A Categorical Account of Bisimulation for Timed Higher Dimensional Automata

The intention of the paper is to show the applicability of the general categorical framework of open maps to the setting of real-time models of concurrency, in order to transfer general concepts of equivalences to the models. In particular, we define a category of timed higher dimensional automata (timed HDA), whose morphisms are to be thought of as simulations, and an accompanying (sub)category of observations, to which the corresponding notion of open maps is developed. We then use the open maps framework to obtain abstract bisimilation which is established to coincide with strong bisimulation on timed HDA. Further, we define a notion of unfolding timed HDA and characterize the structures so obtained as timed higher dimensional event structures (timed HDES). Finally, we establish the similarity of strong bisimulation on timed HDA and strong history preserving bisimulation on timed HDES.