Bisimulation Minimization in an Automata-Theoretic Verification Framework

Abstract

Bisimulation is a seemingly attractive state-space minimization technique because it can be computed automatically and yields the smallest model preserving all mu -calculus formulas. It is considered impractical for symbolic model checking, however, because the required BDDs are prohibitively large for most designs. We revisit bisimulation minimization, this time in an automata-theoretic framework. Bisimulation has potential in this framework because after intersecting the design with the negation of the property, minimization can ignore most of the atomic propositions. We compute bisimulation using an algorithm due to Lee and Yannakakis that represents bisimulation relations by their equivalence classes and only explores reachable classes. This greatly improves on the time and memory usage of naive algorithms. We demonstrate that bisimulation is practical for many designs within the automata-theoretic framework. In most cases, however, the cost of performing this reduction still outweighs that of conventional model checking.