A Process Algebra with Multiple Clocks

In this report we propose a novel approach to the speciication of real-time behaviour based on process algebras. In contrast to the usual pattern, involving a xed, measurable, and global notion of time, we suggest to represent real-time constraints indirectly through uninterpreted clocks enforcing broadcast synchronization between processes. The concept of time underlying the use of clocks is abstract, qualitative, and local. Firstly, it is abstract since it does not prejudice any particular way of realizing a clock. Secondly, it is qualitative since it is not the absolute occurrence time or duration of actions that is constrained but their relative ordering and sequencing with respect to clocks. Finally, clocks admit a local notion of time since independent clocks can be used in diierent subprocesses, which may or may not be realized referring to the same time base. Technically, we present an extension of the Calculus of Communicating Systems CCS by multiple clocks, with associated timeout and clock ignore operators. The semantics of this process algebra, called PMC , is based on transition systems with separate action and clock transitions. Actions are insistent, so that local constraints on the progress of clocks can be expressed. In the report an axiomatization for strong bisimulation equivalence is given, and it is proven complete for a class of nite state processes, namely processes without recursion through static operators. It turns out that in contrast to other timed process algebras nite state processes in PMC enjoy a very simple and compact normal form. This is owing to the carefully chosen deenition of the timeout operator. We illustrate the exibility of PMC by presenting a variety of examples of rather diierent nature, and discuss clock persistence properties of several sublanguages of PMC.