On Two-Sided Approximate Model-Checking: Problem Formulation and Solution via Finite Topologies

We give a general formulation of approximate model-checking, in which both underand 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.