Coverability, Termination, and Finiteness in Recursive Petri Nets

TL;DR

This paper proves that key problems in Recursive Petri nets are EXPSPACE-complete, matching Petri nets, and shows they are more expressive than Petri nets and context-free languages.

Contribution

It establishes complexity bounds for Recursive Petri nets' coverability, termination, boundedness, and finiteness problems, and demonstrates their increased expressiveness.

Findings

Problems are EXPSPACE-complete, same as Petri nets.

Coverability languages strictly include Petri net and context-free languages.

Recursive Petri nets are more expressive than Petri nets.

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.