Constraint-based analysis of concurrent probabilistic hybrid systems: An application to networked automation systems

In previous publications, the authors have introduced the notion of stochastic satisfiability modulo theories (SSMT) and the corresponding SiSAT solving algorithm, which provide a symbolic method for the reachability analysis of probabilistic hybrid systems. SSMT extends satisfiability modulo theories (SMT) with randomized (or stochastic), existential, and universal quantification, as known from stochastic propositional satisfiability. In this paper, we extend the SSMT-based procedures to the symbolic analysis of concurrent probabilistic hybrid systems. After formally introducing the computational model, we provide a mechanized translation scheme to encode probabilistic bounded reachability problems of concurrent probabilistic hybrid automata as linearly sized SSMT formulae, which in turn can be solved by the SiSAT tool. We furthermore propose an algorithmic enhancement which tailors SiSAT to probabilistic bounded reachability problems by caching and reusing solutions obtained on bounded reachability problems of smaller depth. An essential part of this article is devoted to a case study from the networked automation systems domain. We explain in detail the formal model in terms of concurrent probabilistic automata, its encoding into the SiSAT modeling language, and finally the automated quantitative analysis.