An algorithm for the minimum initial marking problem of a structurally live Petri net with inhibitor arcs

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• 作者：Jianhong Ye ; Zhiwu Li and Xiaoliang Chen
• 刊名：IEEJ Transactions on Electrical and Electronic Engineering
• 出版年：2016
• 出版时间：September 2016
• 年：2016
• 卷：11
• 期：5
• 页码：586-592
• 全文大小：462K
• ISSN：1931-4981

文摘

Inhibitor arcs increase the expressive power of Petri nets. However, they also make Petri net analysis more complex. Some properties of an ordinary Petri net are not always inherited in its extended version with inhibitor arcs. This paper reports a necessary and sufficient condition for deciding the structurally live property in an original Petri net and its extended one with inhibitor arcs. In addition, supposing that a net is structurally live, a natural problem is how to distribute the minimal number of tokens into the structurally live net to ensure that the marked net is live. A method is developed to find an optimal token allocation solution by putting tokens only in some key places. The algorithm can be completed within polynomial time, which overcomes the drawback of exhaustive solutions from all possible markings. Examples are given to illustrate the proposed approach.