In: IEEE Trans. on Systems, Man, and Cybernetics - A, Vol. 29, No. 2, pages 164-172. 1999.
Abstract: The purpose of this paper is to consider some special types of Petri nets, introduced by Lien, and propose a complete and unified approach for the study of their structural properties by using techniques of linear algebra of matrices. Four subclasses of nets are distinguished: forward conflict-free, backward conflict-free, forward concurrent-free, and backward concurrent-free nets. A modification of the classical incidence matrix results in a square matrix, named a modified incidence matrix, with nonpositive (nonnegative) off-diagonal elements when backward (forward) conflict-free or concurrent-free Petri nets are considered. The modified incidence matrix eigenvalues are computed and theorems on matrices of this type are used to prove several sufficient and/or necessary conditions for structural boundedness, liveness, repetitiveness, conservativeness, and consistency of these four subclasses of Petri nets.
Keywords: Petri nets, incidence matrix, matrix eigenvalues, structural properties.