Refinement of Actions in Event Structures and Causal Trees

Abstract Refinement of actions allows one to design systems in a top-down style, changing the level of abstraction by interpreting actions on a higher level by more complicated processes on a lower level. We study action refinement in two connected models for true concurrency. The first model is an adaptation of prime event structures, called δ-free event structures. In this model refinement amounts to an expansion of events into event structures. Refinement is compatible with the history-preserving equivalence on event structures. The second model, called causal trees, is an explicit representation for event structures factored by history-preserving bisimulation. Causal trees are equipped with derived refinement operations, defined in an inductive way. The two models for refinement are shown to agree. Causal trees may, therefore, be used to construct a semantic calculus for algebras of process terms enriched with refinement, where terms are interpreted as classes of history-preserving equivalent event structures.