Correspondence:
[*]
Address for correspondence: I. Khmelnitsky, LSV, ENS Paris-Saclay
Note: [†] The work of this author was carried out in the framework of ReLaX, UMI2000 and also supported by ANR-17-CE40-0028 project BRAVAS. The work of this author was partly supported by ERC project EQualIS (FP7-308087)
Abstract: In the early two-thousands, Recursive Petri nets have been introduced in order to model distributed planning of multi-agent systems for which counters and recursivity were necessary. Although Recursive Petri nets strictly extend Petri nets and context-free grammars, most of the usual problems (reachability, coverability, finiteness, boundedness and termination) were known to be solvable by using non-primitive recursive algorithms. For almost all other extended Petri nets models containing a stack, the complexity of coverability and termination are unknown or strictly larger than EXPSPACE. In contrast, we establish here that for Recursive Petri nets, the coverability, termination, boundedness and finiteness problems are EXPSPACE-complete as for Petri nets. From an expressiveness point of view, we show that coverability languages of Recursive Petri nets strictly include the union of coverability languages of Petri nets and context-free languages. Thus we get a more powerful model than Petri net for free.
Keywords: Recursive Petri nets, Expressiveness, Complexity, Coverability, Termination, Finiteness
