Extension of Elementary Siphons in a Class of Generalized Petri Nets

This work presents an effective method on computing strict minimal siphons and elementary siphons based on the concept of initial resource weighted digraphs for a class of generalized Petri nets, namely WS3PR. In addition, the controllability conditions of dependent siphons are developed. Monitors are added for the elementary siphons only and the controllability of a dependent siphon is ensured by properly supervising its elementary siphons. Through fully investigating the structure of the net, especially weight information, the set of elementary siphons obtained by the proposed method is more compact and well suits for WS3PR. An example is illustrated to demonstrate the proposed method.