A quasi-local algorithm for checking bisimilarity

Bisimilarity is one of the most important relations for comparing the behaviour of formal systems in concurrency theory. Decision algorithms for bisimilarity in finite state systems are usually classified into two kinds: global algorithms are generally efficient but require to generate the whole state spaces in advance, local algorithms combine the verification of a system´s behaviour with the generation of the system´s state space, which is often more effective to determine that one system fails to be related to another. In this paper we propose a quasi-local algorithm with worst case time complexity O(m₁m₂), where m₁ and m₂ are the numbers of transitions in two labelled transition systems. With mild modifications, the algorithm can be easily adapted to decide similarity with the same time complexity. For deterministic systems, the algorithm can be simplified and runs in time O(min(m₁, m₂)).