State Space Reduction of Rewrite Theories Using Invisible Transitions

Abstract

AbstractState space explosion is the hardest challenge to the effective application of model checking methods. We present a new technique for achieving drastic state space reductions that can be applied to a very wide range of concurrent systems, namely any system specified as a rewrite theory. Given a rewrite theory \(\mathcal{R}=(\Sigma,E,R)\) whose equational part (Σ,E) specifies some state predicates P, we identify a subset S ⊆ R of rewrite rules that are P-invisible, so that rewriting with S does not change the truth value of the predicates P. We then use S to construct a reduced rewrite theory \(\mathcal{R}/S\) in which all states reachable by S-transitions become identified. We show that if \(\mathcal{R}/S\) satisfies reasonable executability assumptions, then it is in fact stuttering bisimilar to \(\mathcal{R}\) and therefore both satisfy the same \({\it CTL}^{\rm \ast}_{\rm -{\it X}}\) formulas. We can then use the typically much smaller \(\mathcal{R}/S\) to verify such formulas. We show through several case studies that the reductions achievable this way can be huge in practice. Furthermore, we also present a generalization of our construction that instead uses a stuttering simulation and can be applied to an even broader class of systems.KeywordsModel CheckProof ObligationConcurrent SystemKripke StructureRewrite TheoryThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.