Qualitative Determinacy and Decidability of Stochastic Games with Signals

We consider the standard model of finite two-person zero-sum stochastic games with signals. We are interested in the existence of almost-surely winning or positively winning strategies, under reachability, safety, B¨uchi or coB¨uchi winning objectives. We prove two qualitative determinacy results. First, in a reachability game either player ¤ can achieve almost-surely the reachability objective, or player ¥ can ensure surely the complementary safety objective, or both players have positively winning strategies. Second, in a B¨uchi game if player ¤ cannot achieve almostsurely the B¨uchi objective, then player ¥ can ensure positively the complementary co-B¨uchi objective. We prove that players only need strategies with finite-memory, whose sizes range from no memory at all to doubly-exponential number of states, with matching lower bounds. Together with the qualitative determinacy results, we also provide fixpoint algorithms for deciding which player has an almostsurely winn...

• Type: Conference
• Year: 2009
• Where: LICS
• Authors: Nathalie Bertrand, Blaise Genest, Hugo Gimbert
• Keywords: CoB¨uchi Winning Objectives, Computer Science, LICS 2009, Lower Bounds, Zero-sum Stochastic Games