On the Axiomatisability of Parallel Composition

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