Branching bisimilarity is an equivalence indeed!

Abstract

This note presents a detailed proof of a result in the theory of concurrency semantics that is already considered folklore, namely that branching bisimilarity is an equivalence relation. The “simple proof”, which in the literature is always assumed to exist, is shown to be incorrect. The proof in this note is based on the notion of a semi-branching bisimulation taken from (Van Glabbeek and Weijland, 1991). Branching bisimilarity can equivalently be defined in terms of semi-branching bisimulations; the results suggest that such a definition is more intuitive than the original definition of Van Glabbeek and Weijland (1989).