单触发Petri网的一个可达性判定方法

可达性判定问题是Petri网理论研究的一个重要课题.已有文献提出通过构造Petri网的可达树或可覆盖树来分析其可达性,但其中无界量ω的引入导致了无界Petri网运行过程中的信息丢失,使其可达性无法得到判定.众所周知,对于有界Petri网,通过构造其可迭性树或可达标识图来判定其可达性是容易的,但对于大量存在的无界Petri网,找到一个能判定其可达性的一般性算法却不太容易.本文给出一个Petri网子类--单触发Petri网,并给出它的一个可达性判定方法.     

Petri网的符号ZBDD可达树分析技术

Petri网是一种适合于并发系统建模、分析和控制的图形工具.可达树是Petri网分析的典型技术之一,它通过标识向量集合表征系统的状态空间,组合复杂性严重制约了该分析技术可处理系统问题的规模.零压缩决策图(Zero-Suppressed Binary Decision Diagrams,ZBDD)是一种新型的数据结构,是表示和处理稀疏向量集合的一种有效技术.文章基于Petri网町达标识向量的稀疏特征,给出了Petri网分析的符号ZBDD技术,该技术通过对标识向量(状态)的布尔向量表示、可达标识向最(状态)的符号ZBDD生成,实现Petri网可达状态空间的高效符号操作和紧凑符号表示.实验表明,基于ZBDD的符号可达性分析算法能够有效处理较大规模Petri网问题.     

随机Petri网可达树的广度优先可视化编程实现

由于随机Petri网的可达树在整个SPN模型的性能分析中占据着重要的位置,因此本文提出一种广度优先的算法来得到随机Petri网的可达树,并且使用C builder6.0对模型的可达性性质进行了可视化编码实现,为下一步SPN模型的性能分析做好充足的准备。     

利用有限自动机所识别的语言构造petri网的可达性树

可达性树（reachabilty tree）表示petri网的可达标识集。它既和petri网的结构有关，也和petri网的初始标识有关。通过分析petri网的可迭树，可以了解petri网的许多重要性质。因此如何从给出的petri网图转换成奇达性树，是进一步研究petri网的关键。基于此，本文利用有限自动机所识别的语言给出了一种构造petri网可达性树的方法。     

Petri网系统活性的研究

随着Petri网在平行计算、通讯系统、计算机集成制造系统等领域的广泛应用,在以Petri网为实际系统建立模型之后,人们很关心模型系统各种性质与行为,其中,活性是最关心的性质之一。我们知道Petri网系统是动态系统的静态描述,从它可以很容易得到系统的状态转换图,一般称Petri网系统的可达图(系统无界时,得覆盖图)。实质上,可达图是动态系统的动态描述;系统有多少种不同状态(不考虑系统无界时),可达图就有多少个结点;结点间由有向弧连结,表明从一种状态转换为另一种状态发生了什么动作(一种或若干     

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.     

多主体计划的Petri网方法及其研究

利用Petri网对主体Petri的各种行为进行描述和分析，通过Petri网系统的可达性分析考虑主体计划生成问题是求解单个主体计划问题的一种有效方法。系统中的每一个主体可以通过其Petir网系统进行描述，进而得到多主体系统相应的有界层次Petri网系统。利用层次Petri网系统的可达标识图得到多主体系统关于目标状态的可达动作序列的集合，对可行可达动作序列及其中动作间关系确定得到多主体系统的计划。     

基于行为表达式的任意随机Petri网的品质分析

提出一种基于行为表达式的品质分析方法,可以做任意分布的有界或无界随机 Petri网的品质分析.该方法不仅拓广了分析范围,解决了文献[4]中没有解决的问题,而且 不必画出Petri网的可达标识图,使分析过程更为简洁.     

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。     

基于约束优化的Petri网可达性分析

Petri网的可达性判定问题是进行Petri网分析的基础。通过分析目前求解Petri网可达问题的判定方法和基于约束程序的Petri网可达问题判定方法,提出一种基于约束优化的Petri网可达问题判定方法,该方法是在状态方程法的基础上,利用约束程序寻求可行解,再利用优化求最优解,从而减少问题搜索的分支,达到减少状态方程的解空间的目的。最后通过实例的求解验证算法能够提高判定效率。     

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.      

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 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.     

Petri网的标注可达

本文基于Petri网的可达树的概念,给出标注可达树定义,并且证明网N与其标注可达树是一一对应的,然后,我们给出了网N与相应的标注可达树的相互转换算法。     

Comments on “A Modified Reachability Tree Approach to Analysis of Unbounded Petri Nets”

The above paper introduced the construction of a modified reachability tree (MRT) for (unbounded) Petri nets and its application to reachability, liveness, and deadlock analysis. This note shows via a counterexample that some of the MRT properties claimed in the above paper are incorrect.     

Some decision problems related to the reachability problem for Petri nets

In this paper, we show that (1) the question to decide whether a given Petri net is consistent, M_o-reversible or live is reduced to the reachability problem in a unified manner, (2) the reachability problem for Petri nets is equivalent to the equality problem and the inclusion problem for the sets of all firing sequences of two Petri nets, (3) the equality problem for the sets of firing sequences of two Petri nets with only two unbounded places under homomorphism is undecidable, (4) the coverability and reachability problems are undecidable for generalized Petri nets in which a distinguished transition has priority over the other transitions, and (5) the reachability problem is undecidable for generalized Petri nets in which some transitions can reset a certain place to zero marking.     

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     

Synchronizing sequences on a class of unbounded systems using synchronized Petri nets

Determining the state of a system when one does not know its current initial state is a very important problem in many practical applications as checking communication protocols, part orienteers, digital circuit reset, etc. Synchronizing sequences have been proposed in the 60’s to solve the problem on systems modeled by finite state machines. This paper presents a first investigation of the synchronizing problem on unbounded systems, using synchronized Petri nets, i.e., nets whose evolution is driven by external input events. The proposed approach suffers from the fact that no finite space representation can exhaustively answer to the reachability problem but we show that synchronizing sequences may be computed for a particular class of unbounded synchronized Petri nets.     

Hierarchical Reachability Graph Generation for Petri Nets

Reachability analysis is the most general approach to the analysis of Petri nets. Due to the well-known problem of state-space explosion, generation of the reachability set and reachability graph with the known approaches often becomes intractable even for moderately sized nets. This paper presents a new method to generate and represent the reachability set and reachability graph of large Petri nets in a compositional and hierarchical way. The representation is related to previously known Kronecker-based representations, and contains the complete information about reachable markings and possible transitions. Consequently, all properties that it is possible for the reachability graph to decide can be decided using the Kronecker representation. The central idea of the new technique is a divide and conquer approach. Based on net-level results, nets are decomposed, and reachability graphs for parts are generated and combined. The whole approach can be realized in a completely automated way and has been integrated in a Petri net-based analysis tool.