Decision Problems for Petri Nets with Names

TL;DR

This paper explores the computational properties of nu-Petri nets with name creation, establishing decidability and undecidability results for various problems and demonstrating their expressive power surpasses traditional Petri nets.

Contribution

It introduces nu-PN, extending Petri nets with name management, and provides new decidability results for coverability, termination, and boundedness, along with undecidability proofs for certain properties.

Findings

Decidability of coverability and termination for nu-PN.

Undecidability of depth-boundedness.

Ackermann-hardness for all decidable problems.

Abstract

We prove several decidability and undecidability results for nu-PN, an extension of P/T nets with pure name creation and name management. We give a simple proof of undecidability of reachability, by reducing reachability in nets with inhibitor arcs to it. Thus, the expressive power of nu-PN strictly surpasses that of P/T nets. We prove that nu-PN are Well Structured Transition Systems. In particular, we obtain decidability of coverability and termination, so that the expressive power of Turing machines is not reached. Moreover, they are strictly Well Structured, so that the boundedness problem is also decidable. We consider two properties, width-boundedness and depth-boundedness, that factorize boundedness. Width-boundedness has already been proven to be decidable. We prove here undecidability of depth-boundedness. Finally, we obtain Ackermann-hardness results for all our decidable decision problems.