时间Petri网保持活性、有界性的两个充要条件

Two Sufficient and Neccessory Conditions of Time Petri Net Preserving Liveness and Boundedness

活性和有界性是Petri网最重要的性质,对于传统Petri网的这些性质,国内外学者作过大量的研究工作,并且得到了不少成果,而对舍时间因素的Petri网的这些相应性质国内外研究得很少。本文首先介绍了时间Petri网TPN的若干基本定义,然后说明了时间Petri网TPN的活性、有界性和对应传统Petri网的相应性质并无关系,接着给出了时间Petri网保持活性、有界性的时间区间上的两个充分必要条件。为利用传统Petri网的性质判定结果来判定时间Petri网的相应性质提供了可能性。

Liveness and boundedness are the two most important properties of the Petri nets, for the classic Petri nets, many scholars have done a lot of work and obtained satisfactory judging result, but for Petri Net with time factor, most literatures focus on concrete application. Firstly, the basic concepts of Time Petri Net （TPN for short） are introduced in this paper. Then we show that TPN＇s liveness and boundedness behavior has no relation with its corresponding classic Petri Net through some examples. Finally we give two sufficient and neccessory conditions in time interval of TPN preserving liveness and boundedness. It is easy to judge a TPN＇s liveness and boundedness according to our result.