Qualitative Concurrent Stochastic Games with Imperfect Information
ICALP '09 Proceedings of the 36th Internatilonal Collogquium on Automata, Languages and Programming: Part II
Solving simple stochastic tail games
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Qualitative analysis of partially-observable Markov decision processes
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Probabilistic automata on infinite words: decidability and undecidability results
ATVA'10 Proceedings of the 8th international conference on Automated technology for verification and analysis
The complexity of partial-observation parity games
LPAR'10 Proceedings of the 17th international conference on Logic for programming, artificial intelligence, and reasoning
Probabilistic modal µ-calculus with independent product
FOSSACS'11/ETAPS'11 Proceedings of the 14th international conference on Foundations of software science and computational structures: part of the joint European conferences on theory and practice of software
Journal of the ACM (JACM)
Fair adversaries and randomization in two-player games
FOSSACS'10 Proceedings of the 13th international conference on Foundations of Software Science and Computational Structures
Partial-Observation Stochastic Games: How to Win When Belief Fails
LICS '12 Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science
Decidable Problems for Probabilistic Automata on Infinite Words
LICS '12 Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science
Equivalence of games with probabilistic uncertainty and partial-observation games
ATVA'12 Proceedings of the 10th international conference on Automated Technology for Verification and Analysis
A survey of partial-observation stochastic parity games
Formal Methods in System Design
Hi-index | 0.00 |
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, Buchi or co-Buchi winning objectives. We prove two qualitative determinacy results. First, in a reachability game either player $1$ can achieve almost-surely the reachability objective, or player 2 can ensure surely the complementary safety objective, or both players have positively winning strategies. Second, in a Buchi game if player 1 cannot achieve almost-surely the Buchi objective, then player 2 can ensure positively the complementary co-Buchi 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 fix-point algorithms for deciding which player has an almost-surely winning or a positively winning strategy and for computing the finite memory strategy. Complexity ranges from EXPTIME to 2-EXPTIME with matching lower bounds, and better complexity can be achieved for some special cases where one of the players is better informed than her opponent.