A uniformization-based algorithm for continuous-time stochastic games model checking

Abstract

Continuous-time Stochastic Game (CTSG) can be seen as a proper model to analyze probabilistic, non-deterministic, and competitive behaviors as found in Stochastic Multi-Player Game (SMG). The difference is that in an SMG the system under design is analyzed in the discrete-time setting. In comparison, in a CTSG, the system transitions occur in the continuous-time setting with exponentially distributed delays. This paper focuses on the model checking of CTSGs and presents a uniformization-based algorithm, called TPA, to approximate the time-bounded reachability probabilities with an arbitrary error bound. We concentrate on CTSGs with bounded transition rates. To illustrate the strength points of our algorithm, we have implemented it in Java, developed some large examples, and compared our results with the ones from an existing algorithm which is based on discretization. In order to express properties specifying these types of probabilities in the continuous-time setting, we adjusted the existing temporal logic, PATL. Thus, properties like the following can be stated and checked over a CTSG: “A coalition of players has a strategy to guarantee to reach the target states within time boundt∈Q⩾0with a probability equal to or greater than threshold P, regardless of the other players' behaviors.”