Improved On-the-Fly Equivalence Checking Using Boolean Equation Systems

Equivalence checking is a classical verification method for ensuring the compatibility of a finite-state concurrent system (protocol) with its desired external behaviour (service) by comparing their underlying labeled transition systems ( Lts s) modulo an appropriate equivalence relation. The local (or on-the-fly) approach for equivalence checking combats state explosion by exploring the synchronous product of the Lts s incrementally, thus allowing an efficient detection of errors in complex systems. However, when the two Lts s being compared are equivalent, the on-the-fly approach is outperformed by the global one, which completely builds the Lts s and computes the equivalence classes between states using partition refinement. In this paper, we consider the approach based on translating the on-the-fly equivalence checking problem in terms of the local resolution of a boolean equation system ( Bes ). We propose two enhancements of the approach in the case of equivalent Lts s: a new, faster encoding of equivalence relations in terms of Bes s, and a new local Bes resolution algorithm with a better average complexity. These enhancements were incorporated into the Bisimulator 2.0 equivalence checker of the Cadp toolbox, and they led to significant performance improvements w.r.t. existing on-the-fly equivalence checking algorithms.