A novel reduction approach for Petri net systems based on matching theory

In this paper, an efficient method is presented to solve the state explosion problem in Petri nets by using matching theory. It is difficult to analyze a Petri net when there are too many existing states. In order to solve such a problem, it is addressed to label a weight value on a transition according to the relationship between a place and a transition. Then, the transition with the largest weight value is selected. The selected transition is the most important and connective in the entire Petri net. After selecting each transition for several times, the last one denotes the least connective in the whole Petri net and the redundant place is obtained. Furthermore, the Petri net model can be reduced by fusing the transition with the largest weight value and the redundant place. In this novel approach, an incidence matrix, a weight vector, a matching matrix, a compressed incidence matrix, and a reduced and compressed incidence matrix are sequentially built based on the original Petri net model so as to obtain a reduced and compressed Petri net model. Finally, the experimental results regarding the CAVE automatic virtual reality environment demonstrate the high viability of the proposed approach.