The Theory of Universal Graphs for Infinite Duration Games

We introduce the notion of universal graphs as a tool for constructing algorithms solving games of infinite duration such as parity games and mean payoff games. In the first part we develop the theory of universal graphs, with two goals: showing an equivalence and normalisation result between differ...

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Veröffentlicht in:	Logical methods in computer science Jg. 18, Issue 3; H. 3
Hauptverfasser:	Colcombet, Thomas, Fijalkow, Nathanaël, Gawrychowski, Paweł, Ohlmann, Pierre
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	Logical Methods in Computer Science Association 07.09.2022 Logical Methods in Computer Science e.V
Schlagworte:	Computer Science computer science - computer science and game theory computer science - formal languages and automata theory
ISSN:	1860-5974, 1860-5974
Online-Zugang:	Volltext
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Beschreibung
Zusammenfassung:	We introduce the notion of universal graphs as a tool for constructing algorithms solving games of infinite duration such as parity games and mean payoff games. In the first part we develop the theory of universal graphs, with two goals: showing an equivalence and normalisation result between different recently introduced related models, and constructing generic value iteration algorithms for any positionally determined objective. In the second part we give four applications: to parity games, to mean payoff games, to a disjunction between a parity and a mean payoff objective, and to disjunctions of several mean payoff objectives. For each of these four cases we construct algorithms achieving or improving over the best known time and space complexity.
ISSN:	1860-5974 1860-5974
DOI:	10.46298/lmcs-18(3:29)2022