摘要
由于存在可达标识集的爆炸性问题,大型Petri网系统的建模及可达性分析等问题的研究存在难度.文章利用矩阵的半张量积工具,研究了带有同步变迁的有界Petri网系统的建模及可达性问题.一方面,由于该类Petri网系统可以看作是由若干个子Petri网系统组成,所以可以用半张量积工具表述得到整个Petri网系统的矩阵表示.另一方面,在得出的矩阵表示的基础上,研究了两个标识之间可达性的充要判据,并给出了求可达变迁序列的算法.最后,文章用实例验证了该算法的正确性.所提出的方法在一定程度上解决了状态空间爆炸问题,并易于计算机实现.
The modeling and reachability problems of big petri nets are difficult to research for the state explosion problem. Using semi-tensor product （STP） of matrices, this paper investigates the problems of modeling and reachability of bounded petri nets with synchronizing transition. Firstly, this kind of petri nets can be seen as a combination of several subnets by synchronizing transitions such that we can obtain the matrix expression of these petri nets. Secondly, this paper presents a necessary and sufficient condition of reachability in terms of matrix. Based on that, an algorithm of firing transition sequence is also provided. Finally, an example is used to verify the correctness of this algorithm. The proposed method solves the problem of the state space explosion to some extent, which is easy to implement in computer.
出处
《系统科学与数学》
CSCD
北大核心
2016年第7期924-936,共13页
Journal of Systems Science and Mathematical Sciences
基金
国家自然科学基金(61573199
61573200)
天津自然科学基金(14JCYBJC18700)资助课题
关键词
可达性
有界PETRI网
同步变迁
矩阵的半张量积
标识演化方程
Reachability, bounded petri nets, synchronizing transition, semi-tensor product （STP） of matrices, marking evolution equation.
