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.

翻译：本文研究了平行平行组成操作器间断平行组成操作器的有限等式共性的存在。 在将进程代数 BCCSP 设定为一组有限动作的过程中,我们为各种模拟和(装饰的)痕量语义提供了有限、地面完整的异性化。 我们还表明,BCCSP 中包括两样并包含在可能的未来等同中的不相容性没有一种有限、地面完整的等同性;这一负面结果适用于所有嵌入的跟踪和嵌入的模拟语义学。