非确定Petri网

根据描述工作流模型的实际应用背景，提出了非确定变迁，非确定Petri网等概念，并定义了Petri网的等价关系，证明了在这种等价关系的意义下，非确定Petri网与传统的确定Perti网的等价性。     

流体随机Petri网与混合Petri网的比较分析

流体随机Petri网和混合Petri网作为传统Petri网的拓展,可以建模离散成分和连续成分并存的混合系统,也可用于解决离散模型的状态空间爆炸问题.由于这两种建模机制远未发展成熟,分析比较它们的异同点有助于机制本身的进一步发展完善,有助于为特定的应用选择合适的建模方法.本文讨论了流体随机Petri网和混合Petri网的定义、连续标识、分析方法、以及相互转换的可能性.结论是这两种建模机制是互补的,各自适合于特定的应用场合.     

混合Petri网的流体随机Petri网模型

混合Petri网和流体随机Petri网作为混合系统的建模方法,其内在的建模机制和分析方法不尽相同,而且这两种机制远未发展成熟.分析并建立它们之间相互转换的方法有助于机制本身的发展完善,并利用对方的建模原语和分析方法对系统进行多角度的分析.提出了一阶混合Petri网转换成流体随机Petri网的形式化方法及转换后变迁合并的方法,并给出了转换和合并方法的正确性证明,最后结合实例简要阐述了这两种方法的实现过程.     

调度问题的压缩Petri网（RePN）模型研究

本文提出了一种新的Ｐｅｔｒｉ网模型－压缩Ｐｅｔｒｉ网（ＲｅＰＮ）模型，用于调度问题的建模和求解，与以前的模型相比，ＲｅＰＮ模型不仅具有较强的分析能力，而且大大减少了节点数，使可达集杨应减小，从而为搜索调度问题的最优解或近优解提供了方便。     

时间Petri网模拟能力的研究

模型的模拟能力一直是系统建模方面的一个重要研究课题。本文先用一个直观的“零检验”例子说明时间Petri网的模拟能力比传统Petri网要强,并首次证明了时间Petri网与计算科学的最高模型——图灵机有相等的模拟能力;最后给出了另外一种含时间因素的时延Petri网向时间Petri网的转换方法,这说明了时间Petri网虽然形式上较为简单,但其模拟能力却并不比其它含时间因素的Petri网逊色,同时为时延Petri网的研究提供了另外一种有效方法。     

Petri网替换运算

文中给出了Petri的替换运算定义,它是对分层模拟与逐步求精的Petfi网建模思想方法的一个形式化描述。文中还通过Petri网语言讨论了Petri网的替换运算同语言的替换运算之间的关系,结果表明,这两个从不同角度给出的替换运算在实质意义上是协调的。     

模糊Petri网的反馈控制研究

本文首先将模拟技术应用于Ｐｅｔｒｉ网中，得到模糊Ｐｅｔｒｉ网模型，然后基于Ｐｅｔｒｉ网中的库所湾量的概念，在普通Ｐｅｔｒｉ网的反馈控制基础上提出了一种模型Ｐｅｔｒｉ网的反馈控制方法。该方法使得对复杂系统的模糊Ｐｅｔｒｉ多控制器的系统设计成为可能。     

Petri网研究：机遇与挑战

本文是文［２］的姐妹篇，以国际动态为背景展示研究工作可以取得成就的方面，也试图就好面临的难点进行建设性的讨论。     

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.     

Petri网的工作流模型建模研究

实现工作流技术的关键环节在于工作流的概念模型,而其中的过程建模又是构建工作流管理系统的基础,因此,对建立工作流模型的研究和应用比较多。近几年,随着业务流程建模、工作流概念的出现以及Petri网技术的发展,Petri网也被用于工作流模型的建立。该文在介绍工作流模型和Petri网基本概念的基础上,介绍工作流的四种基本流程结构,并以工作流的四种基本流程结构为出发点,给出了如何把它们映射成符合工作流网定义的模型的一种方法。     

基于Petri网下哲学家就餐问题模型的改进与推广

哲学家就餐问题是描述在共享资源下同步与并发的经典案例，活性与无饥饿性是求解此问题的前提，效率是基本要求。基于两个许可卡的传递策略，已经给出了无饥饿解的Petri网模型，并且在该模型基础上的改进解决了许可卡的传递问题同时也解决了拥有许可卡且准备就餐的两位相邻哲学家之间共享资源的冲突问题。然而以上改进并没有真正实现效率上的高效且不易推广到哲学家人数大于5位的情形。     

SAT-Solving the Coverability Problem for Petri Nets

Net unfoldings have attracted great attention as a powerful technique for combating state space explosion in model checking, and have been applied to verification of finite state systems including 1-safe (finite) Petri nets and synchronous products of finite transition systems. Given that net unfoldings represent the state space in a distributed, implicit manner the verification algorithm is necessarily a two step process: generation of the unfolding and reasoning about it. In his seminal work McMillan (K.L. McMillan, Symbolic Model Checking. Kluwer Academic Publishers, 1993) showed that deadlock detection on unfoldings of 1-safe Petri nets is NP-complete. Since the deadlock problem on Petri nets is PSPACE-hard it is generally accepted that the two step process will yield savings (in time and space) provided the unfoldings are small.In this paper we show how unfoldings can be extended to the context of infinite-state systems. More precisely, we show how unfoldings can be constructed to represent sets of backward reachable states of unbounded Petri nets in a symbolic fashion. Furthermore, based on unfoldings, we show how to solve the coverability problem for unbounded Petri nets using a SAT-solver. Our experiments show that the use of unfoldings, in spite of the two-step process for solving coverability, has better time and space characteristics compared to a traditional reachability based implementation that considers all interleavings for solving the coverability problem.     

On Hybrid Petri Nets

Petrinets (PNs) are widely used to model discrete event dynamic systems(computer systems, manufacturing systems, communication systems,etc). Continuous Petri nets (in which the markings are real numbersand the transition firings are continuous) were defined morerecently; such a PN may model a continuous system or approximatea discrete system. A hybrid Petri net can be obtained if onepart is discrete and another part is continuous. This paper isbasically a survey of the work of the authors' team on hybridPNs (definition, properties, modeling). In addition, it containsnew material such as the definition of extended hybrid PNs andseveral applications, explanations and comments about the timingsin Petri nets, more on the conflict resolution in hybrid PNs,and connection between hybrid PNs and hybrid automata. The paperis illustrated by many examples.     

Computation of Minimal Siphons in Petri Nets Using Problem Partitioning Approaches

A large amount of research has shown the vitality of siphon enumeration in the analysis and control of deadlocks in various resource-allocation systems modeled by Petri nets(PNs).In this paper,we propose an algorithm for the enumeration of minimal siphons in PN based on problem decomposition.The proposed algorithm is an improved version of the global partitioning minimal-siphon enumeration(GPMSE)proposed by Cordone et al.(2005)in IEEE Transactions on Systems,Man,and Cybernetics-Part A:Systems and Humans,which is widely used in the literature to compute minimal siphons.The experimental results show that the proposed algorithm consumes lower computational time and memory compared with GPMSE,which becomes more evident when the size of the handled net grows.     

基于随机对象Petri网的柔性制造系统性能分析

为了增强传统对象Petri网的定量分析能力,提出随机对象Petri网模型。该模型具备随机性和层次特性,获得与随机Petri网的等价关系,从宏观和微观2个层面对系统进行性能分析,并将该模型应用到柔性制造系统中。实验结果表明,该系统保留了面向对象的建模能力,具有较强的定量分析能力。     

Identification of Petri Nets from Knowledge of Their Language

In this paper we deal with the problem of identifying a Petri net system, given a finite language generated by it. First we consider the problem of identifying a free labeled Petri net system, i.e., all transition labels are distinct. The set of transitions and the number of places is assumed to be known, while the net structure and the initial marking are computed solving an integer programming problem. Then we extend this approach in several ways introducing additional information about the model (structural constraints, conservative components, stationary sequences) or about its initial marking. We also treat the problem of synthesizing a bounded net system starting from an automaton that generates its language. Finally, we show how the approach can also be generalized to the case of labeled Petri nets, where two or more transitions may share the same label. In particular, in this case we impose that the resulting net system is deterministic. In both cases the identification problem can still be solved via an integer programming problem.

关于Petri网精细化操作及其应用研究

为了解决“顾客投诉”等这一类业务处理问题,提出了用Petri网精细化操作解决问题的方案。定义了一种子网,用这种子网分别对Petri网中的某些变迁进行细化,得到更细致、更精确的Petri网。研究了Petri网精细化操作的性质保持问题,给出了这种精细化操作保持结构有界性、守恒性、可重复性、相容性和活性的充分条件。本文的结果可为复杂大系统的分析提供重要手段,并特别适合于一类业务系统的描述和验证,具有一定的实用价值。     

有色Petri网的一种面向对象扩展形式

Ｐｅｔｒｉ网与面向对象的结合一直是一个令人感兴趣的研究课题。本文把有色Ｐｅｔｒｉ网引入到面向对象方法中,提出了一种面向对象的扩展有色Ｐｅｔｒｉ网,简称为ＯＥＣＰＮ,     

Tutorial and Survey Articles: An introduction to Petri Nets

This paper describes the fundamental concepts and characteristics of Petri nets (PNs) that make them a significant tool for modeling and analyzing asynchronous systems with concurrent and parallel activities and follows the extensions that improved the implementation capabilities of the original PNs.

Their first and most relevant extension was time modeling, a vital aspect of system performances not considered in the original version. There are several possibilities for introducing time in PNs. Among them, a technique that associates time with places is presented in some detail. As PNs tend to become cumbersome and time consuming when large and complex systems are involved, a method for decomposing timed PNs of open queuing networks is reviewed here.

Though initially developed as an information/computer-based technique, PNs were immediately adopted in a variety of application areas, such as manufacturing, design, planning and control. Viewed through a more recently developed programming perspective, the ordinary PNs became “high level” PNs suitable for defining different data types and for applying hierarchical approaches.

It is expected that the robust theoretical basis of this tool coupled with its visual and flexibility features will continue to appeal to researchers and practitioners alike in a variety of domains and as a result will continue to evolve and expand.