True Concurrent Equivalences in Time Petri Nets *

Abstract

The intention of the paper is towards a framework for developing, studying and comparing observational equivalences in the setting of a real-time true concurrent model. In particular, we introduce a family of trace and bisimulation equivalences in interleaving, step, partial order and causal net semantics in the setting of time Petri nets (elementary net systems 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) [3]. 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 and construct a hierarchy of equivalent classes of time Petri nets. This allows studying in complete detail the timing behaviour in addition to the degrees of relative concurrency and nondeterminism of processes.