Assume−Guarantee Verification for Probabilistic Systems
Marta Kwiatkowska‚ Gethin Norman‚ David Parker and Hongyang Qu
We present a compositional verification technique for systems that exhibit both probabilistic and nondeterministic behaviour. We adopt an assume-guarantee ap- proach to verification, where both the assumptions made about system components and the guarantees that they provide are regular safety properties, represented by finite automata. Unlike previous proposals for assume-guarantee reasoning about probabilistic systems, our approach does not require that components interact in a fully synchronous fashion. In addition, the compositional verification method is efficient and fully automated, based on a reduction to the problem of multi-objective probabilistic model checking. We present asymmetric and circular assume-guarantee rules, and show how they can be adapted to form quantitative queries, yielding lower and upper bounds on the actual probabilities that a property is satisfied. Our tech- niques have been implemented and applied to several large case studies, including instances where conventional probabilistic verification is infeasible.