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.2023.122
URN: urn:nbn:de:0030-drops-181740
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/18174/
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Casares, Antonio ; Ohlmann, Pierre

Characterising Memory in Infinite Games

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LIPIcs-ICALP-2023-122.pdf (1 MB)

Abstract

This paper is concerned with games of infinite duration played over potentially infinite graphs. Recently, Ohlmann (TheoretiCS 2023) presented a characterisation of objectives admitting optimal positional strategies, by means of universal graphs: an objective is positional if and only if it admits well-ordered monotone universal graphs. We extend Ohlmann’s characterisation to encompass (finite or infinite) memory upper bounds.
We prove that objectives admitting optimal strategies with ε-memory less than m (a memory that cannot be updated when reading an ε-edge) are exactly those which admit well-founded monotone universal graphs whose antichains have size bounded by m. We also give a characterisation of chromatic memory by means of appropriate universal structures. Our results apply to finite as well as infinite memory bounds (for instance, to objectives with finite but unbounded memory, or with countable memory strategies).
We illustrate the applicability of our framework by carrying out a few case studies, we provide examples witnessing limitations of our approach, and we discuss general closure properties which follow from our results.

BibTeX - Entry

@InProceedings{casares_et_al:LIPIcs.ICALP.2023.122,
  author =	{Casares, Antonio and Ohlmann, Pierre},
  title =	{{Characterising Memory in Infinite Games}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{122:1--122:18},
  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/2023/18174},
  URN =		{urn:nbn:de:0030-drops-181740},
  doi =		{10.4230/LIPIcs.ICALP.2023.122},
  annote =	{Keywords: Infinite duration games, Memory, Universal graphs}
}

Keywords: Infinite duration games, Memory, Universal graphs
Collection: 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)
Issue Date: 2023
Date of publication: 05.07.2023

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