Parity and Exploration Games on Infinite Graphs

Hugo Gimbert (1)

1 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications

This paper examines two players' turn-based perfect-information games played on infinite graphs. Our attention is focused on the classes of games where winning conditions are boolean combinations of the following two conditions: (1) the first one states that an infinite play is won by player $0$ if during the play infinitely many different vertices were visited, (2) the second one is the well known parity condition generalized to a countable number of priorities. We show that, in most cases, both players have positional winning strategies and we characterize their respective winning sets. In the special case of pushdown graphs, we use these results to show that the sets of winning positions are regular and we show how to compute them as well as positional winning strategies in exponential time.

Domaines: Informatique et théorie des jeux [cs.GT]

Hugo Gimbert. Parity and Exploration Games on Infinite Graphs. CSL 2004, Sep 2004, Karpacz, Poland. pp.56-70, ⟨10.1007/b100120⟩. ⟨hal-00160739v1⟩