Partition by Place Invariants and Discrimination of Its Properties in Petri Nets

In this paper, the application of Petri nets is restricted to Sequential Control Systems, which are event-driven type and discrete systems possessing asynchronous and parallel properties. We have already proposed a method to model such Sequential Control Systems by Petri nets with place invariants, and also a method to divide a large Petri net to some small sub nets using the same place invariants. According to the structural character of Sequential Control Systems, the Petri net models have to have place invariants and transition invariants. In this paper, we discuss place invariants of Petri nets and the related problems. First, we prove that a net modeled by Petri nets with place invariants can be divided using the method of partition by the same place invariants. Then, the conditions of the properties holding between the whole and sub nets about covering by place invariants and liveness are clarified. Finally, a method to decide the reachability of a whole net through its sub nets will be introduced. Be based on these results, it can be concluded that the analysis of Petri net models of Sequential Control Systems is able to be treated through the analysis of their sub nets.