Translation from timed Petri nets with intervals on transitions to intervals on places (with urgency)

Abstract

Petri nets where, to my knowledge, the first theoretical model augmented with time constraints [Mer74], and the support of the first reachability algorithm of timed system [BM83, BD91]. Several approaches have been studied in order to add time on Petri nets: associating intervals on transitions [Mer74], or places [KDCD96], or arcs [Wal83, SDLdSS96], with or without urgency. However, the first comparisons between models where done years later [CMS99, BD99]. It had been shown in [CMS99] that, without urgency, all models are equivalent, in [BD99] that, with urgency, Petri nets with interval on transitions (TTPN) are not more powerful that Petri net with intervals on places (TPPN) or arcs (TLPN), and in [BV00] that TLPN are more powerful that TPPN and TTPN. This paper makes a step further in this area, showing that bounded TPPN are more powerful that 1-bounded TTPN. The proof is made using a translation: from a 1-bounded TTPN, a bounded TPPN is build, that is shown to be timely weakly bisimilar.