Complexity of Decision Problems for Mixed and Modal Specifications

International audienceWe present a new algorithm for solving Simple Stochastic Games (SSGs). This algorithm is based on an exhaustive search of a special kind of positional optimal strategies, the f-strategies. The running time is , where and are respectively the number of vertices, random vertices and edges, and the maximum bit-length of a transition probability. Our algorithm improves existing algorithms for solving SSGs in three aspects. First, our algorithm performs well on SSGs with few random vertices, second it does not rely on linear or quadratic programming, third it applies to all SSGs, not only stopping SSGs