License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2023.118
URN: urn:nbn:de:0030-drops-181700
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/18170/
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Bouyer, Patricia ; Fijalkow, Nathanaël ; Randour, Mickael ; Vandenhove, Pierre

How to Play Optimally for Regular Objectives?

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Abstract

This paper studies two-player zero-sum games played on graphs and makes contributions toward the following question: given an objective, how much memory is required to play optimally for that objective? We study regular objectives, where the goal of one of the two players is that eventually the sequence of colors along the play belongs to some regular language of finite words. We obtain different characterizations of the chromatic memory requirements for such objectives for both players, from which we derive complexity-theoretic statements: deciding whether there exist small memory structures sufficient to play optimally is NP-complete for both players. Some of our characterization results apply to a more general class of objectives: topologically closed and topologically open sets.

BibTeX - Entry

@InProceedings{bouyer_et_al:LIPIcs.ICALP.2023.118,
  author =	{Bouyer, Patricia and Fijalkow, Nathana\"{e}l and Randour, Mickael and Vandenhove, Pierre},
  title =	{{How to Play Optimally for Regular Objectives?}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{118:1--118:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-278-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{261},
  editor =	{Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2023/18170},
  URN =		{urn:nbn:de:0030-drops-181700},
  doi =		{10.4230/LIPIcs.ICALP.2023.118},
  annote =	{Keywords: two-player games on graphs, strategy complexity, regular languages, finite-memory strategies, NP-completeness}
}

Keywords: two-player games on graphs, strategy complexity, regular languages, finite-memory strategies, NP-completeness
Collection: 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)
Issue Date: 2023
Date of publication: 05.07.2023

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