Coupled similarity: the first 32 years

Abstract

Coupled similarity is an equivalence on (labeled) transition systems; its distinguishing power lies between (weak) bisimilarity and (may) testing equivalence. Its main feature, compared to weak bisimilarity, is an additional $$\tau $$-law that abstracts from the atomicity of internal choices among several possible branches, thus allowing for gradual commitments. The need for this $$\tau $$-law in applications was motivated by van Glabbeek and Vaandrager in 1988. Parrow and Sjodin coined the term coupled simulation in 1992 as a coinductive proof technique for the comparison of distributed (not “just” concurrent) systems, heavily exploiting gradual commitments. Over the years, coupled similarity also gained significance for the definition and analysis of the correctness of encodings, of action refinement and contraction, and of branching-time semantics for various process calculi. In this paper, we compare variants and formalizations of coupled similarity and highlight its relevance.