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Function Spaces for Orbit-Finite Sets

Authors Mikołaj Bojańczyk , Lê Thành Dũng (Tito) Nguyễn , Rafał Stefański

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Author Details

Mikołaj Bojańczyk
  • University of Warsaw, Poland
Lê Thành Dũng (Tito) Nguyễn
  • École normale supérieure de Lyon, France
Rafał Stefański
  • University of Warsaw, Poland

Funding

  • Bojańczyk, Mikołaj: Supported by Polish NCN Maestro Grant 2022/46/A/ST6/00072.
  • Nguyễn, Lê Thành Dũng (Tito): Supported by the LABEX MILYON (ANR-10-LABX-0070) of Université de Lyon, within the program "France 2030" (ANR-11-IDEX-0007) operated by the French National Research Agency (ANR).
  • Stefański, Rafał: Supported by EPSRC project EP/V040944/1 "Resources in Computation".

Acknowledgements

L. T. D. Nguyễn would like to thank Clovis Eberhart and Cécilia Pradic for their ongoing collaboration on "implicit automata for data words", which inspired some ideas in this paper. R. Stefański would like to thank Samson Abramsky for introducing him to the beautiful world of game semantics and suggesting to study it in the context of this paper.

Cite AsGet BibTex

Mikołaj Bojańczyk, Lê Thành Dũng (Tito) Nguyễn, and Rafał Stefański. Function Spaces for Orbit-Finite Sets. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 130:1-130:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.ICALP.2024.130

Abstract

Orbit-finite sets are a generalisation of finite sets, and as such support many operations allowed for finite sets, such as pairing, quotienting, or taking subsets. However, they do not support function spaces, i.e. if X and Y are orbit-finite sets, then the space of finitely supported functions from X to Y is not orbit-finite. We propose a solution to this problem inspired by linear logic.

Subject Classification

ACM Subject Classification
  • Theory of computation → Formal languages and automata theory
Keywords
  • Orbit-finite sets
  • automata
  • linear types
  • game semantics

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References

  1. Samson Abramsky. Computational interpretations of linear logic. Theoretical Computer Science, 111(1&2):3-57, 1993. URL: https://doi.org/10.1016/0304-3975(93)90181-R.
  2. Samson Abramsky. Semantics of interaction. In Peter Dybjer and Andrew Pitts, editors, Proceedings of the 1996 CLiCS Summer School, Isaac Newton Institute. Cambridge University Press, 1997. URL: https://arxiv.org/abs/1312.0121.
  3. Roberto M. Amadio and Pierre-Louis Curien. Domains and Lambda-Calculi. Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, 1998. URL: https://doi.org/10.1017/CBO9780511983504.
  4. Quentin Aristote. Active learning of deterministic transducers with outputs in arbitrary monoids. In Aniello Murano and Alexandra Silva, editors, 32nd EACSL Annual Conference on Computer Science Logic, CSL 2024, February 19-23, 2024, Naples, Italy, volume 288 of LIPIcs, pages 11:1-11:20. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024. URL: https://doi.org/10.4230/LIPICS.CSL.2024.11.
  5. Mikołaj Bojańczyk. Slightly infinite sets. URL: https://www.mimuw.edu.pl/~bojan/paper/atom-book.
  6. Mikołaj Bojańczyk. Nominal Monoids. Theory of Computing Systems, 53(2):194-222, 2013. URL: https://doi.org/10.1007/S00224-013-9464-1.
  7. Mikołaj Bojańczyk, Bartek Klin, and Slawomir Lasota. Automata theory in nominal sets. Logical Methods in Computer Science, 10(3), 2014. URL: https://doi.org/10.2168/LMCS-10(3:4)2014.
  8. Mikołaj Bojańczyk, Bartek Klin, and Joshua Moerman. Orbit-finite-dimensional vector spaces and weighted register automata. In 36th Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2021, Rome, Italy, June 29 - July 2, 2021, pages 1-13. IEEE, 2021. URL: https://doi.org/10.1109/LICS52264.2021.9470634.
  9. Mikołaj Bojańczyk and Rafał Stefański. Single-Use Automata and Transducers for Infinite Alphabets. In Artur Czumaj, Anuj Dawar, and Emanuela Merelli, editors, International Colloquium on Automata, Languages, and Programming (ICALP 2020), volume 168 of Leibniz International Proceedings in Informatics (LIPIcs), pages 113:1-113:14, Dagstuhl, Germany, 2020. Schloss Dagstuhl - Leibniz-Zentrum für Informatik. URL: https://doi.org/10.4230/LIPIcs.ICALP.2020.113.
  10. Pierre Clairambault. Causal Investigations in Interactive Semantics. Habilitation à diriger des recherches, Université Aix-Marseille, February 2024. URL: https://theses.hal.science/tel-04523273.
  11. Thomas Colcombet and Daniela Petrişan. Automata Minimization: a Functorial Approach. Logical Methods in Computer Science, 16(1), March 2020. URL: https://doi.org/10.23638/LMCS-16(1:32)2020.
  12. Paul Gallot, Aurélien Lemay, and Sylvain Salvati. Linear high-order deterministic tree transducers with regular look-ahead. In Javier Esparza and Daniel Král', editors, 45th International Symposium on Mathematical Foundations of Computer Science, MFCS 2020, August 24-28, 2020, Prague, Czech Republic, volume 170 of LIPIcs, pages 38:1-38:13. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. URL: https://doi.org/10.4230/LIPIcs.MFCS.2020.38.
  13. Jean-Yves Girard. Linear logic: its syntax and semantics. In Jean-Yves Girard, Yves Lafont, and Laurent Regnier, editors, Advances in Linear Logic, volume 222 of London Mathematical Society Lecture Notes, pages 1-42. Cambridge University Press, 1995. URL: https://doi.org/10.1017/CBO9780511629150.002.
  14. Peter Hines. A categorical framework for finite state machines. Mathematical Structures in Computer Science, 13(3):451-480, 2003. URL: https://doi.org/10.1017/S0960129503003931.
  15. Martin Hyland. Game semantics. In Andrew M. Pitts and P. Dybjer, editors, Semantics and Logics of Computation, Publications of the Newton Institute, pages 131-184. Cambridge University Press, 1997. URL: https://doi.org/10.1017/CBO9780511526619.005.
  16. Michael Kaminski and Nissim Francez. Finite-Memory Automata. Theoretical Computer Science, 134(2):329-363, 1994. URL: https://doi.org/10.1016/0304-3975(94)90242-9.
  17. Frank Neven, Thomas Schwentick, and Victor Vianu. Finite state machines for strings over infinite alphabets. ACM Transactions on Computational Logic, 5(3):403-435, 2004. URL: https://doi.org/10.1145/1013560.1013562.
  18. Lê Thành Dũng Nguy~ên. Implicit automata in linear logic and categorical transducer theory. PhD thesis, Université Paris XIII (Sorbonne Paris Nord), December 2021. URL: https://theses.hal.science/tel-04132636.
  19. Lê Thành Dũng Nguy~ên and Cécilia Pradic. Implicit automata in typed λ-calculi I: aperiodicity in a non-commutative logic. In Artur Czumaj, Anuj Dawar, and Emanuela Merelli, editors, 47th International Colloquium on Automata, Languages, and Programming, ICALP 2020, July 8-11, 2020, Saarbrücken, Germany (Virtual Conference), volume 168 of LIPIcs, pages 135:1-135:20. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. URL: https://doi.org/10.4230/LIPIcs.ICALP.2020.135.
  20. Andrew M. Pitts. Nominal Sets: Names and Symmetry in Computer Science, volume 57 of Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, 2013. URL: https://doi.org/10.1017/CBO9781139084673.
  21. Cécilia Pradic and Ian Price. Implicit automata in λ-calculi iii: affine planar string-to-string functions, 2024. URL: https://arxiv.org/abs/2404.03985.
  22. Michał R. Przybyłek. A note on stone-Čech compactification in zfa, 2024. URL: https://arxiv.org/abs/2304.09986.
  23. Alexandra Silva, Filippo Bonchi, Marcello M. Bonsangue, and Jan J. M. M. Rutten. Generalizing determinization from automata to coalgebras. Logical Methods in Computer Science, 9(1), 2013. URL: https://doi.org/10.2168/LMCS-9(1:9)2013.
  24. Rafał Stefański. The single-use restriction for register automata and transducers over infinite alphabets. PhD thesis, University of Warsaw, 2023. Google Scholar
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