Qualitative Reachability in Stochastic BPA Games

Details Qualitative Reachability in Stochastic BPA Games Qualitative Reachability in Stochastic BPA Games

2010-02-27

arxiv.org/abs/1003.0118v1

Computer Science

Computer Science and Game Theory

Submitted to Information and Computation. 48 pages, 3 figures

Scientific paper

10.1016/j.ic.2011.02.002

We consider a class of infinite-state stochastic games generated by stateless pushdown automata (or, equivalently, 1-exit recursive state machines), where the winning objective is specified by a regular set of target configurations and a qualitative probability constraint `>0' or `=1'. The goal of one player is to maximize the probability of reaching the target set so that the constraint is satisfied, while the other player aims at the opposite. We show that the winner in such games can be determined in PTIME for the `>0' constraint, and both in NP and coNP for the `=1' constraint. Further, we prove that the winning regions for both players are regular, and we design algorithms which compute the associated finite-state automata. Finally, we show that winning strategies can be synthesized effectively.

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