1 1/2-player stochastic StopWatch games

Abstract

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 212-player, 112-player, and 12-player games where the 12 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 112-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. © anasse chafik, fahima cheikh-alili, jean-françois condotta, and ivan varzinczak; licensed under creative commons license cc-by 4.0 28th international symposium on temporal representation and reasoning (time 2021).