摘要
一个Petri网系统的有效可重复向量的集合为CSX0∪CSX+,有效受控可重复向量的集合为CSX-∪CSX+-。本文给出了用有效(受控)可重复向量判定Petri网系统公平性相关问题的一个充分必要条件。任意的两个变迁ti,tj,则tj公平依赖于ti,当且仅当在CSX0∪CSX+∪CSX-∪CSX+-中不存在这样的向量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。
The set of the effective repetitive vector of a Petri net is denoted by CSX0∪CSX＋,while the effective controlled repetitive vector of a Petri net is denoted by CSX-∪CSX＋-.Based on the effective（controlled） repetitive vector of a Petri net,this paper proposes a necessary and sufficient condition for determining the fairness-related problem in the Petri net system.Suppose ti and tj are two arbitrary transitions in a Petri net system.The main conclusion is that tj fair depends on ti,if and only if the set CSX0∪CSX＋∪CSX-∪CSX＋-does not contain such a vector that satisfies X（j）0 and X（i）=0.Finally,the applications of the conclusions are illustrated with an actual example.
基金
福建省教育厅资助科技项目(JK2010037)
国家自然科学基金资助项目(60673053)
漳州师范学院博士科研启动基金资助项目
