基于矩阵半张量积(the semi-tensor product, STP)方法研究了有界Petri网系统的可逆性和活性问题. 首先, 利用先前所建立的有界Petri网系统的状态演化方程, 分别给出了有界Petri网系统的可逆性和活性判别的充要条件. 文章的结果是基于矩阵形式的, 利用Matlab的STP工具箱, 可将Petri网系统的可逆性和活性判别问题转化为简单直接的矩阵计算问题. 所提出的方法不仅形式简单、计算方便, 而且易于计算机实现. 其次, 两个实例说明了文章所提出方法的可行性和有效性.

In this paper, we investigate the problems of reversibility and liveness of bounded Petri net systems (BPNSs) by using the semi-tensor product (STP) of matrices. First, several necessary and sufficient conditions for the reversibility and liveness of BPNSs are respectively obtained by using the state evolution equation of BPNSs. The new results, in this paper, are based on the matrix form, thus the problems of verifying reversibility and liveness of BPNSs are expressed into the matrix computation which are very simple and straightforward work with the help of Matlab toolbox of STP. The main advantage of the proposed method not only is that its form is a very simple and easy to calculate, but also is that it is a very convenient to implementation on a computer. Second, two examples are presented to illustrate the theoretical results in this paper and show that the new results are very effective in investigating the problems of the reversibility and liveness in BPNSs.