Stochastic Real-Time Games with Qualitative Timed Automata Objectives

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 ^ 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.