Complexity Bounds for Regular Games (Extended Abstract)
Paul Hunter · 2005
Abstract. We consider the complexity of infinite games played on finite graphs. We establish a framework in which the expressiveness and succinctness of different types of winning conditions can be compared. We show that the problem of deciding the winner in Muller games is PSPACE-complete. This is then used to establish PSPACE-completeness for Emerson-Lei games and for games described by Zielonka DAGs. Adaptations of the proof show PSPACE-completeness for the emptiness problem for Muller automata as well as the model-checking problem for such automata on regular trees. We also show co-NP-completeness for two classes of union-closed games: games specified by a basis and superset Muller games. 1