English

On the Axiomatisability of Parallel Composition

Logic in Computer Science 2023-06-22 v5

Abstract

This paper studies the existence of finite equational axiomatisations of the interleaving parallel composition operator modulo the behavioural equivalences in van Glabbeek's linear time-branching time spectrum. In the setting of the process algebra BCCSP over a finite set of actions, we provide finite, ground-complete axiomatisations for various simulation and (decorated) trace semantics. We also show that no congruence over BCCSP that includes bisimilarity and is included in possible futures equivalence has a finite, ground-complete axiomatisation; this negative result applies to all the nested trace and nested simulation semantics.

Keywords

Cite

@article{arxiv.2102.11166,
  title  = {On the Axiomatisability of Parallel Composition},
  author = {Luca Aceto and Valentina Castiglioni and Anna Ingolfsdottir and Bas Luttik and Mathias R. Pedersen},
  journal= {arXiv preprint arXiv:2102.11166},
  year   = {2023}
}
R2 v1 2026-06-23T23:24:33.374Z