A Congruence for Petri Nets

We introduce a way of viewing Petri nets as open systems. This is done by considering a bicategory of cospans over a category of p/t nets and embeddings. We derive a labelled transition system (LTS) semantics for such nets using GIPOs and characterise the resulting congruence. Technically, our results are similar to the recent work by Milner on applying the theory of bigraphs to Petri Nets. The two main differences are that we treat p/t nets instead of c/e nets and we deal directly with a category of nets instead of encoding them into bigraphs.     

模糊时间Petri网及扩展的模糊时间Petri网

网络实时系统对时间和QoS有严格要求,因此对设计、实现和测试的技术和工具都有很高的要求。模糊时间Petri网是将模糊集合理论用于不确定的或主观的时间信息的表示,在每个变迁上添加时间间隔约束对模糊时间Petri网进行扩展得到扩展的模糊时间Petri网,它是一种对网络实时系统进行建模和分析的形式化模型,Petri网数学理论基础能保证并发系统的可靠性和正确性。本文详细地介绍了模糊时间Petri网及可扩展的时间Petri网,可扩展的时间Petri网的网精简方法,使用design／CPN仿真,及使用EFTN对多媒体同步建模,并探讨了进一步研究的方向。     

一种基于线性逻辑的Petri网分析方法

1 引言 Petri网是一种用网状图形表示系统模型的方法,能够从组织结构、控制和管理的角度,精确描述系统中事件(变迁)之间的依赖(顺序)和不依赖(并发)关系。Petri网理论提供了强大的分析方法,如不变量分析、系统性能分析(如活性)等以证明系统的正确性。近年来Petri网也被用来表示知识推理,例如用于诊断和监控,这就需要发展一种关于Petri网行为的推理主题。有些学者把经典逻辑和Petri网相结合,用Petri网表示产生式规则系统,网的框架代表基于产生式规则     

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.     

Ambient Petri Nets

Both the Ambient Calculus by L. Cardelli and the Elementary Object Systems by R. Valk model the behaviour of mobile systems. The Ambient Calculus is based on the concept of ambient, which is an environment with a given name that is delimited by a boundary, where some internal processes are executed. The main property of these ambients is that they can be moved to a new location thus modeling mobility. Elementary Object Systems are two-level net systems composed of a system net and one or more object nets, which can be seen as high-level token objects of the system net modeling the execution of mobile processes. This paper intends to contribute to the relationship between both frameworks by defining a multilevel extension of Elementary Object Systems, which will be used to provide a denotational semantics of a new process algebra called APBC (Ambient Petri Box Calculus). Such process algebra is an extension of the Petri Box Calculus that includes both ambients and their mobility capabilities, which conversely can be also interpreted as an extension of the Ambient Calculus with the main operations from the PBC.     

流体随机Petri网的一阶混杂Petri网模型

为了借用一阶混杂Petri网(First-Order Hybrid Petri Nets)的建模原语和分析方法来分析流体随机Petri网(Fluid Stochastic Petri Nets)以克服流体随机Petri网数值分析方法的局限性,本文提出了一种流体随机Petri网转换成一阶混杂Petri网的形式化描述方法,并对其转换的正确性进行了证明,最后通过实例分析了流体随机Petri网转换成一阶混杂Petri网的必要性.     

Stubborn Sets for Real-Time Petri Nets

The stubborn-set method attempts to reduce the number of states that must be explicitly enumerated during reachability analysis of a concurrent system, while preserving crucial concurrency properties in the reduced state space. Here we extend the method to the analysis of certain timed models. We also prove that timing properties of interest, such as minimum and maximum delays between events, are preserved in the reduced model. Finally, we report on some experimental results that we have obtained with our extension. These results show that real-time stubborn sets can often provide significant reductions in state space size.     

面向范畴类型数据的双聚类框架

双聚类是一种理想的概念聚类方法。对范畴类数据而言,双聚类可以给出相关联的数据对象和属性值的簇集(包括重叠的情况)。该文提出了一种通用的双聚类框架,由局部模式群集计算双划分。该局部模式反映了数据对象和属性之间的强关联。     

基于线性时态逻辑的Petri网模型检测研究

线性时态逻辑Petri网结合了Petri网和时序逻辑的优点,清晰简洁的描述并发系统事件间的时序和因果关系,包括系统的活性和安全性.其中自动机的体积是模型检验的一个关键性问题,为了得到尽可能小体积的自动机,在LTL公式转换为Büchi自动机之前,对LTL公式进行预处理来减少冗余,然后通过布尔技术优化自动机.     

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.     

Transformations of Petri Nets

The aim of this paper is an introduction to the area of Petri net transformations, a rule-based approach for dynamic changes of the net structure of Petri nets. This is especially important for the stepwise construction of Petri nets in the sense of the software development process in software engineering. The concept of Petri net transformations is based on that of graph transformations and high-level replacement systems and it is introduced within a small case study logistics.     

一种构造时间Petri网状态类的方法

提出一种基于全局时间的时间Petri网状态类构造方法——扩展时间戳状态类方法。该方法通过添加变迁的同步使能信息到时间戳状态类,并修改可实施条件和实施规则,解决了时间戳状态类方法中同步使能变迁的可实施性问题。     

一种利用UML的Petri网软件实现方法

Petri网既是一种图形化建模工具,又是一种形式化数学工具。Petri网具有对并发、并行、分布、异步系统进行验证仿真的能力。但是,Petri网是用来描述和分析要开发的系统模型的工具。不是计算机的实现工具,必须要通过一定的方法才能将Petri网用软件来实现。由于UML(统一建模语言)具有友善的用户界面,易于编程实现,故提出一种利用UML作为过渡的Petri网软件实现方法。     

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.     

基于 Petri 网的保险索赔工作流模型

Petri网是一种有效的形式化建模工具,能自然地描述并发、冲突、同步等系统特性。给出基于Petri网的保险索赔工作流模型,将Petri网三要素以对象的形式描述出来,并对此工作流模型的正确性定义和验证进行了说明。     

Petri网的广义组合积网研究

本文提出了Petri网的P-划分组合积网和T-划分组合积网，讨论了保持网的结构性质的条件。为大系统的分析与综合提供了新途径。     

Petri 网的步问题研究

在基于Petri 网的模型验证方法中,步被广泛用于减少变迁实施产生的语义交织.为了研究基于步的构造算法的计算复杂性,提出步的判定问题,并证明该问题是NP 完全的.进一步给出了极大步问题的多项式时间算法和最大步问题的NP 等价性证明.最后分析两类特殊子问题是P 问题.     

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.