A Method to Quickly Determine Some Non-Reachable Markings in Cyclic Petri Nets Based on State Equation

Abstract

Reachability is the basis of studying the dynamic characteristics of a system, and is also one of the important properties of Petri nets (PNs). For acyclic PNs, the existence of non-negative integer solutions of the state equation is a sufficient and necessary condition of a reachable marking. For cyclic PNs, it has been proved to be only a sufficient condition. This paper presents a reachability analysis method for cyclic ordinary PNs. It determines markings that are not reachable from some initial markings. Firstly, according to the structural relationship between the incidence matrix and the PN, a subnet is generated by a transformation method. Then, the marking reachability is determined by judging the structural characteristics of the subnet. Finally, we give an algorithm to identify the non-reachable markings. This work is an important complement to PNs’ reachability analysis methods.