Modelling Causality via Action Dependencies in Branching Time Semantics

We show that the approach of Mazurkiewicz trace theory --- modelling causalities between action occurrences using a global dependency relation --- can be generalised to branching time semantics (modelling both causalities and points of choice). More precisely, we show that the usual notion of bisimulation coincides with history preserving bisimulation and that usual testing coincides with "causal testing" for a system model with a global dependency relation. Keywords. Concurrency, formal semantics, equivalence notions, trace theory. 1 Introduction An important branch of research in concurrency theory was initiated by Mazurkiewicz [10]: Trace theory gives semantics for concurrent systems by presupposing a notion of dependency of actions describing which actions in a system may occur concurrently and which may not. This gives a "noninterleaving semantics" where causalities between action occurrences are represented. However, this is a special approach since it requires that it is indee..