 13-17, 1989.

• H. James Hoover. Feasible real functions and arithmetic circuits. SIAM Journal on Computing, 19(1):182-204, 1990.

• H. James Hoover. Real functions, contraction mappings, and P-completeness. Information and Computation, 93(2):333-349, 1991.

• H. James Hoover. Computational models for feasible real analysis. In Samuel R. Buss and Philip J. Scott, editors, Feasible mathematics, volume 9 of Progress in Computer Science and Applied Logic, pages 221-237. Birkhäuser, 1993. Proceedings of the workshop held at Cornell University, Ithaca, New York, June 26-28, 1989.

• Tie Hou. Coinductive proofs for basic real computation. 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 221-230, Berlin, 2006. Springer. Second Conference on Computability in Europe, CiE 2006, Swansea, UK, June 30-July 5, 2006.

• Mathieu Hoyrup, Arda Kolçak, and Giuseppe Longo. Computability and the morphological complexity of some dynamics on continuous domains. Theoretical Computer Science, 398:170-182, 2008.

• L. Hudes. Hyperarithmetical real numbers and hyperarithmetical analysis. Ph.d. dissertation, Massachusetts Institute of Technology, Cambridge, Mass., 1962.

• Jesse Hughes and Milad Niqui. Admissible digit sets. Theoretical Computer Science, 351(1):61-73, 2006.

• Namhyun Hur and James H. Davenport. A generic root operation for exact real arithmetic. In Jens Blanck, Vasco Brattka, and Peter Hertling, editors, Computability and Complexity in Analysis, volume 2064 of Lecture Notes in Computer Science, pages 82-87, Berlin, 2001. Springer. 4th International Workshop, CCA 2000, Swansea, UK, September 2000.

• Shinji Iizuka. Effective continuities on effective topological spaces. Journal of Complexity, 22(6):894-908, 2006.

• Dieter Ilse. Zur Stetigkeit berechenbarer reeller Funktionen. Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, 11:297-342, 1965.

• Wei Jiang, Yuan Wang, and Jeffery Zucker. Universality and semicomputability for nondeterministic programming languages over abstract algebras. The Journal of Logic and Algebraic Programming, 71(1):44-78, 2007.

• I. Kalantari and A. Leggett. Simplicity in effective topology. The Journal of Symbolic Logic, 47:169-183, 1982.

• I. Kalantari and A. Leggett. Maximality in effective topology. The Journal of Symbolic Logic, 48:100-112, 1983.

• I. Kalantari and J.B. Remmel. Degrees of recursively enumerable topological spaces. The Journal of Symbolic Logic, 48:610-622, 1983.

• I. Kalantari and A. Retzlaff. Recursive constructions in topological spaces. The Journal of Symbolic Logic, 44:609-625, 1979.

• I. Kalantari and G. Weitkamp. Effective topological spaces, I. A definability theory. Annals of Pure and Applied Logic, 29:1-27, 1985.

• I. Kalantari and G. Weitkamp. Effective topological spaces, II. A hierarchy. Annals of Pure and Applied Logic, 29:207-224, 1985.

• I. Kalantari and G. Weitkamp. Effective topological spaces, III. forcing and definability. Annals of Pure and Applied Logic, 36:17-27, 1985.

• Iraj Kalantari and Lawrence Welch. Point-free topological spaces, functions and recursive points; filter foundation for recursive analysis. I. Annals of Pure and Applied Logic, 93(1-3):125-151, 1998.

• Iraj Kalantari and Lawrence Welch. Recursive and nonextendible functions over the reals; filter foundation for recursive analysis, II. Annals of Pure and Applied Logic, 98(1-3):87-110, 1999.

• Iraj Kalantari and Lawrence Welch. Recursive quantum functions, avoidable points, & shadow points in recursive analysis. 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.

• Iraj Kalantari and Larry Welch. A blend of methods of recursion theory and topology. Annals of Pure and Applied Logic, 124(1-3):141-178, 2003.

• Iraj Kalantari and Larry Welch. Density and Baire category in recursive topology. Mathematical Logic Quarterly, 50(4,5):381-391, 2004.

• Iraj Kalantari and Larry Welch. On degree-preserving homeomorphisms between trees in computable topology. Archive for Mathematical Logic, 46(7-8):679–--693, 2008.

• Iraj Kalantari. Major subsets in effective topology. In G. Metakides, editor, Patras Logic Symposion, Studies in Logic and the Foundations of Mathematics, pages 77-94, Amsterdam, 1982. North-Holland. Proc. Logic Sympos. Patras, Greece, Aug. 18-22, 1980.

• Iraj Kalantari. Density & Baire category in recursive topology. In Vasco Brattka, Matthias Schröder, Klaus Weihrauch, and Ning Zhong, editors, Computability and Complexity in Analysis, volume 302 of Informatik Berichte, pages 15-18. FernUniversität in Hagen, August 2003. International Conference, CCA 2003, Cincinnati, USA, August 28-30, 2003.

• Hiroyasu Kamo and Kiko Kawamura. Computability of self-similar sets. Mathematical Logic Quarterly, 45:23-30, 1999.

• Hiroyasu Kamo, Kiko Kawamura, and Izumi Takeuti. Hausdorff dimension and computational complexity. In Ker-I Ko, Anil Nerode, Marian B. Pour-El, Klaus Weihrauch, and Jirí Wiedermann, editors, Computability and Complexity in Analysis, volume 235 of Informatik Berichte, pages 41-50. FernUniversität Hagen, August 1998. CCA Workshop, Brno, Czech Republic, August, 1998.

• Hiroyasu Kamo, Kiko Kawamura, and Izumi Takeuti. Computational complexity of fractal sets. Real Analysis Exchange, 26(2):773-793, 2000/01.

• Hiroyasu Kamo. Effective contraction theorem and its application. In Jens Blanck, Vasco Brattka, and Peter Hertling, editors, Computability and Complexity in Analysis, volume 2064 of Lecture Notes in Computer Science, pages 88-100, Berlin, 2001. Springer. 4th International Workshop, CCA 2000, Swansea, UK, September 2000.

• Hiroyasu Kamo. Computability and computable uniqueness of Urysohn's universal metric space. In Tanja Grubba, Peter Hertling, Hideki Tsuiki, and Klaus Weihrauch, editors, Computability and Complexity in Analysis, volume 326 of Informatik Berichte, pages 149-159. FernUniversität in Hagen, July 2005. Proccedings, Second International Conference, CCA 2005, Kyoto, Japan, August 25-29, 2005.

• Hiroyasu Kamo. Effective Dini's theorem on effectively compact metric spaces. 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 73-82, Amsterdam, 2005. Elsevier. 6th International Workshop, CCA 2004, Wittenberg, Germany, August 16-20, 2004.

• George Kapoulas. Computable p-adic numbers. CDMTCS Research Report Series 115, University of Auckland, Auckland, November 1999.

• George Kapoulas. Polynomially time computable functions over p-adic fields. In Jens Blanck, Vasco Brattka, and Peter Hertling, editors, Computability and Complexity in Analysis, volume 2064 of Lecture Notes in Computer Science, pages 101-118, Berlin, 2001. Springer. 4th International Workshop, CCA 2000, Swansea, UK, September 2000.

• Bruce M. Kapron. Feasibly continuous type-two functionals. C