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 the strategy. Using a translation into mean-payoff parity games, we prove that the problem of computing (the permissiveness of) a most permissive winning strategy is in NP intersected coNP. Along the way, we provide a new study of mean-payoff parity games. In particular, we prove that the opponent player has a memoryless optimal strategy and give a new algorithm for solving these games. 
Patricia Bouyer, Nicolas Markey, J\"org Olschewski, Michael Ummels
cs.LO cs.GT