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CORR
2006
Springer

Positional Determinacy of Games with Infinitely Many Priorities

13 years 3 months ago
Positional Determinacy of Games with Infinitely Many Priorities
We study two-player games of infinite duration that are played on finite or infinite game graphs. A winning strategy for such a game is positional if it only depends on the current position, and not on the history of the play. A game is positionally determined if, from each position, one of the two players has a positional winning strategy. The theory of such games is well studied for winning conditions that are defined in terms of a mapping that assigns to each position a priority from a finite set C. Specifically, in Muller games the winner of a play is determined by the set of those priorities that have been seen infinitely often; an important special case are parity games where the least (or greatest) priority occurring infinitely often determines the winner. It is well-known that parity games are positionally determined whereas Muller games are determined via finite-memory strategies. In this paper, we extend this theory to the case of games with infinitely many priorities. Such g...
Erich Grädel, Igor Walukiewicz
Added 11 Dec 2010
Updated 11 Dec 2010
Type Journal
Year 2006
Where CORR
Authors Erich Grädel, Igor Walukiewicz
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