The parallel composition of processes

TL;DR

This paper models parallel process composition using category theory, specifically spans of reflexive graphs, and derives classical process algebra operations from monoid objects, emphasizing broadcast communication protocols.

Contribution

It introduces a categorical framework for parallel process composition, deriving classical process algebra operations from monoid objects in a compact closed category.

Findings

Parallel composition modeled categorically as spans of reflexive graphs.

Classical process algebra operations derived from monoid objects.

Framework emphasizes broadcast communication protocols.

Abstract

We suggest that the canonical parallel operation of processes is composition in a well-supported compact closed category of spans of reflexive graphs. We present the parallel operations of classical process algebras as derived operations arising from monoid objects in such a category, representing the fact that they are protocols based on an underlying broadcast communication.