Publications

2024

• Brattka, Vasco and Smischliaew, Hendrik, Computability of Initial Value Problems, arXiv arXiv:2501.00451 (2024)

2023

• Brattka, Vasco, On the complexity of learning programs, in: Della Vedova, Gianluca and Dundua, Besik and Lempp, Steffen and Manea, Florin (eds.), Unity of Logic and Computation, vol. 13967 of Lecture Notes in Computer Science, Springer, Cham, 2023, pages 166-177
• Brattka, Vasco, The Discontinuity Problem, Journal of Symbolic Logic 88:3 (2023) 1191-1212
• Brattka, Vasco, On the complexity of computing Gödel numbers, arXiv 2302.04213 (2023)

2022

• Brattka, Vasco and Greenberg, Noam and Kalimullin, Iskander and Soskova, Mariya (eds.), Special issue: Oberwolfach Workshop on Computability Theory 2021, vol. 11 of Computability - The Journal of the Association CiE, IOS Press, 2022
• Brattka, Vasco, Weihrauch complexity and the Hagen school of computable analysis, in: Löwe, Benedikt and Sarikaya, Deniz (eds.), 60 Jahre DVMLG, vol. 48 of Tributes, College Publications, London, 2022, pages 13-44

2021

• Brattka, Vasco and Hertling, Peter (eds.), Handbook of Computability and Complexity in Analysis, Theory and Applications of Computability, Springer, Cham, 2021
• Brattka, Vasco, Stashing-Parallelization Pentagons, Logical Methods in Computer Science 17:4 (2021) 20:1-20:29
• Brattka, Vasco, Stashing-Parallelization Pentagons, arXiv 2102.11832 (2021)
• Brattka, Vasco and Gherardi, Guido, Completion of Choice, Annals of Pure and Applied Logic 172:3 (2021) 102914
• Brattka, Vasco and Gherardi, Guido and Pauly, Arno, Weihrauch Complexity in Computable Analysis, in: Brattka, Vasco and Hertling, Peter (eds.), Handbook of Computability and Complexity in Analysis, Theory and Applications of Computability, Springer, Cham, 2021, pages 367-417
• Brattka, Vasco and Greenberg, Noam and Kalimullin, Iskander and Soskova, Mariya, Computability theory, Oberwolfach Reports 18:2 (2021) 1149-1190

2020

• Brattka, Vasco and Dzhafarov, Damir and Marcone, Alberto and Pauly, Arno (eds.), Special issue: Dagstuhl Seminar on Measuring the Complexity of Computational Content 2018, vol. 9 of Computability - The Journal of the Association CiE, IOS Press, 2020
• Brattka, Vasco, The Discontinuity Problem, arXiv 2012.02143 (2020)
• Brattka, Vasco and Gherardi, Guido, Weihrauch Goes Brouwerian, The Journal of Symbolic Logic 85:4 (2020) 1614-1653

2019

• Brattka, Vasco and Downey, Rod G. and Knight, Julia F. and Lempp, Steffen (eds.), Special issue: Oberwolfach Workshop on Computability Theory 2018, vol. 8 of Computability - The Journal of the Association CiE, IOS Press, 2019
• Brattka, Vasco and Dzhafarov, Damir D. and Marcone, Alberto and Pauly, Arno (eds.), Measuring the Complexity of Computational Content: From Combinatorial Problems to Analysis (Dagstuhl Seminar 18361), vol. 8 of Dagstuhl Reports, Schloss Dagstuhl-Leibniz-Zentrum für Informatik, Dagstuhl, Germany, 2019
• Brattka, Vasco and Gherardi, Guido, Completion of Choice, arXiv 1910.13186 (2019)
• Brattka, Vasco and Le Roux, Stéphane and Miller, Joseph S. and Pauly, Arno, Connected Choice and the Brouwer Fixed Point Theorem, Journal of Mathematical Logic 19:1 (2019) 1-46

2018

• Brattka, Vasco, A Galois connection between Turing jumps and limits, Logical Methods in Computer Science 14:3:13 (2018) 1-37
• Brattka, Vasco, A Galois connection between Turing jumps and limits, arXiv 1802.01355 (2018)
• Brattka, Vasco and Downey, Rod and Knight, Julia F. and Lempp, Steffen, Computability theory, Oberwolfach Reports 15:1 (2018) 5-41
• Brattka, Vasco and Gherardi, Guido, Weihrauch Goes Brouwerian, arXiv 1809.00380 (2018)
• Brattka, Vasco and Hendtlass, Matthew and Kreuzer, Alexander P., On the Uniform Computational Content of the Baire Category Theorem, Notre Dame Journal of Formal Logic 59:4 (2018) 605-636
• Brattka, Vasco and Pauly, Arno, On the Algebraic Structure of Weihrauch Degrees, Logical Methods in Computer Science 14:4:4 (2018) 1-36

2017

• Brattka, Vasco and Cettolo, Andrea and Gherardi, Guido and Marcone, Alberto and Schröder, Matthias, Addendum to: "The Bolzano-Weierstrass Theorem is the Jump of Weak Kőnig's Lemma", Annals of Pure and Applied Logic 168:8 (2017) 1605-1608
• Brattka, Vasco and Cettolo, Andrea and Gherardi, Guido and Marcone, Alberto and Schröder, Matthias, Addendum to: "The Bolzano-Weierstrass Theorem is the Jump of Weak Kőnig's Lemma", arXiv 1101.0792 (2017)
• Brattka, Vasco and Gherardi, Guido and Hölzl, Rupert and Pauly, Arno, The Vitali Covering Theorem in the Weihrauch Lattice, in: Day, Adam and Fellows, Michael and Greenberg, Noam and Khoussainov, Bakhadyr and Melnikov, Alexander and Rosamond, Frances (eds.), Computability and Complexity: Essays Dedicated to Rodney G. Downey on the Occasion of His 60th Birthday, vol. 10010 of Lecture Notes in Computer Science, Springer, Cham, 2017, pages 188-200
• Brattka, Vasco and Gherardi, Guido and Pauly, Arno, Weihrauch Complexity in Computable Analysis, arXiv 1707.03202 (2017)
• Brattka, Vasco and Hendtlass, Matthew and Kreuzer, Alexander P., On the Uniform Computational Content of Computability Theory, Theory of Computing Systems 61:4 (2017) 1376-1426
• Brattka, Vasco and Hölzl, Rupert and Kuyper, Rutger, Monte Carlo Computability, in: Vollmer, Heribert and Vallée, Brigitte (eds.), 34th Symposium on Theoretical Aspects of Computer Science (STACS 2017), vol. 66 of Leibniz International Proceedings in Informatics (LIPIcs), Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik, Dagstuhl, Germany, 2017, pages 17:1-17:14
• Brattka, Vasco and Rakotoniaina, Tahina, On the Uniform Computational Content of Ramsey's Theorem, Journal of Symbolic Logic 82:4 (2017) 1278-1316

2016

• Brattka, Vasco and Kawamura, Akitoshi and Marcone, Alberto and Pauly, Arno (eds.), Measuring the Complexity of Computational Content: Weihrauch Reducibility and Reverse Analysis (Dagstuhl Seminar 15392), vol. 5 of Dagstuhl Reports, Schloss Dagstuhl-Leibniz-Zentrum für Informatik, Dagstuhl, Germany, 2016
• Brattka, Vasco, Computability and Analysis, a Historical Approach, in: Beckmann, Arnold and Bienvenu, Laurent and Jonoska, Nataša (eds.), Pursuit of the Universal, vol. 9709 of Lecture Notes in Computer Science, Springer, Switzerland, 2016, pages 45-57
• Brattka, Vasco, Computability and Analysis, a Historical Approach, arXiv 1602.07509 (2016)
• Brattka, Vasco and Gherardi, Guido and Hölzl, Rupert and Pauly, Arno, The Vitali Covering Theorem in the Weihrauch Lattice, arXiv 1605.03354 (2016)
• Brattka, Vasco and Le Roux, Stéphane and Miller, Joseph S. and Pauly, Arno, The Brouwer Fixed Point Theorem Revisited, in: Beckmann, Arnold and Bienvenu, Laurent and Jonoska, Nataša (eds.), Pursuit of the Universal, vol. 9709 of Lecture Notes in Computer Science, Springer, Switzerland, 2016, pages 58-67
• Brattka, Vasco and Le Roux, Stéphane and Miller, Joseph S. and Pauly, Arno, Connected Choice and the Brouwer Fixed Point Theorem, arXiv 1206.4809 (2016)
• Brattka, Vasco and Miller, Joseph S. and Nies, André, Randomness and Differentiability, Transactions of the American Mathematical Society 368:1 (2016) 581-605
• Brattka, Vasco and Pauly, Arno, On the Algebraic Structure of Weihrauch Degrees, arXiv 1604.08348 (2016)

2015

• Berger, Ulrich and Brattka, Vasco and Selivanov, Victor and Spreen, Dieter and Tsuiki, Hideki (eds.), Computing with Infinite Data: Topological and Logical Foundations Part 1, vol. 25 of Mathematical Structures in Computer Science, Cambridge University Press, Cambridge, 2015
• Berger, Ulrich and Brattka, Vasco and Selivanov, Victor and Spreen, Dieter and Tsuiki, Hideki (eds.), Computing with Infinite Data: Topological and Logical Foundations Part 2, vol. 25 of Mathematical Structures in Computer Science, Cambridge University Press, Cambridge, 2015
• Brattka, Vasco and Gherardi, Guido and Hölzl, Rupert, Las Vegas Computability and Algorithmic Randomness, in: Mayr, Ernst W. and Ollinger, Nicolas (eds.), 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015), vol. 30 of Leibniz International Proceedings in Informatics (LIPIcs), Schloss Dagstuhl-Leibniz-Zentrum für Informatik, Dagstuhl, Germany, 2015, pages 130-142
• Brattka, Vasco and Gherardi, Guido and Hölzl, Rupert, Probabilistic Computability and Choice, Information and Computation 242 (2015) 249-286
• Brattka, Vasco and Hendtlass, Matthew and Kreuzer, Alexander P., On the Uniform Computational Content of Computability Theory, arXiv 1501.00433 (2015)
• Brattka, Vasco and Hendtlass, Matthew and Kreuzer, Alexander P., On the Uniform Computational Content of the Baire Category Theorem, arXiv 1510.01913 (2015)
• Brattka, Vasco and Rakotoniaina, Tahina, On the Uniform Computational Content of Ramsey's Theorem, arXiv 1508.00471 (2015)

2014

• Brattka, Vasco and Diener, Hannes and Spreen, Dieter (eds.), Logic, Computation, Hierarchies, vol. 4 of Ontos Mathematical Logic, Walter de Gruyter, Boston, 2014
• Avigad, Jeremy and Brattka, Vasco, Computability and analysis: the legacy of Alan Turing, in: Downey, Rod (ed.), Turing's Legacy: Developments from Turing's Ideas in Logic, vol. 42 of Lecture Notes in Logic, Cambridge University Press, Cambridge, UK, 2014, pages 1-47

2013

• Archibald, Margaret and Brattka, Vasco and Escardó, Martín and Hertling, Peter (eds.), Special Issue for the Conference Computability and Complexity in Analysis (CCA 2011), Cape Town, South Africa, January 31-February 4, 2011, Logical Methods in Computer Science, 2013
• Bonizzoni, Paola and Brattka, Vasco and Löwe, Benedikt (eds.), The Nature of Computation: Logic, Algorithms, Applications, 9th Conference on Computability in Europe, CiE 2013, Milan, Italy, July 1-5, 2013, Proceedings, vol. 7921 of Lecture Notes in Computer Science, Springer, Berlin, 2013
• Brattka, Vasco and Gherardi, Guido and Hölzl, Rupert, Probabilistic Computability and Choice, arXiv 1312.7305 (2013)

2012

• Berger, Ulrich and Brattka, Vasco and Morozov, Andrei S. and Spreen, Dieter (eds.), Continuity, Computability, Constructivity: From Logic to Algorithms, vol. 163 of Annals of Pure and Applied Logic, Elsevier, Amsterdam, 2012
• Avigad, Jeremy and Brattka, Vasco, Computability and analysis: the legacy of Alan Turing, arXiv 1206.3431 (2012)
• Avigad, Jeremy and Brattka, Vasco, Computability and analysis: the legacy of Alan Turing, technical report, Isaac Newton Institute for Mathematical Sciences, Cambridge, UK, 2012
• Brattka, Vasco and de Brecht, Matthew and Pauly, Arno, Closed Choice and a Uniform Low Basis Theorem, Annals of Pure and Applied Logic 163 (2012) 986-1008
• Brattka, Vasco and Gherardi, Guido and Marcone, Alberto, The Bolzano-Weierstrass Theorem is the Jump of Weak Kőnig's Lemma, Annals of Pure and Applied Logic 163 (2012) 623-655
• Brattka, Vasco and Le Roux, Stéphane and Pauly, Arno, On the Computational Content of the Brouwer Fixed Point Theorem, in: Cooper, S. Barry and Dawar, Anuj and Löwe, Benedikt (eds.), How the World Computes, vol. 7318 of Lecture Notes in Computer Science, Springer, Berlin, 2012, pages 57-67
• Brattka, Vasco and Le Roux, Stéphane and Pauly, Arno, Connected Choice and the Brouwer Fixed Point Theorem, arXiv 1206.4809 (2012)
• Brattka, Vasco and Le Roux, Stéphane and Pauly, Arno, Connected Choice and the Brouwer Fixed Point Theorem, technical report, Isaac Newton Institute for Mathematical Sciences, Cambridge, UK, 2012

2011

• Brattka, Vasco and Gherardi, Guido, Weihrauch Degrees, Omniscience Principles and Weak Computability, The Journal of Symbolic Logic 76:1 (2011) 143-176
• Brattka, Vasco and Gherardi, Guido, Effective Choice and Boundedness Principles in Computable Analysis, The Bulletin of Symbolic Logic 17:1 (2011) 73-117
• Brattka, Vasco and Gherardi, Guido and Marcone, Alberto, The Bolzano-Weierstrass Theorem is the Jump of Weak Kőnig's Lemma, arXiv 1101.0792 (2011)
• Brattka, Vasco and Miller, Joseph S. and Nies, André, Randomness and Differentiability, arXiv 1104.4465 (2011)

2010

• Brattka, Vasco and de Brecht, Matthew and Pauly, Arno, Closed Choice and a Uniform Low Basis Theorem, arXiv 1002.2800 (2010)
• Brattka, Vasco and Dillhage, Ruth, Computability of finite-dimensional linear subspaces and best approximation, Annals of Pure and Applied Logic 162 (2010) 182-193
• Brattka, Vasco and Pauly, Arno, Computation with Advice, in: Zheng, Xizhong and Zhong, Ning (eds.), CCA 2010, Proceedings of the Seventh International Conference on Computability and Complexity in Analysis, vol. 24 of Electronic Proceedings in Theoretical Computer Science, 2010, pages 41-55

2009

• Archibald, Margaret and Brattka, Vasco and Goranko, Valentin and Löwe, Benedikt (eds.), Infinity in Logic and Computation, Selected Papers of the International Conference ILC 2007 held in Cape Town, South Africa, November 2007, vol. 5489 of Lecture Notes in Artificial Intelligence, Springer, Berlin, 2009
• Brattka, Vasco and Collins, Pieter and Rettinger, Robert (eds.), Computability and Complexity in Analysis, Selected Papers of the Fifth International Conference on Computability and Complexity in Analysis, August 21-24, 2008, Hagen, Germany, vol. 15 of Journal of Universal Computer Science, Graz University of Technology, Graz, 2009
• Brattka, Vasco, A computable version of Banach's Inverse Mapping Theorem, Annals of Pure and Applied Logic 157 (2009) 85-96
• Brattka, Vasco and Gherardi, Guido, Weihrauch Degrees, Omniscience Principles and Weak Computability, in: Bauer, Andrej and Hertling, Peter and Ko, Ker-I (eds.), CCA 2009, Proceedings of the Sixth International Conference on Computability and Complexity in Analysis, Leibniz-Zentrum für Informatik, Schloss Dagstuhl, Germany, 2009, pages 83-94
• Brattka, Vasco and Gherardi, Guido, Effective Choice and Boundedness Principles in Computable Analysis, in: Bauer, Andrej and Hertling, Peter and Ko, Ker-I (eds.), CCA 2009, Proceedings of the Sixth International Conference on Computability and Complexity in Analysis, Leibniz-Zentrum für Informatik, Schloss Dagstuhl, Germany, 2009, pages 95-106
• Brattka, Vasco and Gherardi, Guido, Borel Complexity of Topological Operations on Computable Metric Spaces, Journal of Logic and Computation 19:1 (2009) 45-76
• Brattka, Vasco and Gherardi, Guido, Effective Choice and Boundedness Principles in Computable Analysis, arXiv 0905.4685 (2009)
• Brattka, Vasco and Gherardi, Guido, Weihrauch Degrees, Omniscience Principles and Weak Computability, arXiv 0905.4679 (2009)

2008

• Brattka, Vasco and Dillhage, Ruth and Grubba, Tanja and Klutsch, Angela (eds.), Proceedings of the Fifth International Conference on Computability and Complexity in Analysis, CCA 2008, Hagen, Germany, August 21-24, 2008, vol. 221 of Electronic Notes in Theoretical Computer Science, Elsevier, Amsterdam, 2008
• Brattka, Vasco and Ishihara, Hajime and Schröder, Matthias and Zhong, Ning (eds.), Computability and Complexity in Analysis, Selected Papers of the Fourth International Conference on Computability and Complexity in Analysis, June 16-18, 2007, Siena, Italy, vol. 14 of Journal of Universal Computer Science, Graz University of Technology, Graz, 2008
• Brattka, Vasco and Ishihara, Hajime and Schröder, Matthias and Zhong, Ning (eds.), Computability and Complexity in Analysis, Selected Papers of the Fourth International Conference on Computability and Complexity in Analysis, June 16-18, 2007, Siena, Italy, vol. 54 of Mathematical Logic Quarterly, Wiley-VCH, Weinheim, 2008
• Brattka, Vasco and Jäger, Gerhard and Künzi, Hans-Peter (eds.), Logic and Information, From Logic to Constructive Reasoning, Selected Papers of the Swiss-South-African joint seminar, University of Bern, Switzerland, January 22-25, 2007, vol. 76 of The Journal of Logic and Algebraic Programming, Elsevier, Amsterdam, 2008
• Archibald, Margaret and Brattka, Vasco and Heuberger, Clemens, Randomness with respect to the Signed-Digit Representation, Fundamenta Informaticae 83:1-2 (2008) 1-19
• Brattka, Vasco, Plottable real number functions and the computable graph theorem, SIAM Journal on Computing 38:1 (2008) 303-328
• Brattka, Vasco, Borel Complexity and Computability of the Hahn-Banach Theorem, Archive for Mathematical Logic 46:7-8 (2008) 547-564
• Brattka, Vasco and Hertling, Peter and Weihrauch, Klaus, A Tutorial on Computable Analysis, in: Cooper, S. Barry and Löwe, Benedikt and Sorbi, Andrea (eds.), New Computational Paradigms: Changing Conceptions of What Is Computable, Springer, New York, 2008, pages 425-491
• Dillhage, Ruth and Brattka, Vasco, Computability of the Metric Projection Onto Finite-dimensional Linear Subspaces, in: Brattka, Vasco and Dillhage, Ruth and Grubba, Tanja and Klutsch, Angela (eds.), CCA 2008, Fifth International Conference on Computability and Complexity in Analysis, vol. 221 of Electronic Notes in Theoretical Computer Science, Elsevier, 2008, pages 45-60

2007

• Brattka, Vasco and Frougny, Christiane and Müller, Norbert (eds.), Real Numbers, Selected Papers of the 6th conference on Real Numbers and Computers, Dagstuhl, Germany, November 15-17, 2004, vol. 41 of Theoretical Informatics and Applications, EDP Sciences, Les Ulis, 2007
• Archibald, Margaret and Brattka, Vasco and Heuberger, Clemens, Randomness with respect to the Signed-Digit Representation, technical report, Institut für Optimierung und Diskrete Mathematik, TU Graz, Graz, 2007
• Brattka, Vasco, From Hilbert's 13th Problem to the theory of neural networks: constructive aspects of Kolmogorov's Superposition Theorem, in: Charpentier, Éric and Lesne, Annick and Nikolski, Nikolaï (eds.), Kolmogorov's Heritage in Mathematics, Springer, Berlin, 2007, pages 253-280
• Brattka, Vasco and Dillhage, Ruth, On Computable Compact Operators on Banach Spaces, in: Cenzer, Douglas and Dillhage, Ruth and Grubba, Tanja and Weihrauch, Klaus (eds.), Proceedings of the Third International Conference on Computability and Complexity in Analysis, vol. 167 of Electronic Notes in Theoretical Computer Science, Elsevier, Amsterdam, 2007, pages 365-386
• Brattka, Vasco and Dillhage, Ruth, On Computable Compact Operators on Computable Banach Spaces with Bases, Mathematical Logic Quarterly 53:4-5 (2007) 345-364
• Brattka, Vasco and Gherardi, Guido, Borel Complexity of Topological Operations on Computable Metric Spaces, in: Cooper, S. Barry and Löwe, Benedikt and Sorbi, Andrea (eds.), Computation and Logic in the Real World, vol. 4497 of Lecture Notes in Computer Science, Springer, Berlin, 2007, pages 83-97

2006

• Brattka, Vasco and Hertling, Peter and Ko, Ker-I and Tsuiki, Hideki (eds.), Computability and Complexity in Analysis, Selected Papers of the International Conference CCA 2005, held in Kyoto, Japan, August 25-29, 2005, vol. 522 of Journal of Complexity, Elsevier, Amsterdam, 2006
• Brattka, Vasco, Computable Versions of the Uniform Boundedness Theorem, in: Chatzidakis, Z. and Koepke, P. and Pohlers, W. (eds.), Logic Colloquium 2002, vol. 27 of Lecture Notes in Logic, Association for Symbolic Logic, Urbana, 2006, pages 130-151
• Brattka, Vasco and Dillhage, Ruth, On computable compact operators on Banach spaces, in: Cenzer, Douglas and Dillhage, Ruth and Grubba, Tanja and Weihrauch, Klaus (eds.), CCA 2006, Third International Conference on Computability and Complexity in Analysis, vol. 333 of Informatik Berichte, FernUniversität in Hagen, 2006, pages 49-66
• Brattka, Vasco and Yoshikawa, Atsushi, Towards computability of elliptic boundary value problems in variational formulation, Journal of Complexity 22:6 (2006) 858-880

2005

• Brattka, Vasco and Staiger, Ludwig and Weihrauch, Klaus (eds.), Proceedings of the 6th Workshop on Computability and Complexity in Analysis, 6th International Workshop, CCA 2004, Wittenberg, Germany, August 16-20, 2004, vol. 120 of Electronic Notes in Theoretical Computer Science, Elsevier, Amsterdam, 2005
• Brattka, Vasco, On the Borel Complexity of Hahn-Banach Extensions, in: Brattka, Vasco and Staiger, Ludwig and Weihrauch, Klaus (eds.), Proceedings of the 6th Workshop on Computability and Complexity in Analysis, vol. 120 of Electronic Notes in Theoretical Computer Science, Elsevier, Amsterdam, 2005, pages 3-16
• Brattka, Vasco, Computability on Non-Separable Banach Spaces and Landau's Theorem, in: Crosilla, Laura and Schuster, Peter (eds.), From Sets and Types to Topology and Analysis: Towards Practicable Foundations for Constructive Mathematics, Oxford University Press, 2005, pages 316-333
• Brattka, Vasco, Some aspects of computable functional analysis (abstract), in: Grubba, Tanja and Hertling, Peter and Tsuiki, Hideki and Weihrauch, Klaus (eds.), Computability and Complexity in Analysis, vol. 326 of Informatik Berichte, FernUniversität in Hagen, 2005, page vii
• Brattka, Vasco, Effective Borel measurability and reducibility of functions, Mathematical Logic Quarterly 51:1 (2005) 19-44
• Brattka, Vasco and Dillhage, Ruth, Computability of the Spectrum of Self-Adjoint Operators, Journal of Universal Computer Science 11:12 (2005) 1884-1900
• Brattka, Vasco and Schröder, Matthias, Computing with Sequences, Weak Topologies and the Axiom of Choice, in: Ong, Luke (ed.), Computer science logic, vol. 3634 of Lecture Notes in Computer Science, Springer, 2005, pages 462-476

2004

• Brattka, Vasco and Hertling, Peter and Ko, Ker-I and Zhong, Ning (eds.), Special Issue Computability and Complexity in Analysis, Selected Papers of the International Conference CCA 2003, held in Cincinnati, Ohio, August 28-30, 2003, vol. 50 of Mathematical Logic Quarterly, Wiley-VCH, Weinheim, 2004
• Brattka, Vasco, On the Borel Complexity of Hahn-Banach Extensions, in: Brattka, Vasco and Staiger, Ludwig and Weihrauch, Klaus (eds.), Computability and Complexity in Analysis, vol. 320 of Informatik Berichte, FernUniversität in Hagen, 2004, pages 1-13
• Brattka, Vasco, Du 13-ième problème de Hilbert à la théorie des réseaux de neurones : aspects constructifs du théorème de superposition de Kolmogorov, in: Charpentier, Éric and Lesne, Annick and Nikolski, Nikolaï (eds.), L'héritage de Kolmogorov en mathématiques, Éditions Belin, Paris, 2004, pages 241-268
• Brattka, Vasco and Staiger, Ludwig and Weihrauch, Klaus, Computability and Complexity in Analysis, technical report, FernUniversität Hagen, Hagen, 2004
• Frougny, Christiane and Brattka, Vasco and Müller, Norbert, RNC'6, 6th Conference on Real Numbers and Computers, technical report, Fachbereich Mathematik/Informatik, Unversität Trier, Trier, 2004
• Ziegler, Martin and Brattka, Vasco, Computability in Linear Algebra, Theoretical Computer Science 326:1-3 (2004) 187-211

2003

• Brattka, Vasco, The Inversion Problem for Computable Linear Operators, in: Alt, Helmut and Habib, Michel (eds.), STACS 2003, vol. 2607 of Lecture Notes in Computer Science, Springer, Berlin, 2003, pages 391-402
• Brattka, Vasco, Effective Borel measurability and reducibility of functions, in: Brattka, Vasco and Schröder, Matthias and Weihrauch, Klaus and Zhong, Ning (eds.), Computability and Complexity in Analysis, vol. 302 of Informatik Berichte, FernUniversität in Hagen, 2003, pages 117-152
• Brattka, Vasco, Computability over Topological Structures, in: Cooper, S. Barry and Goncharov, Sergey S. (eds.), Computability and Models, Kluwer Academic Publishers, New York, 2003, pages 93-136
• Brattka, Vasco, Plottable real number functions, in: Daumas, Marc and et al. (eds.), RNC'5 Real Numbers and Computers, 2003, pages 13-30
• Brattka, Vasco, The Emperor's New Recursiveness: The Epigraph of the Exponential Function in Two Models of Computability, in: Ito, Masami and Imaoka, Teruo (eds.), Words, Languages & Combinatorics III, World Scientific Publishing, Singapore, 2003, pages 63-72
• Brattka, Vasco, Generated quasi-metric hyper and function spaces, Topology and its Applications 127 (2003) 355-373
• Brattka, Vasco, Effective Representations of the Space of Linear Bounded Operators, Applied General Topology 4:1 (2003) 115-131
• Brattka, Vasco, Plottable real number functions and the computable graph theorem, technical report, FernUniversität in Hagen, Fachbereich Informatik, Hagen, 2003
• Brattka, Vasco, Recursive Quasi-Metric Spaces, Theoretical Computer Science 305 (2003) 17-42
• Brattka, Vasco, Computability on Asymmetric Spaces, technical report, FernUniversität in Hagen, Fachbereich Informatik, Hagen, 2003
• Brattka, Vasco and Presser, Gero, Computability on subsets of metric spaces, Theoretical Computer Science 305 (2003) 43-76
• Brattka, Vasco and Schröder, Matthias and Weihrauch, Klaus and Zhong, Ning, Computability and Complexity in Analysis, technical report, FernUniversität in Hagen, Hagen, 2003

2002

• Brattka, Vasco and Hertling, Peter and Yasugi, Mariko and Zhong, Ning (eds.), Selected Papers of the Dagstuhl Seminar on Computability and Complexity in Analysis 2001, vol. 48 (Suppl. 1) of Mathematical Logic Quarterly, Wiley-VCH, Weinheim, 2002
• Brattka, Vasco and Schröder, Matthias and Weihrauch, Klaus (eds.), Computability and Complexity in Analysis, 5th International Workshop, CCA 2002, Málaga, Spain, July 12-13, 2002, vol. 66(1) of Electronic Notes in Theoretical Computer Science, Elsevier, Amsterdam, 2002
• Brattka, Vasco, Computing Uniform Bounds, in: Brattka, Vasco and Schröder, Matthias and Weihrauch, Klaus (eds.), CCA 2002 Computability and Complexity in Analysis, vol. 66 of Electronic Notes in Theoretical Computer Science, Elsevier, Amsterdam, 2002
• Brattka, Vasco, Recursion and Computability over Topological Structures (Abstract), in: Hurley, Ted and Mac an Airchinnigh, Mícheál and Schellekens, Michel and Seda, Anthony (eds.), The First Irish Conference on the Mathematical Foundations of Computer Science and Information Technology, vol. 40 of Electronic Notes in Theoretical Computer Science, Elsevier, Amsterdam, 2002
• Brattka, Vasco, Random Numbers and an Incomplete Immune Recursive Set, in: Widmayer, Peter and Triguero, Francisco and Morales, Rafael and Hennessy, Matthew and Eidenbenz, Stephan and Conejo, Ricardo (eds.), Automata, Languages and Programming, vol. 2380 of Lecture Notes in Computer Science, Springer, Berlin, 2002, pages 950-961
• Brattka, Vasco, Some notes on Fine computability, Journal of Universal Computer Science 8:3 (2002) 382-395
• Brattka, Vasco, Computability on Asymmetric Spaces, Habilitation Thesis, Department of Computer Science, University of Hagen, Hagen, Germany, 2002
• Brattka, Vasco and Hertling, Peter, Topological properties of real number representations, Theoretical Computer Science 284:2 (2002) 241-257
• Brattka, Vasco and Schröder, Matthias and Weihrauch, Klaus, Computability and Complexity in Analysis, technical report, FernUniversität Hagen, Hagen, 2002
• Brattka, Vasco and Ziegler, Martin, Computability of linear equations, in: Baeza-Yates, Ricardo and Montanari, Ugo and Santoro, Nicola (eds.), Foundations of Information Technology in the Era of Network and Mobile Computing, vol. 223 of IFIP International Federation for Information Processing, Kluwer Academic Publishers, Dordrecht, 2002, pages 95-106
• Yasugi, Mariko and Brattka, Vasco and Washihara, Masako, Computability aspects of some discontinuous functions, Scientiae Mathematicae Japonicae 55:3 (2002) 427-441
• Yasugi, Mariko and Brattka, Vasco and Washihara, Masako, Limit computation of some discontinuous functions, in: Theoretical development and feasibility of mathematical analysis on the computer, vol. 1286 of Sūrikaisekikenkyūsho Kōkyūroku, Research Institute for Mathematical Sciences, Kyoto, 2002, pages 79-84

2001

• Blanck, Jens and Brattka, Vasco and Hertling, Peter (eds.), Computability and Complexity in Analysis, 4th International Workshop, CCA 2000, Swansea, UK, September 17-19, 2000. Selected Papers, vol. 2064 of Lecture Notes in Computer Science, Springer, Berlin, 2001
• Brattka, Vasco, Computable versions of Baire's category theorem, in: Sgall, Jiří and Pultr, Aleš and Kolman, Petr (eds.), Mathematical Foundations of Computer Science 2001, vol. 2136 of Lecture Notes in Computer Science, Springer, Berlin, 2001, pages 224-235
• Brattka, Vasco, Computability of Banach Space Principles, technical report, FernUniversität Hagen, Fachbereich Informatik, Hagen, 2001
• Brattka, Vasco and Ziegler, Martin, Computability of linear equations, technical report, Universität Paderborn, Fachbereich Mathematik-Informatik, Paderborn, 2001
• Yasugi, Mariko and Brattka, Vasco and Washihara, Masako, Computability aspects of some discontinuous functions, Scientiae Mathematicae Japonicae Online 5 (2001) 405-419
• Ziegler, Martin and Brattka, Vasco, Turing Computability of (Non-)Linear Optimization, in: Therese Biedl (ed.), Thirteenth Canadian Conference on Computational Geometry, University of Waterloo, 2001, pages 181-184
• Ziegler, Martin and Brattka, Vasco, A Computable Spectral Theorem, in: Blanck, Jens and Brattka, Vasco and Hertling, Peter (eds.), Computability and Complexity in Analysis, vol. 2064 of Lecture Notes in Computer Science, Springer, Berlin, 2001, pages 378-388

2000

• Blanck, Jens and Brattka, Vasco and Hertling, Peter and Weihrauch, Klaus, Computability and Complexity in Analysis, technical report, FernUniversität Hagen, Hagen, 2000
• Brattka, Vasco, A Computable Kolmogorov Superposition Theorem, in: Blanck, Jens and Brattka, Vasco and Hertling, Peter and Weihrauch, Klaus (eds.), Computability and Complexity in Analysis, vol. 272 of Informatik Berichte, FernUniversität Hagen, 2000, pages 7-22
• Brattka, Vasco, Realistic models of computability on the real numbers, in: Yoshikawa, Atsushi (ed.), Relevance and Feasibility of Mathematical Analysis on the Computer, vol. 1169 of Sūrikaisekikenkyūsho Kōkyūroku, Research Institute for Mathematical Sciences, Kyoto, 2000, pages 62-75
• Ziegler, Martin and Brattka, Vasco, A Computable Spectral Theorem, in: Blanck, Jens and Brattka, Vasco and Hertling, Peter and Weihrauch, Klaus (eds.), Computability and Complexity in Analysis, vol. 272 of Informatik Berichte, FernUniversität Hagen, 2000, pages 469-479
• Ziegler, Martin and Brattka, Vasco, Computing the Dimension of Linear Subspaces, in: Hlaváč, Václav and Jeffery, Keith G. and Wiedermann, Jiří (eds.), SOFSEM 2000: Theory and Practice of Informatics, vol. 1963 of Lecture Notes in Computer Science, Springer, Berlin, 2000, pages 450-458

1999

• Brattka, Vasco, A Stability Theorem for Recursive Analysis, in: Cristian S. Calude and Michael J. Dinneen (eds.), Combinatorics, Computation & Logic, Discrete Mathematics and Theoretical Computer Science, Springer, Singapore, 1999, pages 144-158
• Brattka, Vasco, Computable invariance, Theoretical Computer Science 210 (1999) 3-20
• Brattka, Vasco, Recursive and Computable Operations over Topological Structures, technical report, FernUniversität Hagen, Fachbereich Informatik, Hagen, 1999
• Brattka, Vasco and Weihrauch, Klaus, Computability on Subsets of Euclidean Space I: Closed and Compact Subsets, Theoretical Computer Science 219 (1999) 65-93
• Zheng, Xizhong and Brattka, Vasco and Weihrauch, Klaus, Approaches to Effective Semi-Continuity of Real Functions, Mathematical Logic Quarterly 45:4 (1999) 481-496

1998

• Brattka, Vasco, A Stability Theorem for Recursive Analysis, in: Ko, Ker-I and Nerode, Anil and Pour-El, Marian B. and Weihrauch, Klaus and Wiedermann, Jiří (eds.), Computability and Complexity in Analysis, vol. 235 of Informatik Berichte, FernUniversität Hagen, 1998, pages 1-15
• Brattka, Vasco, Recursive and Computable Operations over Topological Structures, Ph.D. thesis, Department of Computer Science, University of Hagen, Hagen, Germany, 1998
• Brattka, Vasco and Hertling, Peter, Feasible real random access machines, Journal of Complexity 14:4 (1998) 490-526
• Brattka, Vasco and Kalantari, Iraj, A Bibliography of Recursive Analysis and Recursive Topology, in: Ershov, Yu. L. and Goncharov, S.S. and Nerode, A. and Remmel, J.B. (eds.), Handbook of Recursive Mathematics, vol. 138 of Studies in Logic and the Foundations of Mathematics, Elsevier, Amsterdam, 1998, pages 583-620
• Brattka, Vasco and Weihrauch, Klaus, Recursive and Recursively Enumerable Closed Subsets of Euclidean Space, in: Margenstern, Maurice (ed.), Actes de MCU'98, I.U.T. de Metz, 1998, pages 214-234
• Brattka, Vasco and Weihrauch, Klaus and Zheng, Xizhong, Approaches to Effective Semi-continuity of Real Functions, in: Hsu, Wen-Lian and Kao, Ming-Yang (eds.), Computing and Combinatorics, vol. 1449 of Lecture Notes in Computer Science, Springer, Berlin, 1998, pages 184-193

1997

• Brattka, Vasco, Computable Invariance, in: Jiang, Tao and Lee, D.T. (eds.), Computing and Combinatorics, vol. 1276 of Lecture Notes in Computer Science, Springer, Berlin, 1997, pages 146-155
• Brattka, Vasco, Order-free Recursion on the Real Numbers, Mathematical Logic Quarterly 43 (1997) 216-234

1996

• Brattka, Vasco, Computable Invariance, in: Ko, Ker-I and Müller, Norbert and Weihrauch, Klaus (eds.), Computability and Complexity in Analysis, Universität Trier, 1996, pages 5-22
• Brattka, Vasco, Recursive characterization of computable real-valued functions and relations, Theoretical Computer Science 162 (1996) 45-77
• Brattka, Vasco and Hertling, Peter, Feasible real random access machines, in: Allouche, Jean-Paul and Bajard, Jean-Claude and Didier, Laurent-Stephane and Liardet, Pierre (eds.), Second Real Numbers and Computer Conference, 1996, pages 139-172
• Brattka, Vasco and Hertling, Peter, Feasible real random access machines, in: Jeffrey, Keith G. and Král, Jaroslav and Bartošek, Miroslav (eds.), SOFSEM'96: Theory and Practice of Informatics, vol. 1175 of Lecture Notes in Computer Science, Springer, Berlin, 1996, pages 335-342

1995

• Brattka, Vasco, Computable selection in analysis, in: Ko, Ker-I and Weihrauch, Klaus (eds.), Computability and Complexity in Analysis, vol. 190 of Informatik Berichte, FernUniversität Hagen, 1995, pages 125-138
• Brattka, Vasco and Hertling, Peter, Feasible real random access machines, in: Ko, Ker-I and Weihrauch, Klaus (eds.), Computability and Complexity in Analysis, vol. 190 of Informatik Berichte, FernUniversität Hagen, 1995, pages 71-82
• Brattka, Vasco and Hertling, Peter, Feasible real random access machines, technical report, FernUniversität Hagen, Hagen, 1995

1994

• Brattka, Vasco and Hertling, Peter, Continuity and computability of relations, technical report, FernUniversität Hagen, Hagen, 1994