Jumping Petri Nets. Specific Properties Jumping Petri Nets. Speciic Properties

A Jumping Petri Net ((18], 12]), JP T N for short, is deened as a classical net which can spontaneously jump from a marking to another one. In 18] it has been shown that the reachability problem for JP T N 's is undecidable, but it is decidable for nite JP T N 's (FJPTN). In this paper we establish some speciic properties and investigate the computational power of such nets, via the interleaving semantics. Thus, we show that the non-labelled JP T N 's have the same computational power as the labelled or-labelled JP T N 's. When nal markings are considered, the power of JP T N 's equals the power of Tur-ing machines. The family of regular languages and the family of languages generated by JP T N 's with nite state space are shown to be equal. Languages generated by F JP T N 's can be represented in terms of regular languages and substitutions with classical Petri net languages. This characterization result leads to many important consequences , e.g. the recursiveness (context-sensitiveness, resp.) of languages generated by arbitrarily labelled (labelled, resp.) F JP T N 's. A pumping lemma for nonterminal jumping net languages is also established. Finally, some comparisons between families of languages are given, and a connection between F JP T N 's and a subclass of inhibitor nets is presented.