Structural Liveness of Immediate Observation Petri Nets

TL;DR

This paper investigates the computational complexity of the structural liveness problem in specific subclasses of Petri nets, revealing PSPACE-hardness for IO nets and PSPACE membership for BIMO nets, with bounds on token numbers influencing liveness.

Contribution

It establishes complexity bounds for the structural liveness problem in IO and BIMO Petri nets, a recent area of study, and discusses token bounds relevant to liveness.

Findings

SLP is PSPACE-hard for IO nets.

SLP is in PSPACE for BIMO nets.

Token bounds are crucial for determining liveness.

Abstract

We look in detail at the structural liveness problem (SLP) for subclasses of Petri nets, namely immediate observation nets (IO nets) and their generalized variant called branching immediate multi-observation nets (BIMO nets), that were recently introduced by Esparza, Raskin, and Weil-Kennedy. We show that SLP is PSPACE-hard for IO nets and in PSPACE for BIMO nets. In particular, we discuss the (small) bounds on the token numbers in net places that are decisive for a marking to be (non)live.