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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.

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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

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