Title :
A research on Petri net properties using transitive matrix
Author :
Liu, Jinghong ; Itoh, Yoshiaki ; Miyazawa, Iko ; Sekiguchi, Tadashi
Author_Institution :
Div. of Electr. & Comput. Eng., Yokohama Nat. Univ., Japan
Abstract :
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
Keywords :
Petri nets; discrete event systems; formal specification; graph theory; Petri net properties; behavioral properties; boundedness; coverability tree; discrete event systems; firing times; graphical and mathematical tool; liveness; reduction techniques; state equations; structural properties; transitive matrix; weighted place transitive matrix; Computer industry; Discrete event systems; Equations; Flowcharts; Graph theory; Information analysis; Mathematical model; Matrix converters; Power system modeling; Tree graphs;
Conference_Titel :
Systems, Man, and Cybernetics, 1999. IEEE SMC '99 Conference Proceedings. 1999 IEEE International Conference on
Conference_Location :
Tokyo
Print_ISBN :
0-7803-5731-0
DOI :
10.1109/ICSMC.1999.814209