Action Refinement for Probabilistic Processes with True Concurrency Models

In this paper, we develop techniques of action refinement for probabilistic processes within the context of a probabilistic process algebra. A semantic counterpart is carried out in a non-interleaving causality based setting, probabilistic bundle event structures. We show that our refinement notion has the following nice properties: the behaviour of the refined system can be inferred compositionally from the behaviour of the original system and from the behaviour of the systems substituted for actions; the probabilistic extensions of pomset trace equivalence and history preserving bisimulation equivalence are both congruences under the refinement; and with respect to a cpo-based denotational semantics the syntactic and semantic refinements coincide with each other up to the aforementioned equivalence relations when the internal actions are