Petri网系统活性保持的充分与必要条件

On Sufficient and Necessary Conditions for Liveness of Petri Nets

研究了Petri网活性保持的充分条件与必要条件.借助于Siphon非前阻塞的概念得到了Petri网活性的必要条件.以一类简单网为例,利用线性规划方法判定Siphon是非前阻塞的,降低了计算复杂性.在讨论Petri网活性的充分条件时,对弱活性的网增加约束条件使其保持活性,并借助增广Petri网的活性导出原网的活性,进而将讨论的范围拓广至通用的Petri网,最后通过例子验证了方法的有效性.

The sufficient and necessary conditions for liveness of Petri nets were studied.The necessary conditions for the liveness of petri nets were obtained by means of the concept of Siphon non-pre-blocked.Taking a class of simple nets as an example,the linear programming method was used to determine that Siphon was non-pre-blocked,which reduced the computational complexity.In the discussion of sufficient conditions for the liveness of Petri nets,constraint conditions were added to the weakly live nets to keep them live,and the liveness for the original nets was derived by means of the liveness for the extended Petri nets,and then the scope of discussion was extended to the general Petri nets.Finally,the effectiveness of the method was verified by an example.