Refining Model Checking by Abstract Interpretation

Formal methods combining abstract interpretation and model-checking have been considered for automated analysis of software. In abstract model-checking, the semantics of an infinite transition system is abstracted to get a finite approximation on which temporal-logic/μ-calculus model-checking can be directly applied. The paper proposes two improvements of abstract model-checking which can be applied to infinite abstract transition systems: - A new combination of forwards and backwards abstract fixed-point model-checking computations for universal safety. It computes a more precise result than that computed by conjunction of the forward and backward analyses alone, without needing to refine the abstraction; - When abstraction is unsound (as can happen in minimum/maximum path-length problems), it is proposed to use the partial results of a classical combination of forward and backward abstract interpretation analyses for universal safety in order to reduce, on-the-fly, the concrete state space to be searched by model-checking.