Deterministic weak-and-marked Petri net languages are regular

The intersection of the class of deterministic weak and the class of deterministic marked Petri net languages is the class of regular languages. We prove this result using a lemma that characterizes regular deterministic Petri net languages     

Decidability and closure properties of weak Petri net languages insupervisory control

We extend the class of control problems that can be modeled by Petri nets considering the notion of weak terminal behavior. Deterministic weak languages represent closed-loop terminal behaviors that may be enforced by nonblocking Petri net supervisors if controllable. The class of deterministic weak PN languages is not closed under the supremal controllable sublanguage operator     

Petri nets and regular languages

It is shown that the regularity problem for firing sequence sets of Petri nets is decidable. For the proof, new techniques to characterize unbounded places are introduced. In the class $\text{L}$₀ of terminal languages of labelled Petri nets the regularity problem in undecidable. In addition some lower bounds for the undecidability of the equality problems in $\text{L}$₀ and $\text{L}$ are given. L₀^λ is shown to be not closed under complementation without reference to the reachability problem.     

基于Petri网的工作流模型的研究

介绍了一般Petri网及工作流网的基本定义,在基本的工作流网系统定义的基础上,引入面向对象技术及分层技术,提出了一种面向对象的工作流网的模型,以提高模型的可读性和重用性,实现流程的分层建模,降低建模复杂度.通过一个具体实例阐述了如何建立扩展工作流网模型,并通过简化技术和可达树分析方法,验证了模型的活性.     

价格着色Petri网在工作流建模中的应用

在着色网的基础上扩展了价格信息,提出了价格着色网,用来对业务流程进行价格建模并对其作相应的成本预算分析.其中讨论了价格着色网的变迁步规则,提出了价格着色网中的标识--经济标识的定义,并有针对性地提出了最小成本构造算法.最后以一个业务流程实例演示了该模型的应用,得出结论为价格着色网能够较好地解决业务流程建模中的成本预算分析问题而且该模型中的最小成本构造算法是有效的.     

借助Petri网进行流程审计

信息的使用者往往关注保存在介质上的信息而忽视处理信息的程序。由于保存在介质上的信息有多个操作入口,即使处理信息的程序真实地反映了组织的业务流程,也难保证信息使用者所获得的信息是正确的,也就是说对于访问数据的程序,存在外部干扰。引入数据库中的审计表功能,协助信息系统审计人员识别信息系统中数据的形成是否遵循了既定的业务流程。由于Petri网是描述流程的有力工具,对于复杂的业务流程,引入Petri网对流程进行审计是必要的。     

Canonical prefixes of Petri net unfoldings

In this paper, we develop a general technique for truncating Petri net unfoldings, parameterized according to the level of information about the original unfolding one wants to preserve. Moreover, we propose a new notion of completeness of a truncated unfolding. A key aspect of our approach is an algorithm-independent notion of cut-off events, used to truncate a Petri net unfolding. Such a notion is based on a cutting context and results in the unique canonical prefix of the unfolding. Canonical prefixes are complete in the new, stronger sense, and we provide necessary and sufficient conditions for its finiteness, as well as upper bounds on its size in certain cases. A surprising result is that after suitable generalization, the standard unfolding algorithm presented in [8], and the parallel unfolding algorithm proposed in [12], despite being non-deterministic, generate the canonical prefix. This gives an alternative correctness proof for the former algorithm, and a new (much simpler) proof for the latter one.Received: 29 April 2003, Published online: 2 September 2003     

基于Petri网的哲学思考

近年来,Petri网以其优秀的描述异步并发的能力以及简单、清晰的图形表示方法获得了长足的发展.同时,Petri网技术和其它技术的完美结合使其在应用领域如鱼得水.哲学高度深刻分析了Petri网之所以获得成功的思想渊源,通过诠释Petri网思想与哲学思想的诸多相通之处,帮助大家以一种全新的视角重新认识和理解Petri网.     

面向对象Petri网建模技术综述

阐述了面向对象技术和Petri网的结合方式,提出了面向对象Petri网的建模过程,给出其详细的建模步骤和流程图,讨论了面向对象Petri网的动态特性分析方法,分析和总结了OOPN,OOCPN、OOAPN以及OOTPN的研究现状和各自建模的利弊,最后对面向对象Petri网的相关技术和发展趋势进行了综述与展望.     

A generalized fuzzy Petri net model

The paper proposes a new model of Petri nets based on the use of logic based neurons. In contrast to the existing generalizations, this approach is aimed at neural-type modeling of the entire concept with a full exploitation of the learning capabilities of the processing units being used there. The places and transitions of the net are represented by OR and AND-type and DOMINANCE neurons, respectively. A correspondence between this model and the previous two-valued counterpart is also revealed. The learning aspects associated with the nets are investigated     

Petri网的依赖关系

为了分析变迁不处于公平关系或弱公平关系时在运行中的依赖关系,本文提出了公平依赖和弱公平依赖的概念。研究了伪可重复向量的性质及在判断公平依赖关系时起的作用。给出了判断变迁处于公平依赖关系和弱公平依赖关系的充分必要条件。     

POC net,a subclass of Petri nets,and its application to timed Petri nets

Liveness is one of the most important properties of the Petri net analysis. This property is concerned with a capability for firing of transitions. On the other hand, place-liveness is another notion related to liveness, which is concerned with a capability for having tokens in places. Concerning these liveness and place-liveness problems, this paper suggests a new subclass of Petri net, ‘POC nets’, as a superclass of AC nets and DC nets. For this subclass, the equivalence between liveness and place-liveness is shown and a sufficient condition for liveness for this POC net is derived. Then the results are extended to liveness problem of timed Petri nets which have transitions with finite firing durations and the earliest firing rule. Although liveness of a (non-timed) Petri net is neither necessary nor sufficient condition for liveness of a timed Petri net, it is shown that liveness is preserved if the net has POC structure. Furthermore, it is pointed out that if a POC net satisfies some additional condition, Petri net liveness is equivalent to timed Petri net liveness. Finally, it is shown that liveness of timed POC nets with TC structure and the earliest firing rule is decidable with deterministic polynomial time complexity.     

Comparing digraph and Petri net approaches to deadlock avoidance inFMS

Flexible manufacturing systems (FMSs) are modern production facilities with easy adaptability to variable production plans and goals. These systems may exhibit deadlock situations occurring when a circular wait arises because each piece in a set requires a resource currently held by another job in the same set. Several authors have proposed different policies to control resource allocation in order to avoid deadlock problems. These approaches are mainly based on some formal models of manufacturing systems, such as Petri nets (PNs), directed graphs, etc. Since they describe various peculiarities of the FMS operation in a modular and systematic way, PNs are the most extensively used tool to model such systems. On the other hand, digraphs are more synthetic than PNs because their vertices are just the system resources. So, digraphs describe the interactions between jobs and resources only, while neglecting other details on the system operation. The aim of this paper is to show the tight connections between the two approaches to the deadlock problem, by proposing a unitary framework that links graph-theoretic and PN models and results. In this context, we establish a direct correspondence between the structural elements of the PN (empty siphons) and those of the digraphs (maximal-weight zero-outdegree strong components) characterizing a deadlock occurrence. The paper also shows that the avoidance policies derived from digraphs can be implemented by controlled PNs.     

The Petri Net Kernel An infrastructure for building Petri net tools

The Petri Net Kernel is an infrastructure for building Petri net tools. It relieves the programmer of a Petri net tool from implementing standard operations on Petri nets and a graphical user interface. In this paper, we discuss the motivation, the concepts, and the implementation of the Petri Net Kernel. Published online: 25 July 2001     

Supervisory control of deterministic Petri nets with regularspecification languages

Algorithms for computing a minimally restrictive control in the context of supervisory control of discrete-event systems have been well developed when both the plant and the desired behaviour are given as regular languages. In this paper the authors extend such prior results by presenting an algorithm for computing a minimally restrictive control when the plant behaviour is a deterministic Petri net language and the desired behaviour is a regular language. As part of the development of the algorithm, the authors establish the following results that are of independent interest: i) the problem of determining whether a given deterministic Petri net language is controllable with respect to another deterministic Petri net language is reducible to a reachability problem of Petri nets and ii) the problem of synthesizing the minimally restrictive supervisor so that the controlled system generates the supremal controllable sublanguage is reducible to a forbidden marking problem. In particular, the authors can directly identify the set of forbidden markings without having to construct any reachability tree     

A comparison of two Petri net types

In this article we pick up a problem stated in [1], namely the question whether PNlog-nets allow to solve synchronization problems not solvable by ordinary Petri nets under certain simulation rules. We show that a slight and reasonable strengthening of the simulation rules defined in [1] enables us to answer the raised question in the positive. As will be pointed out in the introduction, with this result we “partially” solve the original problem.