Assume-Guarantee Abstraction Refinement for Probabilistic Systems

We describe an automated technique for assume-guarantee style checking of strong simulation between a system and a specification, both expressed as non-deterministic Labeled Probabilistic Transition Systems (LPTSes). We first characterize counterexamples to strong simulation as "stochastic" trees and show that simpler structures are insufficient. Then, we use these trees in an abstraction refinement algorithm that computes the assumptions for assume-guarantee reasoning as conservative LPTS abstractions of some of the system components. The abstractions are automatically refined based on tree counterexamples obtained from failed simulation checks with the remaining components. We have implemented the algorithms for counterexample generation and assume-guarantee abstraction refinement and report encouraging results.