Playing Safe, Ten Years Later

We consider two-player games over graphs and give tight bounds on the memory size of strategies ensuring safety objectives. More specifically, we show that the minimal number of memory states of a strategy ensuring a safety objective is given by the size of the maximal antichain of left quotients wi...

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Bibliographic Details
Published in:	Logical methods in computer science Vol. 20, Issue 1
Main Authors:	Colcombet, Thomas, Fijalkow, Nathanaël, Horn, Florian
Format:	Journal Article
Language:	English
Published:	Logical Methods in Computer Science Association 01.01.2024 Logical Methods in Computer Science e.V
Subjects:	Computer Science computer science - computer science and game theory computer science - formal languages and automata theory Logic in Computer Science Games on graphs, Memory
ISSN:	1860-5974, 1860-5974
Online Access:	Get full text
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Summary:	We consider two-player games over graphs and give tight bounds on the memory size of strategies ensuring safety objectives. More specifically, we show that the minimal number of memory states of a strategy ensuring a safety objective is given by the size of the maximal antichain of left quotients with respect to language inclusion. This result holds for all safety objectives without any regularity assumptions. We give several applications of this general principle. In particular, we characterize the exact memory requirements for the opponent in generalized reachability games, and we prove the existence of positional strategies in games with counters.
ISSN:	1860-5974 1860-5974
DOI:	10.46298/lmcs-20(1:10)2024