Jumping Petri Nets. Specific Properties

A Jumping Petri Net ([18], [12]), JPTN for short, is defined 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 JPTN's is undecidable, but it is decidable for finite JPTN's (FJPTN). In this paper we establish some specific properties and investigate the computational power of such nets, via the interleaving semantics. Thus, we show that the non-labelled JPTN's have the same computational power as the labelled or λ-labelled JPTN's. When final markings are considered, the power of JPTN's equals the power of Turing machines. The family of regular languages and the family of languages generated by JPTN's with finite state space are shown to be equal. Languages generated by FJPTN'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.) FJPTN'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 FJPTN's and a subclass of inhibitor nets is presented.