基于Petri网的可达树与可达图的构造与算法实现

Petri网是一种系统设计和分析的工具，为了完成Petri网的各项分析，还需要借助如可达树、可达图等工具。讨论了Petri网可达树与可达图的构造方法，并给出了相应的算法。     

Petri网仿真和自动化分析中的存储结构及算法研究

存储结构及算法是Petri网仿真和自动化分析研究中的重要内容，Petri网是一种特殊的有向图，通过对图的存储问题进行研究，提出了一种有向图的存储结构-树链式结构，给出了其构造算法，与其它有向图存储结构相比，它既可提高算法速度又能降低算法复杂性，树链式结构在Petri网仿真和自动化分析中应用优势明显，着重讨论了Petri网的树逻式存储结构，提出了基于该存储结构的可达树生成算法，所生成的可达树的树链结构形式，利于展开Petri网的各种分析算法。     

应用Petri网求解事故树最小割集的方法研究

为简化事故树分析过程中最小割集求解算法的步骤,在构建事故树Petri网模型的基础上,探讨了事故树Petri网模型的性质,给出了事故树的逻辑表达式与事故树Petri网模型的可达死标识之间的关系,进而提出了利用Petri网可达图求解事故树最小割集的算法,以及在给定基本事件发生时,中间事件和顶事件发生与否的判断方法。结合实例,借助开源的Petri网工具PIPE实现了事故树最小割集的求解,表明了该算法的有效性和可行性。     

一种生成具有变量标识的高级Petri网可达树的算法

Petri网动态性质的考察一般基于网不变量(Net Invariants)和可达树(Reachability Tree).这两个概念已被扩展到高级Petri网中.高级Petri网可达集空间随着网的复杂性而指数性增长是计算可达树问题中的一个主要难 点.本文定义了具有变量标识的高级Petri网并给出了构造该类网的可达树的算法.本文的算法以变量标识的等价关系(equivalent relation)和覆盖关系(covering relation)为基础,明显地简化了可达集空间.个体标识的信息可从变量标识的定义域中获得.     

基于着色Petri网的TCP协议的形式化描述及验证

根据着色Petri网的建模的方法和工具CPNT001．对TCP协议的连接建立模块建立了着色Petri网模型。得到了可达树,通过可达树的方法对协议模型的正确性进行验证。     

移动网可达树

随着计算机技术和网络通信技术的高速发展,对于并发分布式系统,已经提出了进程代数以及Petri网等形式化分析方法。近年来由于移动互联网的出现和快速发展,通过在进程代数中增加移动性得到了pi演算,与此同时,Petri网领域也采用谓词/变迁网、颜色网等构建移动系统模型。但它们仍存在一些不足之处。在此基础上,A.Asperti和N.Busi提出了移动网这一系统模型。移动网是在Petri网的基础上增加了移动性并结合了进程代数的优势得到的,适用于描述和刻画移动计算系统。然而,目前并没有对于移动网相应分析方法的研究。为此开展了移动网模型分析方法的研究,给出了移动网可达树的构造算法,提供了移动网模型可达性分析方法,并对移动车辆电话通信系统实例进行了分析。     

无界Petri网的可达树的综述

Petri网自提出以来得到了学术界和工业界的广泛关注. Petri网系统的可达性是最基本性质之一.系统的其他相关性质都可以通过可达性进行分析.利用等价的有限可达树来研究无界Petri网可达性,依然是一个开放性问题.该研究可以追溯到40年前,但由于问题本身的复杂性和难度太大,直到最近20年,经过国内外诸多学者的不懈努力,才逐渐取得了一些阶段性的成果和部分突破.本文回顾了近40年来国内外学者为彻底解决该问题作出的贡献.重点对4种开创性的研究成果展开讨论,分别为有限可达树、扩展可达树、改进可达树及新型改进可达树.探讨了今后无界Petri网可达性问题的研究方向.     

基于．Net平台的Petri网建模和分析软件的设计与实现

应用面向对象思想和采用C#语言在．NET可视化编程平台下开发了图形化的Petri网建模软件,该软件作为一个计算机辅助设计和分析工具,使用户可在交互式的计算机图形方式下进行Petri网模型的建立、移动和存储。并可通过运行Petri网生成可达树,可达图来分析Petri网基本特性以及系统性能指标。     

混合动态系统SPN的可达性分析

根据混合动态系统SPN(StochasticPetriNets)模型的运行规则,给出了几种典型结构(串行结构、并行结构、冲突结构)中变迁的可激发以及可激发成功概率的计算方法,在此基础上,计算出托肯沿几种基本路径(简单串行路径、简单并行路径、简单Fork/Join路径)从起始库所到达终止库所的可达概率,同时从宏观状态的角度构建了该SPN模型的状态可达树,通过可达树可以判断状态间的可达性并计算可达概率。     

混合动态系统SPN的可达性分析

根据混合动态系统SPN(Stochastic Petri Nets)模型的运行规则,给出了几种典型结构(串行结构、并行结构、冲突结构)中变迁的可激发以及可激发成功概率的计算方法,在此基础上,计算出托肯沿几种基本路径(简单串行路径、简单并行路径、简单Fork/Join路径)从起始库所到达终止库所的可达概率,同时从宏观状态的角度构建了该SPN模型的状态可达树,通过可达树可以判断状态间的可达性并计算可达概率.     

无界公平Petri网的进程表达式

Ｐｅｔｒｉ网的进程表达式是以该网系统的基本子进程集为字母的一个正规表达式．它用有限形式给出了网系统的所有（无限多个）进程的集合．作者于１９９５年给出了对任意给定的有界Ｐｅｔｒｉ网求其进程表达式的一个算法．这个算法对无界Ｐｅｔｒｉ网是不适用的,其原因在于子进程同构的概念在无界网系统中没有意义．对此,作者通过定义进程段行为等价的概念,导出了无界Ｐｅｔｒｉ网的进程表达式的一般形式,并借助无界公平网的特征     

Deadlock checking for one-place unbounded Petri nets based on modified reachability trees.

A deadlock-checking approach for one-place unbounded Petri nets is presented based on modified reachability trees (MRTs). An MRT can provide some useful information that is lost in a finite reachability tree, owing to MRT's use of the expression a + bn(i) rather than symbol omega to represent the value of the components of a marking. The information is helpful to property analysis of unbounded Petri nets. For the deadlock-checking purpose, this correspondence paper classifies full conditional nodes in MRT into two types: true and fake ones. Then, an algorithm is proposed to determine whether a full conditional node is true or not. Finally, a necessary and sufficient condition of deadlocks is presented. Examples are given to illustrate the method.     

A Reduced Reachability Tree for a Class of Unbounded Petri Nets

As a powerful analysis tool of Petri nets, reachability trees are fundamental for systematically investigating many characteristics such as boundedness, liveness and reversibility. This work proposes a method to generate a reachability tree, called ωRT for short, for a class of unbounded generalized nets called ω-independent nets based on new modified reachability trees (NMRTs). ωRT can effectively decrease the number of nodes by removing duplicate and ω-duplicate nodes in the tree, and verify properties such as reachability, liveness and deadlocks. Two examples are provided to show its superiority over NMRTs in terms of tree size.      

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     

Commodification of accelerations for the Karp and Miller Construction

Karp and Miller’s algorithm is based on an exploration of the reachability tree of a Petri net where, the sequences of transitions with positive incidence are accelerated. The tree nodes of Karp and Miller are labeled with ω-markings representing (potentially infinite) coverability sets. This set of ω-markings allows us to decide several properties of the Petri net, such as whether a marking is coverable or whether the reachability set is finite. The edges of the Karp and Miller tree are labeled by transitions but the associated semantic is unclear which yields to a complex proof of the algorithm correctness. In this work we introduce three concepts: abstraction, acceleration and exploration sequence. In particular, we generalize the definition of transitions to ω-transitions in order to represent accelerations by such transitions. The notion of abstraction makes it possible to greatly simplify the proof of the correctness. On the other hand, for an additional cost in memory, which we theoretically evaluated, we propose an “accelerated” variant of the Karp and Miller algorithm with an expected gain in execution time. Based on a similar idea we have accelerated (and made complete) the minimal coverability graph construction, implemented it in a tool and performed numerous promising benchmarks issued from realistic case studies and from a random generator of Petri nets.

     

On reachability graphs of Petri nets

Petri net is a powerful tool for system analysis and design. Several techniques have been developed for the analysis of Petri nets, such as reachability trees, matrix equations and reachability graphs. This article presents a novel approach to constructing a reachability graph, and discusses the application of the reachability graph to Petri nets analysis.     

Augmented reachability trees for 1-place-unbounded generalizedPetri nets

An augmented reachability tree (ART) is proposed to extend the capability of the classical reachability tree (RT) for analyzing qualitative properties, such as liveness, of a class of unbounded generalized Petri nets, called 1-place-unbounded nets, where there is at most one unbounded place for each net. The idea is based on the computation of the minimal marking of each node in the tree. An algorithm for obtaining the minimal marking is shown. Examples are given to illustrate the technique. In addition to liveness, the proposed method can verify other properties such as reversibility and feasible firing sequences. Furthermore, properties verifiable by RT are also verifiable by ART     

A modified reachability tree approach to analysis of unbounded Petri nets.

Reachability trees, especially the corresponding Karp-Miller's finite reachability trees generated for Petri nets are fundamental for systematically investigating many characteristics such as boundedness, liveness, and performance of systems modeled by Petri nets. However, too much information is lost in a FRT to render it useful for many applications. In this paper, modified reachability trees (MRT) of Petri nets are introduced that extend the capability of Karp-Miller's FRTs in solving the liveness, deadlock, and reachability problems, and in defining or determining possible firing sequences. The finiteness of MRT is proved and several examples are presented to illustrate the advantages of MRT over FRT.