Research On Reachability Tree For Unbounded Petri Nets

As we all know, Petri nets are a powerful modeling tool in describing and analyzing the behavior of discrete event systems with graphical representation, numerous analysis methods, and a solid mathematical foundation. Although many achievements for Petri nets are presented, there exists a worldwide problem, that is, the reachability problem. Obviously, a varity of properties, such as deadlock, boundedness, liveness, conservation and coverablity, can be analyzed by reachability. As a result, reachability is the most basic property for a system.As a kind of important tool to analyze Petri nets, a reachability tree can indicate the relationship between markings and transitions. Meanwhile, it is applicable for different kinds of systems. However, there is still a problem in the area of Petri net, that is, analyzing the reachability problem of unbounded Petri nets by finite reachabitlity trees. Although some progresses are achieved by the efforts of researchers, there exist inadequacy. For example, the information of a system cannot be represented completely and accurately by the existed finite reachability trees. As a result, a research on the reachability problem is done in this paper, which is summarized as follows:1. A new finite reachability tree called coRT is proposed for a class of unbounded Petri nets, co-independent nets. The resulting ωRT consists of all reachable markings from its initial marking. Furthermore, there are not any spurious markings in an ωRT. Compared with an MRT, the number of nodes in an ωRT is much smaller than that in an MRT. Moreover, some properties are proposed and verified to solve some reachability problems, such as finiteness and deadlock.2. A new finite reachability tree called AcoRT is proposed for unbounded Petri nets. The proposed method is applicable for every Petri net. Obviously, the method has a larger application scope than all the existing methods. Moreover, a thereom is privided for deadlock detection base on the previous result.3. A modified AωRT is proposed to further simplify the structure of the finite reachability trees.Finally, conclusions and future research are provided.