Petri网系统的弱公平性判定

Determination of the Weak Fairness in Petri Net Systems

本文首先给出了一个Petri网系统的有效可重复向量的两个性质.随后,又给出了用有效可重复向量判断Petri网系统弱公平性相关问题的一个充分必要条件.在一个Petri网系统中,任意的两个变迁ti,tj,则tj弱公平依赖于ti,当且仅当不存在这样的有效可重复向量X,使得X(j)>0且X(i)=0.最后,用一个实例展示结论的应用过程.

This paper firstly gives two properties of the effective repetitive vectors in a Petri net system.Second,the sufficient and necessary condition,which is for determining the problems concern weak fairness in a Petri net,is proposed.Suppose ti and tj are two arbitrary transitions in a Petri net system.The main conclusion is that tj weakly fair depends on ti,if and only if there does not exist such a effective repetitive vector that satisfies X（j）0 and X（i）=0.Finally,the applications of the conclusions are illustrated with an actual example.