Petri网的进程网系统

Process Net System of Petri Net

提出了 Petri网的进程网系统的概念 .一个 Petri网的进程网系统是以其基本进程段的集合为新的变迁集 ,以各个基本进程段集的输入和输出库所集的并集为新的库所集 ,以原网系统的初始标识为初始标识而得到的网系统 ,它可以很好地描述原网系统的进程行为 .文中讨论了求取任意 Petri网的基本进程段的算法 ,该算法是通过研究网中的极小可重复向量和极小受控可重复向量在可覆盖树上的分布特征实现的 ,文中还给出了通过网结构来描述各个基本进程段之间关系的方法 ,从而求出一个 Petri网的进程网系统 .

The concept of process net system, which is a variation of process expression, of a 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 and 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 overcome 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 Σ is a new net system Σ′, where the transition set of Σ′ is the basic process sections of Σ, the place set of Σ′ is the union of input and output place set for all basic process sections of Σ, the flow relation of Σ′ can be defined by the union of input relation and output relation between the transition set and place set of Σ, and the initial marking of Σ′ is same to Σ. 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 Σ (bounded or unbounded) and the set of firing sequence of its process net system Σ′. 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.