扩展颜色逻辑Petri网及其可达性分析  

Extended colored logic Petri net and its reachability analysis

作　　者：王振 杜玉越 亓亮 WANG Zhen;DU Yuyue;QI Liang(College of Computer Science and Engineering,Shandong University of Science and Technology,Qingdao,Shandong 266590,China)

机构地区：[1]山东科技大学计算机科学与工程学院,山东青岛266590

出　　处：《山东科技大学学报（自然科学版）》2020年第3期84-98,共15页Journal of Shandong University of Science and Technology(Natural Science)

基　　金：国家自然科学基金项目(61903229,61973180)。

摘　　要：逻辑Petri网是一种增广Petri网模型,具有与图灵机等价的建模能力。颜色逻辑Petri网解决了逻辑Petri网中输出的不确定性表达问题。然而颜色逻辑Petri网描述不同子系统的并发过程,需要对每一个子系统建立一个子网模型。如果所有子网模型的结构相同,则可以引入多个有色托肯,从而用一个子网模型表示多个子系统的并发过程。因此,提出了扩展颜色逻辑Petri网模型及其可达性分析方法。首先,为了方便可达标识的表示和计算,引入多重集的素数表示法,用素数幂的乘积来表示一个多重集,并给出了判断变迁使能的方法。其次,通过定义颜色逻辑关联矩阵,给出了一步可达标识的计算公式以及可达树构造方法。最后,针对一个电子商务实例,分别用颜色逻辑Petri网和所提出的扩展颜色逻辑Petri网建立模型并进行比较分析,从而证明了提出的模型具有更简单的网结构,丰富了逻辑Petri网理论。Logic Petri net(LPN)is an extended Petri net model which has the same modeling capability of Turing machine.Colored logic Petri nets(CLPNs)have solved the problem of passing value indeterminacy.However,CLPNs need to build a model for each of the sub-system when they are used to describe a concurrent process of sub-system.If all sub-systems have the same structure,the concurrent process can be described by many colored tokens with only one sub-system model.In this paper,an extended colored logic Petri nets(ECLPN)and its reachability analysis were presented.Firstly,to describe and calculate the reachable markings,a multiset prime representation was introduced,in which the multiset is denoted by the product of prime power,and a method for judging whether a transition enabled is given.Secondly,the computation formula of reachable markings and the construction method of reachable trees were given by defining the colored logic incidence matrix.Finally,an e-commerce application is modeled by both CLPNs and ECLPNs for comparison.The results show that the proposed method can ensure the system model with a simpler net structure,thus improving the state-of-the-art of the LPNs theory.

关 键 词：并发系统 逻辑Petri网 颜色逻辑Petri网 可达性分析 电子商务系统 

分 类 号：TP393[自动化与计算机技术—计算机应用技术]