Modelling real-time behavior with an interval time calculus

Abstract

We present an extension of Milner's CCS [Mil89] with interval time. The notion of time is introduced in terms of time intervals which specify when actions are allowed to occur. We define three equivalences: strong, timed weak, and weak bisimulation equivalence. The strong bisimulation equivalence refines the corresponding relation in CCS by requiring strongly bisimilar processes to have the same timing behavior, the weak bisimulation equivalence is in essence the weak bisimulation equivalence of CCS, while the timed weak equivalence lays strictly between strong and weak equivalence, since it in addition to weak bisimularity also considers the timing of observable actions.We define a refinement relation for processes specified in our calculus, which can be used to order processes according to their real-time behavior. This relation can be interpreted as “having a more precise timing specification than”. For example, the refinement relation can be used to show that an implementation (which normally has more precise time requirements) meets an abstract specification in which the time requirements are specified more generously.KeywordsExternal ActionInternal ActionOperational SemanticParallel CompositionLabel Transition SystemThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.