A Finite Equational Base for CCS with Left Merge and Communication Merge

TL;DR

This paper develops a finite set of equations that completely characterizes the algebraic properties of a fragment of CCS, incorporating left merge and communication merge, especially when the set of actions is finite.

Contribution

It introduces a finite, ground-complete, and ω-complete equational base for CCS with specific operators, extending algebraic understanding of process calculi.

Findings

Finite equational base for CCS fragment established

Equational base is ground-complete and ω-complete

Base is finite when the set of actions is finite

Abstract

Using the left merge and communication merge from ACP, we present an equational base (i.e., a ground-complete and $\omega$-complete set of valid equations) for the fragment of CCS without recursion, restriction and relabelling. Our equational base is finite if the set of actions is finite.