The Infinite Evolution Mechanism of ϵ-Bisimilarity

Yanfang Ma, Min Zhang

Abstract: In this paper, we focus on the convergence mechanism of ϵ-bisimulation under probabilistic processes to discuss the dynamic correctness of the software. Firstly, ϵ-limit bisimulation is defined for reflecting the dynamic relation between software specification and implementation. Some special ϵ-limit bisimulations are showed. Secondly, ϵ-bisimulation limit is proposed, which states the specification is the limit of implementation under ϵ-bisimulation. The uniqueness of ϵ-bisimulation limit and consistence with ϵ-bisimulation are presented. Finally, the substitutivity laws of ϵ-bisimulation limit with various combinators are proved.