Characterising liveness using a structure based approach is a key issue in theory of Petri nets. In this paper, we introduce a structure causality relation from which a topological characterisation of liveness in Petri nets is defined. This characterisation relies on a controllability property of siphons and allows to determine the borders of the largest abstract class of Petri nets for which equivalence between liveness and deadlock-freeness holds. Hence, interesting subclasses of P/T systems, for which membership can be easily determined, are presented. Moreover, this paper resumes, from a new point of view, similar results related to this issue and, provides a unified interpretation of the causes of the non-equivalence between liveness and deadlock-freeness.

Petri nets, structural analysis, siphons, liveness, deadlock-freeness