A research on Petri net properties using transitive matrix

Petri net (PN) is a useful graphical and mathematical tool to model and analyze discrete event systems. The properties of PN can be classified into two types, i.e., behavioral properties and structural properties. The behavioral properties are investigated in association with the markings of PN, e.g., reachability, boundedness and liveness. On the other hand, the structural properties are just considered based on PN structure without marking, e.g., transition and place invariant. These two types of PN properties can be generally examined in order to analyze systems modeled. These properties have been studied by three methods of analysis, i.e., the coverability tree, reduction techniques, and state equations. However, many problems concerning these properties are still left unsolved. In this paper, we propose the new concept to analyze behavioral properties of PN using by the transitive matrix derived from graph theory. First, we indicate the method to convert PN into the directed graph, and introduce the labeled place transitive matrix of PN and relationship between them. Second, the behavioral properties are discussed with the power of weighted place transitive matrix. Thus, several useful concepts to obtain transition enabling firing vectors, firing times and possible firing sequence vectors are also proposed