Process Algebra with Explicit Termination

In ACP-style process algebra, the interpretation of a constant atomic action combines action execution with termination. In a setting with timing, different forms of termination can be distinguished: some time termination, current time slice termination, urgent termination, termination in a virtual state. In a setting with the silent action τ , we also have silent termination. This leads to problems with the interpretation of atomic actions in timed theories that involve some form of the empty process or some form of the silent action. Reflection on these problems lead to a re-design of basic process algebra, where action execution and termination are separated. Instead of actions as constants, we have action prefix operators. Sequential composition remains a basic operator, and thus we have two basic constants for termination, δ for unsuccessful termination (deadlock) and ǫ for successful termination (skip). Standard BPA, PA, ACP become SRM specifications of the new approach. The new approach has definite advantages over the standard approach.