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On the Size of Good-For-Games Rabin Automata and Its Link with the Memory in Muller Games

Authors Antonio Casares , Thomas Colcombet , Karoliina Lehtinen

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Author Details

Antonio Casares
  • LaBRI, Université de Bordeaux, France
Thomas Colcombet
  • CNRS, IRIF, Université Paris Cité, France
Karoliina Lehtinen
  • CNRS, Aix-Marseille Université, Université de Toulon, LIS, France

Funding

  • Colcombet, Thomas: ANR Delta and Duall

Acknowledgements

We would like to thank Marthe Bonamy and Pierre Charbit for their help with graph theory.

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Antonio Casares, Thomas Colcombet, and Karoliina Lehtinen. On the Size of Good-For-Games Rabin Automata and Its Link with the Memory in Muller Games. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 117:1-117:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022) https://doi.org/10.4230/LIPIcs.ICALP.2022.117

Abstract

In this paper, we look at good-for-games Rabin automata that recognise a Muller language (a language that is entirely characterised by the set of letters that appear infinitely often in each word). We establish that minimal such automata are exactly of the same size as the minimal memory required for winning Muller games that have this language as their winning condition. We show how to effectively construct such minimal automata. Finally, we establish that these automata can be exponentially more succinct than equivalent deterministic ones, thus proving as a consequence that chromatic memory for winning a Muller game can be exponentially larger than unconstrained memory.

Subject Classification

ACM Subject Classification
  • Theory of computation → Automata over infinite objects
Keywords
  • Infinite duration games
  • Muller games
  • Rabin conditions
  • omega-regular languages
  • memory in games
  • good-for-games automata

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