Luca Aceto ; Valentina Castiglioni ; Anna Ingolfsdottir ; Bas Luttik ; Mathias R. Pedersen - On the Axiomatisability of Parallel Composition

lmcs:7217 - Logical Methods in Computer Science, January 19, 2022, Volume 18, Issue 1 - https://doi.org/10.46298/lmcs-18(1:15)2022
On the Axiomatisability of Parallel Composition

Authors: Luca Aceto ; Valentina Castiglioni ; Anna Ingolfsdottir ; Bas Luttik ; Mathias R. Pedersen

    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.


    Volume: Volume 18, Issue 1
    Published on: January 19, 2022
    Accepted on: December 2, 2021
    Submitted on: February 24, 2021
    Keywords: Computer Science - Logic in Computer Science

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