Analyzing divergence in bisimulation semantics

Abstract

Some bisimulation based abstract equivalence relations may equate divergent systems with non-divergent ones, examples including weak bisimulation equivalence and branching bisimulation equivalence. Thus extra efforts are needed to analyze divergence for the compared systems. In this paper we propose a new method for analyzing divergence in bisimulation semantics, which relies only on simple observations of individual transitions. We show that this method can verify several typical divergence preserving bisimulation equivalences including two well-known ones. As an application case study, we use the proposed method to verify the HSY collision stack to draw the conclusion that the stack implementation is correct in terms of linearizability with lock-free progress condition.