In: Chinese Journal of Computer, pages 1308-1315. December 2002.
Abstract: The concept of process net system which is a variation of process expression, of Petri net is presented in this paper. It can be used to define the set of all processes for this Petri net. In the case of bounded Petri nets and unbounded fair Petri nets, algorithms were given to find process expression for them by [4] and [5] respectively. However, three kinds of operation of regular expression(i. e. addition, concatenation and Kleene-closure) cannot reflect the relationship among process sections of a Petri net if it is unbounded and unfair. In order to overcom this difficulty, we use net structure to replace regular expression for the relation description among process sections. This results the concept of process net system. The process net system of a Petri net P is a new net system P', where the transition set of P' is the basic process sections of P, the place set of P' is the union of the input and output place set for all basic process sections of P, the flow relation of P' can be defined by the union of input relation and output relation between the transition set and place set of P, and the initial marking of P' is same to P. It is easy to know that from the construction of process net system of a Petri net, there is a one to one correspondence between the set of subjective process of any Petri net P (bounded or unbounded) and the set of firing sequence of its process net system P'. The process net system can be obtained by jointing with two algorithms presented in this paper. One is to find the set of basic process sections that is based on the concepts of repetitive vector, controlled repetitive vector and characteristic reachability tree of a Petri net, another is to describe the relations among basic process sections.
Keywords: Petri net; Process; process net system; basic process section; repetitive vector.