Measuring Permissiveness in Parity Games: Mean-Payoff Parity Games Revisited

We study nondeterministic strategies in parity games with the aim of computing a most permissive winning strategy. Following earlier work, we measure permissiveness in terms of the average number/weight of transitions blocked by a strategy. Using a translation into mean-payoff parity games, we prove that deciding (the permissiveness of) a most permissive winning strategy is in NP∩coNP. Along the way, we provide a new study of mean-payoff parity games. In particular, we give a new algorithm for solving these games, which beats all previously known algorithms for this problem