S-组合Petri网的活性分析与实现

ANALYSIS AND IMPLEMENTATION OF LIVENESS OF S-COMPOSITION PETRI NET

设∑1=（N1，M1），∑2=（N2，M2）是两个Petri网，且不含有冻结标志，Ni=（Si，Ti；Fi），i=1，2，T1∩T2=Φ，S1∩S2≠Φ，本文定义了∑1，∑2的S-组合Petri网∑s，通过引入Petri网互逆位置序偶的概念，深入研究了义的活性，给出了∑s有界活的几个判定条件．若∑1，∑2是两个活的Petri网，最后提出了一种实现S-组合Petri网活性的控制装置．

Let ∑1 = (N1,M1),∑2 = (N2,M2) be two Petri nets, and do not contain freezing tokens. Ni = (Si,Ti;Fi), i = 1, 2,, T1 ∩ T2 = Φ, S1 ∩ S2 ≠Φ, s-composition Petri net ∑s is defined on Petri nets ∑1 and ∑2 in this paper. The liveness of ∑s is discussed, and if ∑1 and ∑2 are live, some deciding conditions for preserving liveness of ∑s is given based on the concept of the mutually inverse ordered pair places of Scomposition Petri net. For two live and bounded Petri nets, if any two merging places are not a mutually inverse ordered pair places, then their S-composition Petri net is live and bounded. If ∑s, is not live, a control device for irnplementing liveness is presented.