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.
Bibliographical noteFunding Information:
This work has been supported by the project ‘Open Problems in the Equational Logic of Processes’ (OPEL) of the Icelandic Research Fund (grant No. 196050-051).
© L. Aceto, V. Castiglioni, A. Ingólfsdóttir, B. Luttik, and M. R. Pedersen.
- Linear time-branching time spectrum
- Parallel composition