A class of generalized Petri nets and its state equation

Abstract

By analyzing the evolution nature of a Petri net, this article reports a generalized state equation for Petri nets, including Petri nets with inhibitor and enabling arcs. By proposing the generalized state equations, all enabled transitions meeting the firing condition can fire concurrently. Conflicts can be found when any component of a resulting marking vector by firing the enabled transitions at some marking becomes negative. We first formulate a novel state equation for regular Petri nets. Then, it is extended to the nets with inhibitor and enabling arcs. A classical problem with conflicts and concurrency, that is, the dining philosophers problem, is taken as an example to validate the proposed state equations of Petri nets.