Unique Parallel Decomposition for the Pi-calculus

TL;DR

This paper proves that finite processes in the pi-calculus have a unique parallel decomposition into indecomposable components, using a general technique based on decomposition orders.

Contribution

It establishes the property of unique parallel decomposition for finite pi-calculus processes under bisimilarity, advancing understanding of process algebra structure.

Findings

Finite pi-calculus processes satisfy unique parallel decomposition

Results hold under both strong and weak bisimilarity

Uses a general technique with decomposition orders

Abstract

A (fragment of a) process algebra satisfies unique parallel decomposition if the definable behaviours admit a unique decomposition into indecomposable parallel components. In this paper we prove that finite processes of the pi-calculus, i.e. processes that perform no infinite executions, satisfy this property modulo strong bisimilarity and weak bisimilarity. Our results are obtained by an application of a general technique for establishing unique parallel decomposition using decomposition orders.