On liveness and deadlockability in subclasses of weighted Petri nets

Abstract

Structural approaches have greatly simplified the analysis of intractable properties in Petri nets, notably liveness. In this paper, we further develop these structural methods in particular weighted subclasses of Petri nets to analyze liveness and deadlockability, the latter property being a strong form of non-liveness. For homogeneous join-free nets, from the analysis of specific substructures, we provide the first polynomial-time characterizations of structural liveness and structural deadlockability, expressing respectively the existence of a live marking and the deadlockability of every marking. For the join-free class, assuming structural boundedness and leaving out the homogeneity constraint, we show that liveness is not monotonic, meaning not always preserved upon any increase of a live marking. Finally, we use this new material to correct a flaw in the proof of a previous characterization of monotonic liveness and boundedness for homogeneous asymmetric-choice nets, published in 2004 and left unnoticed.