Refinement and Difference for Probabilistic Automata

Benoit Delahaye (1) , Uli Fahrenberg (2) , Kim Guldstrand Larsen (3) , Axel Legay (2)

1 AELOS
2 ESTASYS - Efficient STAtistical methods in SYstems of systems
3 AAU - Aalborg University [Denmark]

This paper studies a difference operator for stochastic systems whose specifications are represented by Abstract Probabilistic Automata (APAs). In the case refinement fails between two specifications, the target of this operator is to produce a specification APA that represents all witness PAs of this failure. Our contribution is an algorithm that allows to approximate the difference of two APAs with arbitrary precision. Our technique relies on new quantitative notions of distances between APAs used to assess convergence of the approximations, as well as on an in-depth inspection of the refinement relation for APAs. The procedure is effective and not more complex to implement than refinement checking.

Domaines: Logique en informatique [cs.LO]

Benoit Delahaye, Uli Fahrenberg, Kim Guldstrand Larsen, Axel Legay. Refinement and Difference for Probabilistic Automata. Logical Methods in Computer Science, 2014, pp.LMCS-2013-936. ⟨hal-01010866⟩