On analysis of Petri net properties based on transitive matrix

Abstract

Petri nets (PNs) are a useful graphical and mathematical tool to model and analyze discrete event systems. In this paper, the authors provide a new concept to analyze PN properties based on graph theory. First, they show the method to convert PNs into directed graphs, and then introduce the transitive matrices of PNs. Second, structural properties are examined using the characteristic polynomial and equation of the transitive matrices, and applying the Mason's theorem derived from signal-flow-graphs. Furthermore, behavioral properties concerning the transition firing orders are discussed using the power of the transitive matrices.