Deciding bisimilarity is P-complete

Abstract

On finite labelled transition systems, the problems of deciding strong bisimilarity, observation equivalence, and observation congruence are P-complete under many-one NC-reducibility. As a consequence, algorithms for automated analysis of finite state systems based on bisimulation seem to be inherently sequential in the following sense: the design of an efficient parallel algorithm to solve any of these problems will require an exceedingly hard algorithmic breakthrough.