Selective mu-calculus: New Modal Operators for Proving Properties on Reduced Transition Systems

Abstract

In model checking for temporal logic, the correctness of a (concurrent) system with respect to a desired behavior is verified by checking whether a structure that models the system satisfies a formula describing the behaviour. Most existing verification techniques, and in particular those defined for concurrent calculi like as CCS, are based on a representation of the concurrent system by means of a labelled transition system. In this approach to verification, state explosion is one of the most serious problems. In this paper we present a new temporal logic, the selective mu-calculus, with the property that only the actions occurring in a formula are relevant to check the formula itself. We prove that the selective mu-calculus is as powerful as the mu-calculus. We define the notion of ρ-bisimulation between transition systems: given a set of actions p,a transition system ρ-bisimulates another one if they have the same behaviour with respect to the actions in p. We prove that, if two transition systems are ρ-equivalent, they preserve all the selective mu-calculus formulae with occurring actions in ρ. Consequently, a formula with occurring actions ρ can be more efficiently checked on a transition system ρ-equivalent to the standard one, but smaller than it.KeywordsMu-CalculusState ExplosionAbstractionCCS