Lecture Notes in Computer Science 12813

Founding Editors

Gerhard GoosKarlsruhe Institute of Technology, Karlsruhe, Germany

Juris HartmanisCornell University, Ithaca, NY, USA

Editorial Board Members

Elisa BertinoPurdue University, West Lafayette, IN, USA

Wen GaoPeking University, Beijing, China

Bernhard SteffenTU Dortmund University, Dortmund, Germany

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Moti YungColumbia University, New York, NY, USA

More information about this subseries at http://www.springer.com/series/7407

Liesbeth De Mol • Andreas Weiermann •

Florin Manea • David Fernández-Duque (Eds.)

Connectingwith Computability17th Conference on Computability in Europe, CiE 2021Virtual Event, Ghent, July 5–9, 2021Proceedings

123

EditorsLiesbeth De MolUniversity of LilleLille, France

Andreas WeiermannVakgroep WiskundeGhent UniversityGhent, Belgium

Florin ManeaUniversity of GöttingenGöttingen, Germany

David Fernández-DuqueGhent UniversityGhent, Belgium

ISSN 0302-9743 ISSN 1611-3349 (electronic)Lecture Notes in Computer ScienceISBN 978-3-030-80048-2 ISBN 978-3-030-80049-9 (eBook)https://doi.org/10.1007/978-3-030-80049-9

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Preface

CiE 2021: Connecting with Computability, 5–9 July 2021, virtual conferencehosted in Ghent, Belgium

Computability in Europe (CiE) is an annual conference organized under the auspicesof the Association CiE (ACiE), a European association that brings together researchersfrom a broad variety of backgrounds (mathematics, computer science, logic, history,biology, philosophy, and physics, among others) connected to one another throughtheir work on computability. The conference series has built up a strong tradition fordeveloping a scientific program which is interdisciplinary and embracive at its core,bringing together all aspects of computability and foundations of computer science, aswell as exploring the interplay of these theoretical areas with practical issues in bothcomputer science and other disciplines. Its purpose is not only to report on ongoingresearch but also to broaden perspectives by engaging with the work of others fromdifferent backgrounds. As such, the conference has allowed participants to enlarge andtransform our view on computability and its interface with other areas of knowledge.

Over the years the conference series has been organized in a spirit ofopen-mindedness and generosity, and also this year we have again aimed for this,despite the circumstances. The motto of CiE 2021 was Connecting with Computability,a clear acknowledgement of the connecting and interdisciplinary nature of the con-ference series, which is all the more important in a time when people are more dis-connected from one another than ever due to the COVID-19 pandemic. It wasorganized virtually using the software gather.town as a means to create a virtual socialenvironment with a nod to the host city of Ghent, with its characteristic castle and riveras well as its vibrant social life.

CiE 2021 is the 17th conference in the series. Previous meetings have taken place inAmsterdam (2005), Swansea (2006), Siena (2007), Athens (2008), Heidelberg (2009),Ponta Delgada (2010), Sofia (2011), Cambridge (2012), Milan (2013), Budapest(2014), Bucharest (2015), Paris (2016), Turku (2017), Kiel (2018), Durham (2019),and, virtually, in Salerno (2020).

The conference series has become a major event and is the largest internationalconference that brings together researchers focusing on computability-related issues.The CiE conference series is coordinated by the ACiE conference Steering Committeeconsisting of Alessandra Carbone (Paris), Liesbeth De Mol (Lille), Gianluca Della

Vedova (Executive Officer, Milan), Mathieu Hoyrup (Nancy), Nataša Jonoska(Tampa), Benedikt Löwe (Amsterdam), Florin Manea (Chair, Göttingen), Klaus Meer(Cottbus), Russell Miller (New York), and Mariya Soskova (Wisconsin-Madison),along with ex-officio members Elvira Mayordomo (President of the Association,Zaragoza) and Dag Normann (Treasurer, Oslo).

Structure and Program of the Conference

The conference program is based on invited lectures and tutorials, and a set of specialsessions on a variety of topics; there were also several contributed papers and informalabstract presentations. The Program Committee of CiE 2021 was chaired by LiesbethDe Mol (CNRS and Université de Lille, France) and Andreas Weiermann (GhentUniversity, Belgium). The committee, consisting of 33 members, selected the invitedspeakers, the tutorial speakers, and the special session organizers and coordinated thereviewing process and the selection of submitted contributions. The Program Com-mittee selected for publication in this volume 28 of the 49 non-invited papers submittedto the conference. Each paper received at least three reviews by members of theProgram Committee and their subreviewers. In addition to the contributed papers, thisvolume contains 18 invited papers and abstracts.

Invited Tutorials

Russell Miller (CUNY, USA), Computable procedures for fieldChristine Tasson (Université de Paris, France), Probabilistic Programming andComputation

Invited Lectures

Laura Crosilla (University of Oslo, Norway), Cantor’s paradise and the forbidden fruitMarkus Lohrey (Universität Siegen, Germany), Compression techniques in grouptheoryJoan Rand Moschovakis (Occidental College, USA), Minimum classical extensions ofconstructive theoriesJoël Ouaknine (Max Planck Institute for Software Systems, Germany), HolonomicTechniques, Periods, and Decision ProblemsKeita Yokoyama (Japan Advanced Institute of Science and Technology, Japan),Reverse mathematics and proof and model theory of arithmeticHenry Yuen (Columbia University, USA), Einstein meets Turing: The Computabilityof Nonlocal Games

vi Preface

Special Sessions

Computational Geometry

Organizers: Maike Buchin (Ruhr-Universität Bochum, Germany) and Maarten Löffler(Utrecht University, The Netherlands)

Karl Bringmann (Saarland University, Germany), Conditional lower bounds for geo-metric problems.Esther Ezra (Bar-Ilan University, Israel), On 3SUM-hard problems in the Decision TreeModel.Tillmann Miltzow (Utrecht University, The Netherlands), Recent trends in geometriccomputation models and its relation to the existential theory of the reals.Wolfgang Mulzer (Free University Berlin, Germany), The many computational modelsof computational geometry.

Classical Computability Theory: Open Problems and Solutions

Organizers: Noam Greenberg (Victoria University of Wellington, New Zealand) andSteffen Lempp (University of Wisconsin, USA)

Marat Faizrakhmanov (Kazan Federal University, Russia), Limitwise MonotonicSpectra and Their GeneralizationsAndrea Sorbi (University of Siena, Italy), Effective inseparability and its applicationsLiang Yu (Nanjing University, China), TD implies CCRNing Zhong (University of Cincinnati, USA), Computability of limit sets fortwo-dimensional flows

Proof Theory and Computation

Organizers: David Fernández-Duque (Ghent University, Belgium) and Juan PabloAguilera (Ghent University, Belgium)

Lorenzo Carlucci (University of Rome La Sapienza, Italy), Restrictions of Hindman’sTheorem: an overview with questionsLeszek Kolodziejczyk (University of Warsaw, Poland), Reverse mathematics ofcombinatorial principles over a weak base theoryFrancesca Poggiolesi (CNRS and Université Paris 1 Panthéon-Sorbonne, France),Defining Formal Explanation in Classical Logic by Substructural DerivabilityYue Yang (National University of Singapore, Singapore), Some results on Ramsey’stheorems for trees

Preface vii

Quantum Computation and Information

Organizers: Harry Buhrman (Universiteit van Amsterdam, The Netherlands) and FrankVerstraete (Ghent University, Belgium)

Yfke Dulek (QuSoft and CWI, Netherlands). How to Verify a Quantum ComputationDavid Gross (University of Cologne, Germany), The axiomatic and the operationalapproaches to resource theories of magic do not coincideDavid Pérez-Garciá (Universidad Complutense de Madrid, Spain), Uncomputability inquantum many body problemsJens Eisert (Freie Universität Berlin, Germany), Undecidability in Quantum Physics

Church’s Thesis in Constructive Mathematics (HaPoC Session)

Organizers: Marianna Antonutti-Marfori (Ludwig-Maximilians-Universität München,Germany) and Alberto Naibo (Université Paris 1 Panthéon-Sorbonne, France)

The HaPoC special session was part of a satellite workshop on the same topic. Otherspeakers invited to this workshop were Benno van den Berg, Takako Nemoto, DouglasBridges, and Johanna Franklin.

Liron Cohen (Ben-Gurion University, Israel), Formally Computing with theNon-ComputableAngeliki Koutsoukou-Argyraki (University of Cambridge, UK) On preserving thecomputational content of mathematical proofs: toy examples for a formalising strategyMáté Szabó (University of Oxford, UK), Péter on Church’s Thesis, Constructivity andComputersDavid Turner (University of Kent, UK), Constructive mathematics, Church’s Thesis,and free choice sequences.

Computational Pangenomics

Organizers: Nadia Pisanti (University of Pisa, Italy) and Solon Pissis (CWI and VrijeUniversiteit, The Netherlands)

Brona Brejova (Comenius University in Bratislava, Slovakia), Probabilistic models fork-mer frequenciesRayan Chikhi (Pasteur Institute, France), A tale of optimizing the space taken by deBruijn graphsFrancesca Ciccarelli (King’s College London, UK), Gene deregulations driving cancerat single patient resolutionBenedict Paten (University of California, Santa Cruz, USA), Walk-preserving trans-formation of overlapped sequence graphs into blunt sequence graphs with GetBlunted

viii Preface

Women in Computability Workshop

Since CiE 2007, the Association CiE and the conference have built up a strong traditionof encouraging women to participate in computability-related research. In 2016,a Special Interest Group for Women in Computability was established. This year MariyaSoskova took the initiative of setting up an online mentorship programme for Women inComputability (https://www.acie.eu/women-in-computability-mentorship-programme).These kind of initiatives are anchored in the annual Women in Computability workshop,which was held virtually with the following speakers:

Laura Crosilla (University of Oslo, Norway)Joan Rand Moschovakis (Occidental College, USA)Christine Tasson (Université de Paris, France)

Organization and Acknowledgements

The CiE 2021 conference was organized by the Analysis, Logic and Discrete Math-ematics group at the mathematics department of Ghent University, Belgium. It waschaired by David Fernández-Duque. We wish to thank all the other members of theOrganizing Committee, without their help this conference would not have beenpossible.

We are very happy to acknowledge and thank the following for their basic financialsupport: the Fund for Scientific Research, Flanders (FWO), the National Centre forResearch in Logic (CNRL-NCNL), Facultaire Commissie voor WetenschappelijkOnderzoek (FCWO), and, finally, Springer.

The high quality of the conference was due to the careful work of the ProgramCommittee, the special session organizers, and the external referees, and we are verygrateful that they helped to create an exciting program for CiE 2021.

May 2021 Liesbeth De MolGhent, Belgium Andreas Weiermann

Florin ManeaDavid Fernández-Duque

Preface ix

Organization

Program Committee

Marianna Antonutti Marfori Ludwig Maximilian University of Munich, GermanyNathalie Aubrun ENS de Lyon, CNRS, Inria, and UCBL, FranceChristel Baier TU Dresden, GermanyNikolay Bazhenov Sobolev Institute of Mathematics, RussiaArnold Beckmann Swansea University, UKDavid Belanger Ghent University, BelgiumMarie-Pierre Béal Université Gustave Eiffel, FranceJoel Day Loughborough University, UKLiesbeth De Mol (Co-chair) CNRS and Université de Lille, FranceCarola Doerr Sorbonne University and CNRS, FranceJérôme Durand-Lose LIFO and Université d’Orléans, FranceDavid Fernández-Duque Ghent University, BelgiumZuzana Hanikova Institute of Computer Science, Czech Academy

of Sciences, Czech RepublicMathieu Hoyrup Loria, FranceAssia Mahboubi Inria, FranceFlorin Manea University of Göttingen, GermanyIrène Marcovici Université de Lorraine, FranceKlaus Meer BTU Cottbus-Senftenberg, GermanyLudovic Patey Institut Camille Jordan, FranceCinzia Pizzi University of Padova, ItalyGiuseppe Primiero University of Milan, ItalySimona Ronchi Della Rocca Universita’ di Torino, ItalySvetlana Selivanova KAIST, South KoreaPaul Shafer University of Leeds, UKAlexander Shen LIRMM CNRS and Université de Montpellier, FranceAlexandra Soskova Sofia University, BulgariaMariya Soskova University of Wisconsin-Madison, USAFrank Stephan National University of Singapore, SingaporePeter Van Emde Boas Universiteit van Amsterdam, The NetherlandsSergey Verlan Université Paris-Est Créteil, FranceAndreas Weiermann

(Co-chair)Ghent University, Belgium

Damien Woods Maynooth University, Ireland

Organizing Committee

David Fernández-Duque(Chair)

Ghent University, Belgium

Juan Pablo Aguilera Ghent University, BelgiumDavid Belanger Ghent University, BelgiumAna Borges University of Barcelona, SpainLiesbeth De Mol CNRS and Université de Lille, FranceAndreas Debrouwere Ghent University, BelgiumLorenz Demey Catholic University of Leuven, BelgiumOriola Gjetaj Ghent University, BelgiumEduardo Hermo-Reyes University of Barcelona, SpainBrett McLean Ghent University, BelgiumChristian Michaux University of Mons, BelgiumFedor Pakhomov Ghent University, BelgiumKonstantinos Papafilippou Ghent University, BelgiumPawl Pawlowsky Ghent University, BelgiumFrederik Van De Putte Ghent University, Belgium, Erasmus University

of Rotterdam, The NetherlandsPeter Verdée Catholic University of Leuven, BelgiumAndreas Weiermann Ghent University, Belgium

Additional Reviewers

Aguilera, JuanAnglès d’Auriac, Paul-ElliotBaillot, PatrickBerndt, SebastianBienvenu, LaurentBournez, OlivierBoyar, JoanBuchin, MaikeCalvert, WesleyCardone, FeliceCarlucci, LorenzoCarton, OlivierDean, WalterDürr, ChristophEpstein, LeahFranklin, JohannaGanardi, MosesGao, ZiyuanGregoriades, VassiliosHarizanov, Valentina

Hermo Reyes, EduardoHofstra, PieterKach, AsherKihara, TakayukiKohlenbach, UlrichKrejca, Martin S.Kristiansen, LarsLechine, UlysseLempp, SteffenLoewe, BenediktLubarsky, RobertMartin, EricMelnikov, AlexanderMercas, RobertMinnes, MiaMiquel, AlexandreMiyabe, KenshiMonin, BenoîtNeumann, EikeNeuwirth, Stefan

xii Organization

Normann, DagOllinger, NicolasPagani, MichelePakhomov, FedorPatey, LudovicPisanti, NadiaPissis, SolonPorter, ChristopherPouly, AmauryPéchoux, RomainQuinon, PaulaRaskin, MikhailRichard, Gaétan

Sabili, Ammar FathinSan Mauro, LucaSanders, SamSchmid, Markus L.Schroeder, MatthiasThies, HolgerTirnauca, CristinaValiron, BenoîtVatev, StefanWalsh, JamesWeiss, ArminYokoyama, KeitaZheng, Xizhong

Organization xiii

Invited Talks

Don’t Be Afraid to Burn Your Fingerson the Definition of the Real RAM

Tillmann Miltzow

Utrecht University, The Netherlandst.miltzow@uu.nl

Abstract. We review the real RAM model of computation. The emphasis of thistalk is its relation to the existential theory of the reals

Keywords: Real RAM � Computational geometry � Model of computation.

In Computational Geometry, we design and analyze algorithms for the real RAMmodel of computation. The real RAM is an abstraction of an ordinary computer. Itconsists of an array of registers to store the data, a central processing unit (CPU) tomanipulate the data and a set of instructions for the CPU. The real RAM is capable tostore and manipulate real numbers. It was originally defined by Shamos [3] in his PhDthesis. Unfortunately, the real RAM as defined by Shamos had some seriously unin-tended consequences. In short, it is possible to abuse the power of the real RAM invarious ways by having access to the binary representation of real numbers [2]. Sincethen, researchers used implicitly a version of the real RAM that avoided access to thebinary representation of real numbers. Recently, Erickson, van der Hoog, and Milt-zow [1] made that new real RAM definition explicit. Furthermore, they gave somearguments why this new model may avoid previous pitfalls. In the talk, we will explainand repeat those arguments. Specifically, we will highlight the relation to the existentialtheory of the reals. It is conceivable that the new real RAM model has other weak-nesses that will be discovered in the near or far future. In this case, the authors willhave burned their fingers. Even if some new pitfalls and weaknesses will be found, webelieve that this will not mean the end of Computational Geometry as we know it. Thismotivates the following hypothesis.

There is a rigorous definition of the real RAM model of computation for whichthe majority of algorithms and their analysis in Computational Geometry remainmeaningful.

As the current model of the real RAM has not exposed any weaknesses within thelast forty years, we may have confidence that it will not expose major weaknesses in thenext forty years either.

Supported by NWO Veni grant EAGER.

References

1. Erickson, J., van der Hoog, I., Miltzow, T.: Smoothing the gap between NP and ER. In: 2020IEEE 61st Annual Symposium on Foundations of Computer Science (FOCS), pp. 1022–1033.IEEE (2020)

2. Schönhage, A.: On the power of random access machines. In: Maurer, H.A. (ed.) ICALP1979. LNCS, vol. 71, pp. 520–529. Springer, Heidelberg (1979). https://doi.org/10.1007/3-540-09510-1_42

3. Aichholzer, O., Cetina, M., Fabila-Monroy, R., Leaños, J., Salazar, G., Urrutia, J.: Convex-ifying monotone polygons while maintaining internal visibility. In: Márquez, A., Ramos, P.,Urrutia, J. (eds.) EGC 2011. LNCS, vol. 7579, pp. 98–108. Springer, Heidelberg (2012).https://doi.org/10.1007/978-3-642-34191-5_9

xviii T. Miltzow

The Many Computational Modelsof Computational Geometry

Wolfgang Mulzer

Institut für Informatik, Freie Universität Berlin, 14195 Berlin, Germanymulzer@inf.fu-berlin.de

Abstract. I will present a short survey of the many different computationalmodels that have been used in computational geometry over the last 50 years,both for describing geometric algorithms and for obtaining lower bounds.

Keywords: Real RAM �Word RAM � Algebraic decision tree � Pointer machine

Computational geometry is the subfield of theoretical computer science that is con-cerned with the design and analysis of algorithms that deal with geometric inputs, suchas, e.g., points, lines, triangles, or circles. In many ways, computational geometry isvery similar to the study of traditional combinatorial algorithms: we aim for methodsthat are provably correct on all inputs, we search for upper and lower bounds on theworst-case complexity of well-defined computational problems, and we consider tra-ditional computational resources such as space, time, or randomness.

However, the geometric nature of the inputs presents an additional set of challengesover the combinatorial regime: geometric objects typically live in Euclidean spaces andare represented by arbitrary real numbers. Even if we choose to restrict our attention toinputs with integer coordinates, the need to compute angles and (sums of) distancesarises often. High precision is necessary to evaluate geometric primitives accurately.Thus, in computational geometry, we must be more careful about our model of com-putation and which operations it allows. Over time, several such models have beenproposed, both for describing upper and lower bounds for geometric algorithms.

The two most widespread models for algorithmic results are the real RAM, whichallows operations on arbitrary real numbers, and the word RAM, which can handle onlybit strings of a certain length. Lower bounds are typically proved in the algebraicdecision tree model, which enhances traditional comparison-based decision trees byalgebraic operations. For lower bounds in geometric data structures, the pointermachine model is used frequently.

In my talk, I will provide a survey of these models, their definitions, applications,advantages, and disadvantages.

Supported in part by ERC STG 757609.

Holonomic Techniques, Periods, and DecisionProblems

Joël Ouaknine

Max Planck Institute for Software Systems, Saarland Informatics Campus,Saarbrücken, Germanyjoel@mpi-sws.org

Abstract. Holonomic techniques have deep roots going back to Wallis, Euler,and Gauss, and have evolved in modern times as an important subfield ofcomputer algebra, thanks in large part to the work of Zeilberger and others overthe past three decades. In this talk, I give an overview of the area, and inparticular present a select survey of known and original results on decisionproblems for holonomic sequences and functions. I also discuss some surprisingconnections to the theory of periods and exponential periods, which are classicalobjects of study in algebraic geometry and number theory; in particular, I relatethe decidability of certain decision problems for holonomic sequences to deepconjectures about periods and exponential periods, notably those due to Kont-sevich and Zagier.

Contents

Searching for Applicable Versions of Computable Structures . . . . . . . . . . . . 1P. E. Alaev and V. L. Selivanov

On Measure Quantifiers in First-Order Arithmetic . . . . . . . . . . . . . . . . . . . . 12Melissa Antonelli, Ugo Dal Lago, and Paolo Pistone

Learning Languages with Decidable Hypotheses . . . . . . . . . . . . . . . . . . . . . 25Julian Berger, Maximilian Böther, Vanja Doskoč,Jonathan Gadea Harder, Nicolas Klodt, Timo Kötzing,Winfried Lötzsch, Jannik Peters, Leon Schiller, Lars Seifert,Armin Wells, and Simon Wietheger

Robust Online Algorithms for Dynamic Choosing Problems . . . . . . . . . . . . . 38Sebastian Berndt, Kilian Grage, Klaus Jansen, Lukas Johannsen,and Maria Kosche

On the Degrees of Constructively Immune Sets . . . . . . . . . . . . . . . . . . . . . 50Samuel D. Birns and Bjørn Kjos-Hanssen

Fine-Grained Complexity Theory: Conditional Lower Boundsfor Computational Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

Karl Bringmann

The Lost Melody Theorem for Infinite Time Blum-Shub-Smale Machines . . . 71Merlin Carl

Randomising Realizability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82Merlin Carl, Lorenzo Galeotti, and Robert Passmann

Restrictions of Hindman’s Theorem: An Overview . . . . . . . . . . . . . . . . . . . 94Lorenzo Carlucci

Complexity and Categoricity of Injection Structures Induced by FiniteState Transducers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

Richard Krogman and Douglas Cenzer

A Tale of Optimizing the Space Taken by de Bruijn Graphs . . . . . . . . . . . . 120Rayan Chikhi

Formally Computing with the Non-computable . . . . . . . . . . . . . . . . . . . . . . 135Liron Cohen

Mapping Monotonic Restrictions in Inductive Inference . . . . . . . . . . . . . . . . 146Vanja Doskoč and Timo Kötzing

Normal Forms for Semantically Witness-Based Learnersin Inductive Inference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158

Vanja Doskoč and Timo Kötzing

Walk-Preserving Transformation of Overlapped Sequence Graphsinto Blunt Sequence Graphs with GetBlunted . . . . . . . . . . . . . . . . . . . . . . . 169

Jordan M. Eizenga, Ryan Lorig-Roach, Melissa M. Meredith,and Benedict Paten

On 3SUM-hard Problems in the Decision Tree Model . . . . . . . . . . . . . . . . . 178Esther Ezra

Limitwise Monotonic Spectra and Their Generalizations . . . . . . . . . . . . . . . 189Marat Faizrahmanov

On False Heine/Borel Compactness Principles in Proof Mining. . . . . . . . . . . 199Fernando Ferreira

Placing Green Bridges Optimally, with a Multivariate Analysis. . . . . . . . . . . 204Till Fluschnik and Leon Kellerhals

A Church-Turing Thesis for Randomness? . . . . . . . . . . . . . . . . . . . . . . . . . 217Johanna N. Y. Franklin

Probabilistic Models of k-mer Frequencies (Extended Abstract). . . . . . . . . . . 227Askar Gafurov, Tomáš Vinař, and Broňa Brejová

Defining Formal Explanation in Classical Logicby Substructural Derivability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237

Francesco A. Genco and Francesca Poggiolesi

Dedekind Cuts and Long Strings of Zeros in Base Expansions . . . . . . . . . . . 248Ivan Georgiev

On the Impact of Treewidth in the Computational Complexityof Freezing Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260

Eric Goles, Pedro Montealegre, Martín Ríos Wilson,and Guillaume Theyssier

Towards a Map for Incremental Learning in the Limit from Positiveand Negative Information. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273

Ardalan Khazraei, Timo Kötzing, and Karen Seidel

On Preserving the Computational Content of Mathematical Proofs:Toy Examples for a Formalising Strategy. . . . . . . . . . . . . . . . . . . . . . . . . . 285

Angeliki Koutsoukou-Argyraki

xxii Contents

In Search of the First-Order Part of Ramsey’s Theorem for Pairs . . . . . . . . . 297Leszek Aleksander Kołodziejczyk and Keita Yokoyama

On Subrecursive Representation of Irrational Numbers:Contractors and Baire Sequences. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 308

Lars Kristiansen

Learning Languages in the Limit from Positive Information with FinitelyMany Memory Changes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 318

Timo Kötzing and Karen Seidel

Compression Techniques in Group Theory . . . . . . . . . . . . . . . . . . . . . . . . . 330Markus Lohrey

Computable Procedures for Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342Russell Miller

Minimum Classical Extensions of Constructive Theories . . . . . . . . . . . . . . . 353Joan Rand Moschovakis and Garyfallia Vafeiadou

Subrecursive Equivalence Relations and (non-)Closure Under LatticeOperations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363

Jean-Yves Moyen and Jakob Grue Simonsen

Interactive Physical ZKP for Connectivity: Applications to Nurikabeand Hitori . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373

Léo Robert, Daiki Miyahara, Pascal Lafourcade, and Takaaki Mizuki

Positive Enumerable Functors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385Barbara F. Csima, Dino Rossegger, and Daniel Yu

Splittings and Robustness for the Heine-Borel Theorem . . . . . . . . . . . . . . . . 395Sam Sanders

Non-collapse of the Effective Wadge Hierarchy . . . . . . . . . . . . . . . . . . . . . 407Victor Selivanov

Effective Inseparability and Its Applications . . . . . . . . . . . . . . . . . . . . . . . . 417Andrea Sorbi

Simple Betting and Stochasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 424Tomasz Steifer

Péter on Church’s Thesis, Constructivity and Computers . . . . . . . . . . . . . . . 434Máté Szabó

Constructive Mathematics, Church’s Thesis, and Free Choice Sequences . . . . 446D. A. Turner

Contents xxiii

KL-Randomness and Effective Dimension Under Strong Reducibility . . . . . . 457Bjørn Kjos-Hanssen and David J. Webb

An Algorithmic Version of Zariski’s Lemma . . . . . . . . . . . . . . . . . . . . . . . 469Franziskus Wiesnet

Einstein Meets Turing: The Computability of Nonlocal Games . . . . . . . . . . . 483Henry Yuen

Computability of Limit Sets for Two-Dimensional Flows . . . . . . . . . . . . . . . 494Daniel S. Graça and Ning Zhong

Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 505

xxiv Contents