Some subclasses of Petri nets and the analysis of their structural properties: A new approach

The purpose of this paper is to consider some special types of Petri nets, introduced by Lien, and to propose a complete and unified approach for the study of their structural properties by using techniques of linear algebra of matrices. We distinguish four subclasses: forward-conflict-free, backwar d-conflict-free, forward-concurrent-free, and backward-concurrent-free Petr i nets. A modification of the classical incidence matrix results in a squar e matrix, named a modified incidence matrix, with nonpositive (nonnegative) off-diagonal elements when backward- (forward-) conflict-free or concurren t-free Petri nets are considered. The modified incidence matrix eigenvalues are computed and theorems on matrices of this type are used to prove sever al sufficient and/or necessary conditions for structural boundedness, liven ess, repetitiveness, conservativeness, and consistency of these four subcla sses of Petri nets.