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arXiv · 2102.11166

On the Axiomatisability of Parallel Composition

Luca Aceto·Valentina Castiglioni·Anna Ingolfsdottir·Bas Luttik·Mathias R. Pedersen
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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.

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Luca Aceto, Valentina Castiglioni, Anna Ingolfsdottir, Bas Luttik, Mathias R. Pedersen. 2021-02-22. On the Axiomatisability of Parallel Composition. https://doi.org/10.46298/lmcs-18(1:15)2022

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