In the past, partial order reduction has been used successfully to combat the state explosion problem in the context of model checking for non-probabilistic systems. For both linear time and branching time specifications, methods have been developed to apply partial order reduction in the context of model checking. Only recently, results were published that give criteria on applying partial order reduction for verifying quantitative linear time properties for probabilistic systems. This paper presents partial order reduction criteria for Markov decision processes and branching time properties, such as formulas of probabilistic computation tree logic. Moreover, we provide a comparison of the results established so far about reduction conditions for Markov decision processes.

Abstract. A stochastic timed automaton is a purely stochastic process defined on a timed automaton, in which both delays and discrete choices are made randomly. We study the almost-sure model-checking problem for this model, that is, given a stochastic timed automaton A and a property ϕ, we want to decide whether A satisfies ϕ with probability 1. In this paper, we identify several classes of automata and of properties for which this can be decided. The proof relies on the construction of a finite abstraction, called the thick graph, that we interpret as a finite Markov chain, and for which we can decide the almost-sure model-checking problem. Correctness of the abstraction holds when automata are almost-surely fair, which we show, is the case for two large classes of systems, singleclock automata and so-called weak-reactive automata. Techniques employed in this article gather tools from real-time verification and probabilistic verification, as well as topological games played on timed automata.

No abstract

No abstract

No abstract