Comparing Semantics Under Strong Timing of Petri Nets

The intention of the note is towards a framework for developing, studying and comparing observational semantics in the setting of a real-time true concurrent model. In particular, we introduce trace and bisimulation equivalences based on interleaving, step and causal net semantics in the setting of Petri nets with strong timing, i.e. Petri nets whose transitions are labeled with time firing intervals, can fire only if their lower time bounds are attained, and are forced to fire when their upper time bounds are reached. We deal with the relationships between the equivalences showing the discriminating power of the approaches of the linear-time - branching-time and interleaving - partial order spectra. This allows studying in complete detail the timing behaviour in addition to the degrees of relative concurrency and nondeterminism of processes.