Analysing Mutual Exclusion using Process Algebra with Signals

TL;DR

This paper demonstrates that extending process algebra with a signalling operator enables accurate modeling and verification of mutual exclusion algorithms like Peterson's and Lamport's bakery, under realistic memory assumptions.

Contribution

Introducing a signalling operator to process algebra, which allows precise modeling of mutual exclusion protocols without fairness assumptions, confirmed through correctness proofs.

Findings

Peterson's algorithm verified for two processes under realistic assumptions.

Lamport's bakery algorithm also verified with the extended calculus.

More than two processes require stronger memory assumptions for correctness.

Abstract

In contrast to common belief, the Calculus of Communicating Systems (CCS) and similar process algebras lack the expressive power to accurately capture mutual exclusion protocols without enriching the language with fairness assumptions. Adding a fairness assumption to implement a mutual exclusion protocol seems counter-intuitive. We employ a signalling operator, which can be combined with CCS, or other process calculi, and show that this minimal extension is expressive enough to model mutual exclusion: we confirm the correctness of Peterson's mutual exclusion algorithm for two processes, as well as Lamport's bakery algorithm, under reasonable assumptions on the underlying memory model. The correctness of Peterson's algorithm for more than two processes requires stronger, less realistic assumptions on the underlying memory model.