Qualitative concurrent parity games Chatterjee, Krishnendu ; https://orcid.org/0000-0002-4561-241X De Alfaro, Luca Henzinger, Thomas A ; https://orcid.org/0000−0002−2985−7724 We consider two-player games played on a finite state space for an infinite number of rounds. The games are concurrent: in each round, the two players (player 1 and player 2) choose their moves independently and simultaneously; the current state and the two moves determine the successor state. We consider ω-regular winning conditions specified as parity objectives. Both players are allowed to use randomization when choosing their moves. We study the computation of the limit-winning set of states, consisting of the states where the sup-inf value of the game for player 1 is 1: in other words, a state is limit-winning if player 1 can ensure a probability of winning arbitrarily close to 1. We show that the limit-winning set can be computed in O(n2d+2) time, where n is the size of the game structure and 2d is the number of priorities (or colors). The membership problem of whether a state belongs to the limit-winning set can be decided in NP ∩ coNP. While this complexity is the same as for the simpler class of turn-based parity games, where in each state only one of the two players has a choice of moves, our algorithms are considerably more involved than those for turn-based games. This is because concurrent games do not satisfy two of the most fundamental properties of turn-based parity games. First, in concurrent games limit-winning strategies require randomization; and second, they require infinite memory. ACM 2011 info:eu-repo/semantics/article doc-type:Article Article http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/3354 Chatterjee K, De Alfaro L, Henzinger TA. Qualitative concurrent parity games. <i>ACM Transactions on Computational Logic</i>. 2011;12(4). doi:<a href="https://doi.org/10.1145/1970398.1970404">10.1145/1970398.1970404</a> eng info:eu-repo/semantics/altIdentifier/doi/10.1145/1970398.1970404 info:eu-repo/semantics/altIdentifier/wos/000296202300006 info:eu-repo/semantics/closedAccess