Leakage Notion

The leakage notion was introduced in [5], and its symetric notion in [4] or [6].The aim of this work is to obtain a general tool in order to analyse liveness and boundedness in Petri nets, independently of the initial marking. Our results submitted striking analogies with other results based upon linear algebra. In this paper, after submitting some notations, we introduce the notion of weak leakage from which we deduce a necessary condition for a Petri net to be live. This condition is independent of the initial marking, implies the two first ones, and like the two first ones’shows a symetric notion.