The Influence of Durational Actions on Time Equivalences

The hierarchy of untimed equivalences is well understood for action-based systems. This is not the case for timed systems, where it is, for example, possible to detect concurrency by single timed action execution. To clarify the connection between equivalences in timed systems, a timed version of configuration structures is introduced together with timed equivalence notions adapted from untimed equivalences. There actions (events) have an occurrence time and a duration. The result of this paper is that all timed versions of the equivalences from [15] have the same relative discriminating power as in the untimed case, except that interleaving and step (for trace and bisimulation) equivalences coincide if systems are considered where every action must have a positive duration.