On two-sided approximate model-checking: problem formulation and solution via finite topologies

Abstract

We give a general formulation of approximate model- checking, in which both under- and over-approximations are propagated to give two-sided approximations of the denotation set of an arbitrarily complex formula. As our specification language, we use the modal μ-calculus, since it subsumes standard linear and branching temporal logics over transition systems like LTL, CTL and CTL*. We give a general construction of a topological finite approximation scheme for a Kripke model from a state-space discretization via an A/D-map and its induced finite topology. We further show that under natural coherence conditions, any finite approximation scheme can be refined by a topological one.