1½-Player Stochastic StopWatch Games

Stochastic timed games (STGs), introduced by Bouyer and Forejt, generalize continuous-time Markov chains and timed automata. Depending on the number of players – 2, 1, or 0 – subclasses of stochastic timed games are classified as 2 2 -player, 1 1 2 -player, and 1 2 -player games where the 1 2 symbolizes the presence of the stochastic player. The qualitative and quantitative reachability problem for STGs was studied in [10] and [1]. In this paper, we introduce stochastic stopwatch games (SSG), an extension of (STG) from clocks to stopwatches. We focus on 1 2 -player SSGs and prove that with two variables which can be either a clock or a stopwatch, qualitative reachability is decidable, whereas, if we increase the number of variables to three, with at least one stopwatch, the problem becomes undecidable. 2012 ACM Subject Classification Theory of computation → Timed and hybrid models