Time Processes for Time Nets

The objective of this work is to give Merlin's time Petri nets a partial order semantics based on the nonsequential process semantics for untimed net systems. A time process of a time Petri net is defined as a traditionally constructed causal process whose events are labeled with occurrence times. In a valid timing, the occurrence times satisfy specific criteria that arise from the interaction between timing constraints and the causal ordering of events. The definitions lead to an efficient algorithm for checking the validness of timings. The relationship between the firing schedules of a time Petri net and the interleavings of time processes that preserve both causal and temporal order is shown to be bijective. Also, a sufficient condition is given for inferring invalidity of timings from initial subprocesses. Alternatively, the valid timings can be presented as sets of alternative linear constrains. From them, the existence of a valid timing can be de-