关于有界Petri网的弱进程和弱出现网

On Weakly Process of Bounded Petri Net and Weakly Occurrent Nets

有界Petri网Σ的满进程(N,φ)利用出现网N和网射φ将N的S切对应Σ的可达标识,从而提供研究有界Petri网的可达标识的有力工具。由于出现网中限制每一个库所的后集最多一个变迁,因此,当Σ的库所的后集有多个变迁时,网射就会出现多次重复的现象。从而使得计算过于烦杂。文中提出弱出现网并且利用弱出现网来构造有界Petri网的弱进程,文中对于弱进程证明了在满进程中起重要作用的结论,表明弱进程是满进程的有意义的推广。由于弱出现网取消库所的后集元素个数的限制,在弱进程中,消除了满进程由于上述原因而产生的重复现象,提高了计算的效率。给出的例子表明了弱出现网在计算中的简便性。

The full process(N,φ)of bounded Petri netsΣprovides a powerful tool to study the reachable remarked of bounded Petri netsΣ,mapping the S cut of occurrence net N to the reachable remarked ofΣby using occurrent net N and net mapφ.Since there is no more than one transition in the back-set of any space in the occurrence network,when there are more than one transition in the back-set of some space of the Petri netsΣ,the phenomenon of multiple repeats will appear.It makes the calculation too complication.In this paper,the weakly process of bounded Petri net and weakly occurrent nets are introduced to replace full process of Petri netsΣ.The main results hold in full process are proved hold in weak processes of bounded Petri nets.Thus weak processes are a meaningful extension of full processes.Because the weak occurrence network cancels the restriction on the number of elements in the backset of the space in the weak process,the repetition phenomenon caused by the above reasons in the full process is eliminated.So that the efficiency of calculation are improved.The example given in this paper shows the simplicity of weak occurrence networks in calculation.