Perfect-Information Stochastic Parity Games

We show that in perfect-information stochastic parity games with a finite state space both players have optimal pure positional strategies. Contrary to the recent proofs of this fact by K. Chatterejee, M. Jurdzinski, T.A. Henzinger [2] and A.K. McIver, C.C. Morgan [14] the proof given in this paper proceeds by a straightforward induction on the number of outgoing transitions available to one of the players and is self-contained.

[1]  Rupak Majumdar,et al.  Quantitative solution of omega-regular games , 2004, J. Comput. Syst. Sci..

[2]  J. Filar,et al.  Competitive Markov Decision Processes , 1996 .

[3]  Donald A. Martin,et al.  The determinacy of Blackwell games , 1998, Journal of Symbolic Logic.

[4]  Rupak Majumdar,et al.  Quantitative solution of omega-regular games380872 , 2001, STOC '01.

[5]  L. Shapley,et al.  Stochastic Games* , 1953, Proceedings of the National Academy of Sciences.

[6]  Zohar Manna,et al.  Formal verification of probabilistic systems , 1997 .

[7]  A. Prasad Sistla,et al.  On Model-Checking for Fragments of µ-Calculus , 1993, CAV.

[8]  Anne Condon,et al.  The Complexity of Stochastic Games , 1992, Inf. Comput..

[9]  Annabelle McIver,et al.  Games, Probability and the Quantitative µ-Calculus qMµ , 2002, LPAR.

[10]  Krishnendu Chatterjee,et al.  Simple Stochastic Parity Games , 2003, CSL.

[11]  E. Allen Emerson,et al.  Tree automata, mu-calculus and determinacy , 1991, [1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science.

[12]  Krishnendu Chatterjee,et al.  Quantitative stochastic parity games , 2004, SODA '04.