Abstraction refinement for termination

Authors:
Byron Cook;Andreas Podelski;Andrey Rybalchenko
Affiliations:
Microsoft Research, Cambridge;Max-Planck-Institut für Informatik, Saarbrücken;Max-Planck-Institut für Informatik, Saarbrücken
Venue:
SAS'05 Proceedings of the 12th international conference on Static Analysis
Year:
2005

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Abstract

Abstraction can often lead to spurious counterexamples. Counterexample-guided abstraction refinement is a method of strengthening abstractions based on the analysis of these spurious counterexamples. For invariance properties, a counterexample is a finite trace that violates the invariant; it is spurious if it is possible in the abstraction but not in the original system. When proving termination or other liveness properties of infinite-state systems, a useful notion of spurious counterexamples has remained an open problem. For this reason, no counterexample-guided abstraction refinement algorithm was known for termination. In this paper, we address this problem and present the first known automatic counterexample-guided abstraction refinement algorithm for termination proofs. We exploit recent results on transition invariants and transition predicate abstraction. We identify two reasons for spuriousness: abstractions that are too coarse, and candidate transition invariants that are too strong. Our counterexample-guided abstraction refinement algorithm successively weakens candidate transition invariants and refines the abstraction.