Bibliography on Weihrauch Complexity

By publication type

• Ackerman, Nathanael L. and Freer, Cameron E. and Roy, Daniel M., On computability and disintegration, Mathematical Structures in Computer Science 27:8 (2017) 1287-1314
• Amir, Djamel Eddine and Hoyrup, Mathieu, Strong computable type, Computability 12:3 (2023) 227-269
• Anglès d'Auriac, Paul-Elliot and Kihara, Takayuki, A Comparison of Various Analytic Choice Principles, The Journal of Symbolic Logic 86:4 (2021) 1452-1485
• Astor, Eric P. and Dzhafarov, Damir D. and Solomon, Reed and Suggs, Jacob, The uniform content of partial and linear orders, Annals of Pure and Applied Logic 168:6 (2017) 1153 - 1171
• Bauer, Andrej, Instance reducibility and Weihrauch degrees, Logical Methods in Computer Science 18:3 (2022) 20:1-20:18
• Bazhenov, Nikolay and Fiori-Carones, Marta and Liu, Lu and Melnikov, Alexander, Primitive recursive reverse mathematics, Annals of Pure and Applied Logic 175:1, Part A (2024) 103354
• BeMent, Zach and Hirst, Jeffry and Wallace, Asuka, Reverse mathematics and Weihrauch analysis motivated by finite complexity theory, Computability 10:4 (2021) 343-354
• Brattka, Vasco, Computable invariance, Theoretical Computer Science 210 (1999) 3-20
• Brattka, Vasco, Effective Borel measurability and reducibility of functions, Mathematical Logic Quarterly 51:1 (2005) 19-44
• Brattka, Vasco, Stashing-Parallelization Pentagons, Logical Methods in Computer Science 17:4 (2021) 20:1-20:29
• Brattka, Vasco, The Discontinuity Problem, Journal of Symbolic Logic 88:3 (2023) 1191-1212
• 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 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, Borel Complexity of Topological Operations on Computable Metric Spaces, Journal of Logic and Computation 19:1 (2009) 45-76
• 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, Weihrauch Goes Brouwerian, The Journal of Symbolic Logic 85:4 (2020) 1614-1653
• Brattka, Vasco and Gherardi, Guido, Completion of Choice, Annals of Pure and Applied Logic 172:3 (2021) 102914
• Brattka, Vasco and Gherardi, Guido and Hölzl, Rupert, Probabilistic Computability and Choice, Information and Computation 242 (2015) 249-286
• 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 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 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 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
• Brattka, Vasco and Pauly, Arno, On the Algebraic Structure of Weihrauch Degrees, Logical Methods in Computer Science 14:4:4 (2018) 1-36
• Brattka, Vasco and Rakotoniaina, Tahina, On the Uniform Computational Content of Ramsey's Theorem, Journal of Symbolic Logic 82:4 (2017) 1278-1316
• Brecht, Matthew de and Pauly, Arno and Schröder, Matthias, Overt choice, Computability 9:3-4 (2020) 169-191
• Carl, Merlin, Effectivity and reducibility with ordinal Turing machines, Computability 10:4 (2021) 289-304
• Carroy, Raphaël, A quasi-order on continuous functions, Journal of Symbolic Logic 78:2 (2013) 663-648
• Cholak, Peter A. and Dzhafarov, Damir D. and Hirschfeldt, Denis R. and Patey, Ludovic, Some results concerning the SRT^2_2 vs. COH problem, Computability 9:3-4 (2020) 193-217
• Davis, Caleb and Hirschfeldt, Denis R. and Hirst, Jeffry and Pardo, Jake and Pauly, Arno and Yokoyama, Keita, Combinatorial principles equivalent to weak induction, Computability 9:3-4 (2020) 219-229
• Day, Adam R. and Downey, Rod and Westrick, Linda, Three topological reducibilities for discontinuous functions, Transactions of the American Mathematical Society. Series B 9 (2022) 859-895
• Dorais, François G. and Dzhafarov, Damir D. and Hirst, Jeffry L. and Mileti, Joseph R. and Shafer, Paul, On uniform relationships between combinatorial problems, Transactions of the American Mathematical Society 368:2 (2016) 1321-1359
• Dzhafarov, Damir D., Cohesive avoidance and strong reductions, Proceedings of the American Mathematical Society 143:2 (2015) 869-876
• Dzhafarov, Damir D., Strong reductions between combinatorial principles, Journal of Symbolic Logic 81:4 (2016) 1405-1431
• Dzhafarov, Damir D., Joins in the strong Weihrauch degrees, Mathematical Research Letters 26:3 (2019) 749-767
• Dzhafarov, Damir D. and Goh, Jun Le and Hirschfeldt, Denis R. and Patey, Ludovic and Pauly, Arno, Ramsey's theorem and products in the Weihrauch degrees, Computability 9:2 (2020) 85-110
• Dzhafarov, Damir D. and Hirschfeldt, Denis R. and Reitzes, Sarah C., Reduction Games, Provability, and Compactness, Journal of Mathematical Logic 22:3 (2022) 2250009
• Dzhafarov, Damir D. and Patey, Ludovic, COH, SRT22, and multiple functionals, Computability 10:2 (2021) 111-121
• Dzhafarov, Damir D. and Patey, Ludovic and Solomon, Reed and Westrick, Linda Brown, Ramsey's theorem for singletons and strong computable reducibility, Proceedings of the American Mathematical Society 145 (2017)
• Eike Neumann and Arno Pauly, A topological view on algebraic computation models, Journal of Complexity 44:Supplement C (2018) 1-22
• Fiori-Carones, Marta and Marcone, Alberto, To reorient is easier than to orient: an on-line algorithm for reorientation of graphs, Computability 10:3 (2021) 215-233
• Fiori-Carones, Marta and Shafer, Paul and Soldà, Giovanni, An inside/outside Ramsey theorem and recursion theory, Transactions of the American Mathematical Society 375:3 (2022) 1977-2024
• Flood, Stephen and Jura, Matthew and Levin, Oscar and Markkanen, Tyler, The computational strength of matchings in countable graphs, Annals of Pure and Applied Logic 173:8 (2022) Paper No. 103133, 26
• Fujiwara, Makoto, Weihrauch and constructive reducibility between existence statements, Computability 10:1 (2021)
• Fujiwara, Makoto and Higuchi, Kojiro and Kihara, Takayuki, On the strength of marriage theorems and uniformity, Mathematical Logic Quarterly 60:3 (2014) 136-153
• Gherardi, Guido, Effective Borel degrees of some topological functions, Mathematical Logic Quarterly 52:6 (2006) 625-642
• Gherardi, Guido and Marcone, Alberto, How Incomputable is the Separable Hahn-Banach Theorem?, Notre Dame Journal of Formal Logic 50:4 (2009) 393-425
• Gherardi, Guido and Marcone, Alberto and Pauly, Arno, Projection operators in the Weihrauch lattice, Computability 8:3, 4 (2019) 281-304
• Goh, Jun Le, Compositions of multivalued functions, Computability 9:3-4 (2020) 231-247
• Goh, Jun Le, Embeddings between well-orderings: Computability-theoretic reductions, Annals of Pure and Applied Logic 171:6 (2020) 102789
• Goh, Jun Le and Pauly, Arno and Valenti, Manlio, Finding descending sequences through ill-founded linear orders, The Journal of Symbolic Logic 86:2 (2021) 817-854
• Greenberg, Noam and Kuyper, Rutger and Turetsky, Dan, Cardinal invariants, non-lowness classes, and Weihrauch reducibility, Computability 8:3, 4 (2019) 305-346
• Greenberg, Noam and Miller, Joseph S. and Nies, An, Highness properties close to PA completeness, Israel Journal of Mathematics 244 (2021) 419-465
• Gura, Kirill and Hirst, Jeffry L. and Mummert, Carl, On the existence of a connected component of a graph, Computability 4:2 (2015) 103-117
• Hertling, Peter, Forests describing Wadge degrees and topological Weihrauch degrees of certain classes of functions and relations, Computability 9:3-4 (2020) 249-307
• Higuchi, Kojiro and Kihara, Takayuki, Inside the Muchnik degrees I: Discontinuity, learnability and constructivism, Annals of Pure and Applied Logic 165:5 (2014) 1058-1114
• Higuchi, Kojiro and Kihara, Takayuki, Inside the Muchnik Degrees II: The degree structures induced by the arithmetical hierarchy of countably continuous functions, Annals of Pure and Applied Logic 165:6 (2014) 1201-1241
• Higuchi, Kojiro and Pauly, Arno, The degree structure of Weihrauch reducibility, Log. Methods Comput. Sci. 9:2 (2013) 2:02, 17
• Hirschfeldt, Denis R. and Jockusch, Carl G., On notions of computability-theoretic reduction between Π_2^1 principles, Journal of Mathematical Logic 16:1 (2016) 1650002, 59
• Hirst, Jeffry L., Leaf management, Computability 9:3-4 (2020) 309-314
• Hirst, Jeffry L. and Mummert, Carl, Using Ramsey's theorem once, Archive for Mathematical Logic 58:7-8 (2019) 857-866
• Hirst, Jeffry L. and Mummert, Carl, Banach’s theorem in higher-order reverse mathematics, Computability 12:3 (2023) 203-225
• Hoyrup, Mathieu, Genericity of Weakly Computable Objects, Theory of Computing Systems 60:3 (2017) 396-420
• Hoyrup, Mathieu and Rojas, Cristóbal and Weihrauch, Klaus, Computability of the Radon-Nikodym Derivative, Computability 1:1 (2012) 3-13
• Hölzl, Rupert and Shafer, Paul, Universality, optimality, and randomness deficiency, Annals of Pure and Applied Logic 166:10 (2015) 1049-1069
• Kawamura, Akitoshi, Lipschitz Continuous Ordinary Differential Equations are Polynomial-Space Complete, Computational Complexity 19:2 (2010) 305-332
• Kawamura, Akitoshi and Ota, Hiroyuki and Rösnick, Carsten and Ziegler, Martin, Computational Complexity of Smooth Differential Equations, Logical Methods in Computer Science 10 (2014) 1:6,15
• Kihara, Takayuki, Borel-piecewise continuous reducibility for uniformization problems, Logical Methods in Computer Science 12:4 (2016)
• Kihara, Takayuki, Topological reducibilities for discontinuous functions and their structures, Israel Journal of Mathematics (2022)
• Kihara, Takayuki, Lawvere-Tierney Topologies for Computability Theorists, Transactions of the American Mathematical Society, Series B 10:2 (2023) 48-85
• Kihara, Takayuki and Marcone, Alberto and Pauly, Arno, Searching for an analogue of ATR_0 in the Weihrauch lattice, Journal of Symbolic Logic 85:3 (2020) 1006-1043
• Kohlenbach, Ulrich, On the reverse mathematics and Weihrauch complexity of moduli of regularity and uniqueness, Computability 8:3, 4 (2019) 377-387
• Kreuzer, Alexander P., On the Strength of Weak Compactness, Computability 1:2 (2012) 171-179
• Kreuzer, Alexander P., From Bolzano-Weierstraß to Arzelà-Ascoli, Mathematical Logic Quarterly 60:3 (2014) 177-183
• Kreuzer, Alexander P., Bounded variation and the strength of Helly's selection theorem, Logical Methods in Computer Science 10:4:16 (2014) 1-23
• Kuyper, Rutger, On Weihrauch reducibility and intuitionistic reverse mathematics, Journal of Symbolic Logic 82:4 (2017) 1438-1458
• Le Roux, Stéphane and Pauly, Arno, Finite choice, convex choice and finding roots, Logical Methods in Computer Science 11:4 (2015) 4:6, 31
• Marcone, Alberto and Valenti, Manlio, The open and clopen Ramsey theorems in the Weihrauch lattice, The Journal of Symbolic Logic 86:1 (2021) 316-351
• Marcone, Alberto and Valenti, Manlio, Effective aspects of Hausdorff and Fourier dimension , Computability 11:3-4 (2022) 299-333
• Monin, Benoit and Patey, Ludovic, Π^0_1-encodability and omniscient reductions, Notre Dame Journal of Formal Logic 60:1 (2019) 1-12
• Neumann, Eike, Computational Problems in Metric Fixed Point Theory and their Weihrauch Degrees, Logical Methods in Computer Science 11 (2015) 4:20,44
• Nobrega, Hugo and Pauly, Arno, Game characterizations and lower cones in the Weihrauch degrees, Logical Methods in Computer Science 15:3 (2019) Paper No. 11, 29
• Patey, Ludovic, The weakness of being cohesive, thin or free in reverse mathematics, Israel Journal of Mathematics 216 (2016) 905-955
• Pauly, Arno, How Incomputable is Finding Nash Equilibria?, Journal of Universal Computer Science 16:18 (2010) 2686-2710
• Pauly, Arno, On the (semi)lattices induced by continuous reducibilities, Mathematical Logic Quarterly 56:5 (2010) 488-502
• Pauly, Arno, Many-one reductions and the category of multivalued functions, Mathematical Structures in Computer Science 27:3 (2017) 376-404
• Pauly, Arno and Fouché, Willem L., How constructive is constructing measures?, Journal of Logic & Analysis 9:c3 (2017) 1-44
• Pauly, Arno and Fouché, Willem and Davie, George, Weihrauch-completeness for layerwise computability, Logical Methods in Computer Science 14:2 (2018)
• Pauly, Arno and Steinberg, Florian, Comparing Representations for Function Spaces in Computable Analysis, Theory of Computing Systems 62 (2018) 557-582
• Porter, Michelle and Day, Adam and Downey, Rodney, Notes on computable analysis, Theory of Computing Systems 60:1 (2017) 53-111
• Selivanov, Victor, Total Representations, Logical Methods in Computer Science 9 (2013) 2:5, 30
• Selivanov, Victor, Q-Wadge degrees as free structures, Computability 9:3-4 (2020) 327-341
• Soldà, Giovanni and Valenti, Manlio, Algebraic properties of the first-order part of a problem, Annals of Pure and Applied Logic 174:7 (2023) 103270
• Tavana, Nazanin R. and Weihrauch, Klaus, Turing machines on represented sets, a model of computation for analysis, Logical Methods in Computer Science 7:2 (2011) 2:19, 21
• Uftring, Patrick, The characterization of Weihrauch reducibility in systems containing E-PA^ω + QF-AC^0,0, The Journal of Symbolic Logic 86:1 (2021) 224-261
• Weihrauch, Klaus, Computable planar curves intersect in a computable point, Computability 8:3, 4 (2019) 399-415
• Westrick, Linda, A note on the diamond operator, Computability 10:2 (2021) 107-110

• Carl, Merlin, Ordinal Computability, An Introduction to Infinitary Machines, de Gruyter, Berlin, 2019
• Dzhafarov, Damir D. and Mummert, Carl, Reverse Mathematics, Theory and Applications of Computability, Springer, 2022
• Hirschfeldt, Denis R., Slicing the Truth: On the Computable and Reverse Mathematics of Combinatorial Principles, vol. 28 of Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore, World Scientific, Singapore, 2015
• Weihrauch, Klaus, Computable Analysis, Springer, Berlin, 2000

• Amir, Djamel Eddine and Hoyrup, Mathieu, Comparing computability in two topologies, hal-03702999 (2022)
• Amir, Djamel Eddine and Hoyrup, Mathieu, Strong computable type, arXiv 2210.08309 (2022)
• Bauer, Andrej, Instance Reducibility and Weihrauch Degrees, arXiv 2106.01734 (2021)
• BeMent, Zack and Hirst, Jeffry and Wallace, Asuka, Reverse mathematics and Weihrauch analysis motivated by finite complexity theory, arXiv 2105.01719 (2021)
• Brattka, Vasco, The Discontinuity Problem, arXiv 2012.02143 (2020)
• Brattka, Vasco, On the complexity of computing Gödel numbers, arXiv 2302.04213 (2023)
• Brattka, Vasco and Gherardi, Guido, Weihrauch Goes Brouwerian, arXiv 1809.00380 (2018)
• Brattka, Vasco and Gherardi, Guido, Completion of Choice, arXiv 1910.13186 (2019)
• Brattka, Vasco and Gherardi, Guido and Pauly, Arno, Weihrauch Complexity in Computable Analysis, arXiv 1707.03202 (2017)
• Carl, Merlin, Generalized Effective Reducibility, arXiv 1601.01899 (2016)
• Cipriani, Vittorio and Marcone, Alberto and Valenti, Manlio, The Weihrauch lattice at the level of Π^1_1-CA_0: the Cantor-Bendixson theorem, arXiv 2210.15556 (2022)
• Davis, Caleb and Hirschfeldt, Denis R. and Hirst, Jeffry L. and Pardo, Jake and Pauly, Arno and Yokoyama, Keita, Combinatorial principles equivalent to weak induction, arXiv 1812.09943 (2018)
• Dzhafarov, Damir and Flood, Stephen and Solomon, Reed and Westrick, Linda Brown, Effectiveness for the Dual Ramsey Theorem, arXiv 1710.00070 (2017)
• Dzhafarov, Damir and Solomon, Reed and Valenti, Manlio, The tree pigeonhole principle in the Weihrauch degrees, arXiv 2312.10535 (2023)
• Dzhafarov, Damir D. and Goh, Jun Le and Hirschfeldt, Denis R. and Patey, Ludovic and Pauly, Arno, Ramsey's theorem and products in the Weihrauch degrees, arXiv 1804.10968 (2018)
• Dzhafarov, Damir D. and Hirschfeldt, Denis R. and Reitzes, Sarah C., Reduction Games, Provability, and Compactness, arXiv 2008.00907 (2020)
• Dzhafarov, Damir D. and Solomon, Reed and Yokoyama, Keita, On the first-order parts of problems in the Weihrauch degrees, arXiv 2301.12733 (2023)
• Fiori-Carones, Marta and Shafer, Paul and Soldà, Giovanni, An inside/outside Ramsey theorem and recursion theory, arXiv 2006.16969 (2020)
• Gherardi, Guido and Marcone, Alberto and Pauly, Arno, Projection operators in the Weihrauch lattice, arXiv 1805.12026 (2018)
• Gill, Kenneth, Indivisibility and uniform computational strength, arXiv 2312.03919 (2023)
• Goh, Jun Le, Some computability-theoretic reductions between principles around ATR_0, arXiv 1905.06868 (2019)
• Goh, Jun Le and Pauly, Arno and Valenti, Manlio, Finding descending sequences through ill-founded linear orders, arXiv 2010.03840 (2020)
• Hirst, Jeffry L., Leaf management, arXiv 1812.09762 (2018)
• Kihara, Takayuki, Degrees of Incomputability, Realizability and Constructive Reverse Mathematics, arXiv 2002.10712 (2020)
• Kihara, Takayuki, Lawvere-Tierney Topologies for Computability Theorists, arXiv 2106.03061 (2021)
• Kihara, Takayuki and Marcone, Alberto and Pauly, Arno, Searching for an analogue of ATR in the Weihrauch lattice, arXiv 1812.01549 (2018)
• Lempp, Steffen and Miller, Joseph S. and Pauly, Arno and Soskova, Mariya I. and Valenti, Manlio, Minimal covers in the Weihrauch degrees, arXiv 2311.12676 (2023)
• Lutz, Patrick, The Solecki dichotomy and the Possner-Robinson theorem are almost equivalent, arXiv 2301.07259 (2023)
• Marcone, Alberto and Valenti, Manlio, The open and clopen Ramsey theorems in the Weihrauch lattice, arXiv 2003.04245 (2020)
• Marcone, Alberto and Valenti, Manlio, Effective aspects of Hausdorff and Fourier dimension, arXiv 2108.06941 (2021)
• Nichols, David, Strong Reductions between Relatives of the Stable Ramsey's Theorem, arXiv 1711.06532 (2017)
• Pauly, Arno, Computability on the space of countable ordinals, arXiv 1501.00386 (2015)
• Pauly, Arno, An update on Weihrauch complexity, and some open questions, arXiv 2008.11168 (2020)
• Pauly, Arno and de Brecht, Matthew, Towards Synthetic Descriptive Set Theory: An instantiation with represented spaces, arXiv 1307.1850 (2013)
• Pauly, Arno and Tsuiki, Hideki, Computable dyadic subbases and \mathbbT^ω-representations of compact sets, arXiv 1604.0258 (2016)
• Rod Downey and Alexander Melnikov and Keng Meng Ng, Foundations of Online Structure Theory II: The Operator Approach, arXiv 2007.07401 (2020)
• Soldà, Giovanni and Valenti, Manlio, Algebraic properties of the first-order part of a problem, arXiv 2203.16298 (2022)
• Trotta, Davide and Valenti, Manlio and de Paiva, Valeria, Categorifying Computable Reducibilities, arXiv 2208.08656 (2022)
• Trotta, Davide and Valenti, Manlio and de Paiva, Valeria, Categorifying computable reducibilities, arXiv 2208.08656 (2022)
• Uftring, Patrick, The characterization of Weihrauch reducibility in systems containing E-PA^ω + QF-AC^0,0, arXiv 2003.13331 (2020)
• Uftring, Patrick, Weihrauch degrees without roots, arXiv 2102.11832 (2023)
• Westrick, Linda, A note on the diamond operator, arXiv 2001.09372 (2020)

• Bienvenu, Laurent and Kuyper, Rutger, Parallel and serial jumps of Weak Weak König's Lemma, 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 201-217
• 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
• 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, 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
• de Brecht, Matthew, Levels of Discontinuity, Limit-Computability, and Jump Operators, in: Brattka, Vasco and Diener, Hannes and Spreen, Dieter (eds.), Logic, Computation, Hierarchies, Ontos Mathematical Logic, Walter de Gruyter, Boston, 2014, pages 93-122
• Hertling, Peter and Selivanov, Victor, Complexity issues for preorders on finite labeled forests, in: Brattka, Vasco and Diener, Hannes and Spreen, Dieter (eds.), Logic, Computation, Hierarchies, Ontos Mathematical Logic, Walter de Gruyter, Boston, 2014, pages 165-190
• Hirschfeldt, Denis R., Some Questions in Computable Mathematics, 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 22-55
• Hirst, Jeffry L. and Mummert, Carl, Reverse Mathematics of Matroids, 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 143-159
• Kihara, Takayuki and Pauly, Arno, Dividing by zero–how bad is it, really?, in: 41st International Symposium on Mathematical Foundations of Computer Science, vol. 58 of LIPIcs. Leibniz Int. Proc. Inform., Schloss Dagstuhl. Leibniz-Zent. Inform., Wadern, 2016, page Art. No. 58, 14
• Kihara, Takayuki and Pauly, Arno, Finite choice, convex choice and sorting, in: Gopal, T.V. and Watada, Junzo (eds.), Theory and applications of models of computation, vol. 11436 of Lecture Notes in Computer Science, Springer, Cham, 2019, pages 378-393
• Pradic, Pierre and Soldà, Giovanni, On the Weihrauch degree of the additive Ramsey theorem over the rationals, in: Revolutions and revelations in computability, vol. 13359 of Lecture Notes in Computer Science, Springer, Cham, 2022, pages 259-271

• Boche, H. and Pohl, V., The Solvability Complexity Index of Sampling-based Hilbert Transform Approximations, in: 2019 13th International conference on Sampling Theory and Applications (SampTA), 2019, pages 1-4
• 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, 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, 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 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 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 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 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 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 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
• Carl, Merlin, Generalized Effective Reducibility, 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 225-233
• Cipriani, Vittorio and Pauly, Arno, The Complexity of Finding Supergraphs, 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 178-189
• Fujiwara, Makoto, Parallelizations in Weihrauch Reducibility and Constructive Reverse Mathematics, in: Anselmo, Marcella and Della Vedova, Gianluca and Manea, Florin and Pauly, Arno (eds.), Beyond the Horizon of Computability, Springer International Publishing, Cham, 2020, pages 38-49
• Galeotti, Lorenzo and Nobrega, Hugo, Towards Computable Analysis on the Generalized Real Line, in: Kari, Jarkko and Manea, Florin and Petre, Ion (eds.), Unveiling Dynamics and Complexity, vol. 10307 of Lecture Notes in Computer Science, Springer, Cham, 2017, pages 246-257
• Gherardi, Guido, An Analysis of the Lemmas of Urysohn and Urysohn-Tietze According to Effective Borel Measurability, in: Beckmann, A. and Berger, U. and Löwe, B. and Tucker, J.V. (eds.), Logical Approaches to Computational Barriers, vol. 3988 of Lecture Notes in Computer Science, Springer, Berlin, 2006, pages 199-208
• Gherardi, Guido and Marcone, Alberto, How Incomputable is the Separable Hahn-Banach Theorem?, 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 85-102
• Hertling, Peter and Selivanov, Victor, Complexity issues for preorders on finite labeled forests, in: Löwe, Benedikt and Normann, Dag and Soskov, Ivan and Soskova, Alexandra (eds.), Models of computation in context, vol. 6735 of Lecture Notes in Computer Science, Springer, Heidelberg, 2011, pages 112-121
• Hertling, Peter and Weihrauch, Klaus, Levels of degeneracy and exact lower complexity bounds for geometric algorithms, in: Proceedings of the Sixth Canadian Conference on Computational Geometry, 1994, pages 237-242
• Hoyrup, Mathieu and Rojas, Cristóbal and Weihrauch, Klaus, Computability of the Radon-Nikodym derivative, in: Löwe, Benedikt and Normann, Dag and Soskov, Ivan and Soskova, Alexandra (eds.), Models of Computation in Context, vol. 6735 of Lecture Notes in Computer Science, Springer, Heidelberg, 2011, pages 132-141
• Kawamura, Akitoshi, Lipschitz continuous ordinary differential equations are polynomial-space complete, in: 24th Annual IEEE Conference on Computational Complexity, IEEE Computer Soc., Los Alamitos, CA, 2009, pages 149-160
• Kawamura, Akitoshi and Cook, Stephen, Complexity theory for operators in analysis, in: Proceedings of the 42nd ACM Symposium on Theory of Computing, STOC '10, ACM, New York, 2010, pages 495-502
• Kawamura, Akitoshi and Ota, Hiroyuki, Small complexity classes for computable analysis, in: Mathematical foundations of computer science 2014. Part II, vol. 8635 of Lecture Notes in Comput. Sci., Springer, Heidelberg, 2014, pages 432-444
• Kawamura, Akitoshi and Ota, Hiroyuki and Rösnick, Carsten and Ziegler, Martin, Computational complexity of smooth differential equations, in: Mathematical foundations of computer science 2012, vol. 7464 of Lecture Notes in Comput. Sci., Springer, Heidelberg, 2012, pages 578-589
• Kawamura, Akitoshi and Pauly, Arno, Function spaces for second-order polynomial time, in: Language, life, limits, vol. 8493 of Lecture Notes in Comput. Sci., Springer, Cham, 2014, pages 245-254
• Kihara, Takayuki and Pauly, Arno, Dividing by Zero - How Bad Is It, Really?, in: Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf (eds.), 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016), vol. 58 of Leibniz International Proceedings in Informatics (LIPIcs), Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik, Dagstuhl, Germany, 2016, pages 58:1-58:14
• Kudinov, Oleg V. and Selivanov, Victor L. and Zhukov, Anton V., Undecidability in Weihrauch Degrees, in: Ferreira, Fernando and Löwe, Benedikt and Mayordomo, Elvira and Mendes Gomes, Luís (eds.), Programs, Proofs, Processes, vol. 6158 of Lecture Notes in Computer Science, Springer, Berlin, 2010, pages 256-265
• Le Roux, Stéphane and Pauly, Arno, Closed Choice for Finite and for Convex Sets, in: Bonizzoni, Paola and Brattka, Vasco and Löwe, Benedikt (eds.), The Nature of Computation. Logic, Algorithms, Applications, vol. 7921 of Lecture Notes in Computer Science, Springer, Berlin, 2013, pages 294-305
• Le Roux, Stéphane and Pauly, Arno, Weihrauch Degrees of Finding Equilibria in Sequential Games (Extended Abstract), in: Beckmann, Arnold and Mitrana, Victor and Soskova, Mariya (eds.), Evolving Computability, vol. 9136 of Lecture Notes in Computer Science, Springer, Cham, 2015, pages 246-257
• Nobrega, Hugo and Pauly, Arno, Game Characterizations and Lower Cones in the Weihrauch Degrees, in: Kari, Jarkko and Manea, Florin and Petre, Ion (eds.), Unveiling Dynamics and Complexity, vol. 10307 of Lecture Notes in Computer Science, Springer, Cham, 2017, pages 327-337
• Pauly, Arno, How Discontinuous is Computing Nash Equilibria? (Extended Abstract), in: Bauer, Andrej and Hertling, Peter and Ko, Ker-I (eds.), 6th International Conference on Computability and Complexity in Analysis (CCA'09), vol. 11 of OpenAccess Series in Informatics (OASIcs), Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik, Dagstuhl, Germany, 2009
• Pauly, Arno and de Brecht, Matthew, Non-deterministic computation and the Jayne-Rogers Theorem, in: Löwe, Benedikt and Winskel, Glynn (eds.), Proceedings 8th International Workshop on Developments in Computational Models, DCM 2012, Cambridge, United Kingdom, 17 June 2012., vol. 143 of Electronic Proceedings in Theoretical Computer Science, 2014, pages 87-96
• Pauly, Arno and de Brecht, Matthew, Descriptive Set Theory in the Category of Represented Spaces, in: 30th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS), 2015, pages 438-449
• Pauly, Arno and Steinberg, Florian, Representations of analytic functions and Weihrauch degrees, in: Computer science–theory and applications, vol. 9691 of Lecture Notes in Computer Science, Springer, Cham, 2016, pages 367-381
• Solomon, Reed, Computable Reductions and Reverse Mathematics, 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 182-191

• Amir, Djamel Eddine, Computability of Topological Spaces, PhD thesis, Université de Lorraine, 2023
• Anglès d'Auriac, Paul-Elliot, Infinite Computations in Algorithmic Randomness and Reverse Mathematics, PhD thesis, Université Paris-Est, 2020
• Carroy, Raphaël, Functions of the first Baire class, PhD thesis, University of Lausanne and University Paris 7, 2013
• Cipriani, Vittorio, Many Problems, Different Frameworks, Classification of Problems in Computable Analysis and Algorithmic Learning Theory, PhD thesis, Universitá degli Studi di Udine, 2023
• Gherardi, Guido, Some Results in Computable Analysis and Effective Borel Measurability, PhD thesis, University of Siena, Department of Mathematics and Computer Science, Siena, 2006
• Goh, Jun Le, Measuring the Relative Complexity of Mathematical Constructions and Theorems, PhD thesis, Cornell University, 2019
• Hertling, Peter, Unstetigkeitsgrade von Funktionen in der effektiven Analysis, Dissertation, Fachbereich Informatik, FernUniversität Hagen, 1996
• Higuchi, Kojiro, Degree Structures of Mass Problems and Choice Functions, PhD thesis, Mathematical Institute, Tohoku University, Sendai, Japan, 2012
• Hoyrup, Mathieu, Topological Aspects of Representations in Computable Analysis, Habilitation Thesis, Laboratoire Lorrain de Recherche en Informatique et ses Applications, Nancy, France, 2023
• Lutz, Patrick, Results on Martin's Conjecture, PhD thesis, University of California, Berkeley, 2021
• Mylatz, Uwe, Vergleich unstetiger Funktionen: "Principle of Omniscience" und Vollständigkeit in der C-Hierarchie, Ph.D. thesis, Faculty for Mathematics and Computer Science, University Hagen, Hagen, Germany, 2006
• Nobrega, Hugo, Games for functions - Baire classes, Weihrauch degrees, Transfinite Computations, and Ranks, PhD thesis, Institute for Logic, Language and Computation, Universiteit van Amsterdam, 2018
• Patey, Ludovic, The reverse mathematics of Ramsey-type theorems, PhD thesis, Université Paris Diderot, Paris, France, 2016
• Pauly, Arno, Computable Metamathematics and its Application to Game Theory, Ph.D. thesis, University of Cambridge, Computer Laboratory, Clare College, Cambridge, 2011
• Rakotoniaina, Tahina, On the Computational Strength of Ramsey's Theorem, Ph.D. thesis, Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch, South Africa, 2015
• Thies, Holger, Uniform computational complexity of ordinary differential equations with applications to dynamical systems and exact real arithmetic, PhD thesis, Graduate School of Arts and Sciences, University of Tokyo, Tokyo, Japan, 2018
• Valenti, Manlio, A journey through computability, topology and analysis, PhD thesis, Universitá degli Studi di Udine, 2021

• 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 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 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 and Hertling, Peter (eds.), Handbook of Computability and Complexity in Analysis, Theory and Applications of Computability, Springer, Cham, 2021
• 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

• Hertling, Peter, Topologische Komplexitätsgrade von Funktionen mit endlichem Bild, technical report, FernUniversität Hagen, Hagen, 1993
• Hertling, Peter, Stetige Reduzierbarkeit auf Σ^ω von Funktionen mit zweielementigem Bild und von zweistetigen Funktionen mit diskretem Bild, technical report, FernUniversität Hagen, Hagen, 1993
• Hertling, Peter, A topological complexity hierarchy of functions with finite range, technical report, Centre de recerca matematica, Institut d'estudis catalans, Barcelona, Barcelona, 1993
• Hertling, Peter and Weihrauch, Klaus, On the topological classification of degeneracies, technical report, FernUniversität Hagen, Hagen, 1994
• Weihrauch, Klaus, The degrees of discontinuity of some translators between representations of the real numbers, technical report, International Computer Science Institute, Berkeley, 1992
• Weihrauch, Klaus, The degrees of discontinuity of some translators between representations of the real numbers, technical report, FernUniversität Hagen, Hagen, 1992
• Weihrauch, Klaus, The TTE-interpretation of three hierarchies of omniscience principles, technical report, FernUniversität Hagen, Hagen, 1992

This bibliography web page has currently 218 entries

• Please feel free to send additions, corrections and comments by email to .
• We can only process new submissions in correct BibTeX format (see wei.bib as an example).