Towards action refinement for concurrent systems with causal ambiguity

Action refinement is a core operation in the hierarchical design methodology for concurrent systems. In this paper we develop an action refinement approach for concurrent systems with the notion of causal ambiguity, which often exists and appears in real application areas. The systems are modelled in terms of event structures with causal ambiguity. We demonstrate that the behavior of the lower-level system is itself derived from the behavior of the high-level system : Under a certain partial order semantics, the behavior of the refined system can be inferred compositionally from the behavior of the original system and from the behavior of the systems used to substitute actions with explicitly represented start points. Furthermore, a variant of a linear-time equivalence termed pomset trace equivalence and a variant of a branching-time equivalence termed history preserving bisimulation equivalence based on the partial order semantics are both congruences under the refinement. The refinement operation behaves thus well and meets the commonly expected properties.