eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2009-02-19
207
218
10.4230/LIPIcs.STACS.2009.1837
article
Qualitative Reachability in Stochastic BPA Games
Brazdil, Tomas
Brozek, Vaclav
Kucera, Antonin
Obdrzalek, Jan
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 $\textbf{NP} \cap \textbf{co-NP}$. 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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol003-stacs2009/LIPIcs.STACS.2009.1837/LIPIcs.STACS.2009.1837.pdf
Stochastic games
Reachability
Pushdown automata