Turn-Based Qualitative Solution of Concurrent Parity Games∗

We consider two-player concurrent games played on graphs, where at each state both players choose moves simultaneously and independently. We consider ω-regular winning conditions specified as parity objectives and study the qualitative winning mode, i.e., whether a player can win with probability arbitrarily close to 1 (limit-winning). We provide an efficient reduction from limit-winning concurrent parity games to winning turn-based parity games, where at each state only one player has a choice of moves. From a theoretical point of view, the reduction shows that for the qualitative winning mode, one can eliminate the concurrent nature of a game, and since turn-based games are well-studied, the reduction improves the understanding of concurrent games. From a practical point of view, the reduction provides algorithms for limitwinning concurrent parity games from algorithms for solving turn-based parity games. Every improvement in the latter algorithms will carry over to the former. In particular, using recent results on algorithms for turn-based parity games, we improve the best known time complexity to solve concurrent parity games when the set of available moves at each state is small.