Abstract: The full process (N,φ) of bounded Petri nets Σ provides a powerful tool to study the reachable remarked of bounded Petri nets Σ,mapping the S cut of occurrence net N to the reachable remarked of Σ by using occurrent net N and net map φ.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 nets Σ,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 nets Σ.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.

Key words: Full process, Weakly S cuts, Weakly occurrent net, Weakly process