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