Unique Parallel Decomposition in Branching and Weak Bisimulation Semantics

Abstract

We consider the property of unique parallel decomposition modulo branching and weak bisimilarity. First, we show that totally normed behaviours always have parallel decompositions, but that these are not necessarily unique. Then, we establish that finite behaviours have unique parallel decompositions. We derive the latter result from a general theorem about unique decompositions in partial commutative monoids.

A procedure for splitting data-aware processes and its application to coordination

“…Other contributions to the theory of process decomposition include the work of Kučera [36] (decidability results and constructions of decompositions), Luttik and van Oostrom [39] (generalization of decomposition to partial commutative monoids), Luttik [38] (unique parallel decomposition modulo branching and weak bisimilarity), and Dreier et al [17] (decomposition in the applied π -calculus).…”

On Unique Decomposition of Processes in the Applied π-Calculus

“…They show that if the calculus satisfies certain properties, the unique decomposition result follows directly. Recently Luttik also extended this technique for weak bisimilarity [8]. Unfortunately this result cannot be employed in the Applied π-Calculus as active substitutions are minimal elements (with respect to the transition relation) different from 0.…”