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- W1490729071 abstract "We survey determinacy, definability, and complexity issues of Banach-Mazur games on finite and infinite graphs.Infinite games where two players take turns to move a token through a directed graph, thus tracing out an infinite path, have numerous applications in different branches of mathematicsand computer science. In the usual format,the possible moves of the players are given bythe edges of the graph; in each movea player takes the token from its current position along an edge to a next position. In Banach-Mazur games the players instead select in each move a emph{path} of arbitrary finite length rather than just an edge. In both cases the outcome of a play is an infinite path. A winning condition is thus given by a set of infinite paths which is often specified by a logical formula,for instance from S1S, LTL, or first-order logic. Banach-Mazur games have a long tradition in descriptive set theory and topology, and they have recently been shown to have interesting applications also in computer science, for instance for planning in nondeterministic domains,for the study of fairness in concurrent systems, andfor the semantics of timed automata. It turns out that Banach-Mazur games behave quite differently than the usual graph games. Often they admit simpler winning strategiesand more efficient algorithmic solutions. For instance, Banach-Mazur games with $omega$-regular winning conditions always have positional winning strategies, and winning positionsfor finite Banach-Mazur games with Muller winning conditionare computable in polynomial time." @default.
- W1490729071 created "2016-06-24" @default.
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- W1490729071 date "2008-01-01" @default.
- W1490729071 modified "2023-09-24" @default.
- W1490729071 title "Banach-Mazur Games on Graphs" @default.
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- W1490729071 doi "https://doi.org/10.4230/lipics.fsttcs.2008.1768" @default.
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