Thread-modular counter abstraction: automated safety and termination proofs of parameterized software by reduction to sequential program verification

Abstract

Parameterized programs are composed of an arbitrary number of concurrent, infinite-state threads. Automated safety and liveness proofs of such parameterized software are hard; state-of-the-art methods for their formal verification rely on intricate abstractions and complicated proof techniques that impede automation. In this paper, we introduce thread-modular counter abstraction (TMCA), a lean new abstraction technique to replace the existing heavy proof machinery. TMCA is a structured abstraction framework built from a novel combination of counter abstraction, thread-modular reasoning, and predicate abstraction. Its major strength lies in reducing the parameterized verification problem to the sequential setting, for which powerful proof procedures, efficient heuristics, and effective automated tools have been developed over the past decades. In this work, we first introduce the TMCA abstraction paradigm, then present a fully automated method for parameterized safety proofs, and finally discuss its application to automated termination and liveness proofs of parameterized software.