State Space Reduction of Rewrite Theories Using Invisible Transitions

Abstract

State 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.