### Stochastic Real-Time Games with Qualitative Timed Automata Objectives

by *
Tomáš Brázdil,
Jan Krčál,
Jan Křetínský,
Antonín Kučera,
Vojtěch Řehák,
* A full version of the paper presented at CONCUR 2010. August 2010, 39 pages.

**FIMU-RS-2010-05.**
Available as *Postscript*,
**PDF**.

#### 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 I is to play in such a way that the
play (a timed word) is accepted by the timed automaton with probability
one. Player II aims at the opposite. We prove that whenever
player I 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.