Abstract
We consider two-player stochastic games over real-time probabilistic processes where the winning objective is specified by a timed automaton. The goal of player □ is to play in such a way that the play (a timed word) is accepted by the timed automaton with probability one. Player \(\Diamond\) aims at the opposite. We prove that whenever player □ has a winning strategy, then she also has a strategy that can be specified by a timed automaton. The strategy automaton reads the history of a play, and the decisions taken by the strategy depend only on the region of the resulting configuration. We also give an exponential-time algorithm which computes a winning timed automaton strategy if it exists.
The authors are supported by the Alexander von Humboldt Foundation (T. Brázdil), the Institute for Theoretical Computer Science, project No. 1M0545 (J. Krčál), Brno Municipality (J. Křetínský), and the Czech Science Foundation, grants No. P202/10/1469 (A. Kučera) and No. 201/08/P459 (V. Řehák).
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Brázdil, T., Krčál, J., Křetínský, J., Kučera, A., Řehák, V. (2010). Stochastic Real-Time Games with Qualitative Timed Automata Objectives. In: Gastin, P., Laroussinie, F. (eds) CONCUR 2010 - Concurrency Theory. CONCUR 2010. Lecture Notes in Computer Science, vol 6269. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15375-4_15
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