Towards action refinement for true concurrent real time

Action refinement is an essential operation in the design of concurrent systems, real-time or not. In this paper we develop a theory of action refinement in a real-time non-interleaving causality based setting, a timed extension of bundle event structures that allows for urgent interactions to model timeout. The syntactic action refinement operation is presented in a timed process algebra as incorporated in the internationally standardised specification language LOTOS. We show that the behaviour of the refined system can be inferred compositionally from the behaviour of the original system and from the behaviour of the processes substituted for actions with explicitly represented start points, that the timed versions of a linear-time equivalence, termed pomset trace equivalence, and a branching-time equivalence, termed history preserving bisimulation equivalence, are both congruences under the refinement, and that the syntactic and semantic action refinements developed coincide under these equivalence relations with respect to a metric denotational semantics. Therefore, our refinement operations behave well. They meet the commonly expected properties.