Open maps and behavioural equivalences for timed stable event structures

Using methods of category theory, the paper introduces and investigates timed variants of partial-order based equivalence notions for concurrent and real-time processes represented by timed stable event structures. In particular, categories of the models under consideration are developed, and open maps based characterizations of timed variants of (Pratt trace, trace, testing and history hereditary preserving bisimulation) equivalences are provided.