A methodology of testing high-level Petri nets

Petri nets have been extensively used in the modelling and analysis of concurrent and distributed systems. The verification and validation of Petri nets are of particular importance in the development of concurrent and distributed systems. As a complement to formal analysis techniques, testing has been proven to be effective in detecting system errors and is easy to apply. An open problem is how to test Petri nets systematically, effectively and efficiently. An approach to solve this problem is to develop test criteria so that test adequacy can be measured objectively and test cases can be generated efficiently, even automatically. In this paper, we present a methodology of testing high-level Petri nets based on our general theory of testing concurrent software systems. Four types of testing strategies are investigated, which include state-oriented testing, transition-oriented testing, flow-oriented testing and specification-oriented testing. For each strategy, a set of schemes to observe and record testing results and a set of coverage criteria to measure test adequacy are defined. The subsumption relationships and extraction relationships among the proposed testing methods are systematically investigated and formally proved.     

一种基于模型的测试充分性评估方法

测试充分性评估通常采用覆盖率的方法来评估测试对软件特征的覆盖充分程度。如今,传统的充分性评估方法难以满足复杂软件的测试评估需求。首先,代码覆盖准则难以准确验证软件需求;其次,软件测试还需考虑软件不同特征对系统测试充分性的不同影响。对此,提出一种基于接口的建模方法和基于该模型的综合覆盖充分性评估方法。该方法根据软件接口说明,对系统功能进行特征抽取、建模,并对接口模型的测试用例进行不同层级的充分性评估,对评佑结果进行归一化处理,得到系统的综合测试充分性。通过案例表明,这种评佑方法能够反映功能的测试充分性,对测试用例的设计和优化有一定指导意义。     

Model-based testing for concurrent systems: unfolding-based test selection

Model-based testing has mainly focused on models where concurrency is interpreted as interleaving (like the ioco theory for labeled transition systems), which may be too coarse when one wants concurrency to be preserved in the implementation. In order to test such concurrent systems, we choose to use Petri nets as specifications and define a concurrent conformance relation named co-ioco. We present a test generation algorithm based on Petri net unfolding able to build a complete test suite w.r.t our co-ioco conformance relation. In addition, we propose several coverage criteria that allow to select finite prefixes of an unfolding in order to build manageable test suites.     

基于Petri网的并发程序测试用例产生方法

并发程序的测试路径具有不可预测性,而Pctri网在描述并发方面具有其它系统模型无法比拟的优势。因此通过Petri网来产生并发程序的测试路径:对有并发程序的源代码构造的Petri网模型进行图形矩阵转换;按照一定的规则得出相应的独立段组;合并独立段组得出网的独立段群,此独立段群即为该并发程序的测试路径。实验证明,将Petri网用于并发程序测试用的例生成降低了测试难度,提高了测试效率。     

Timed high-level nets

Petri nets have been widely used for modeling and analyzing concurrent systems. Several reasons contribute to their success: the simplicity of the model, the immediate graphical representation, the easy modeling of asynchronous aspects, the possibility of reasoning about important properties such as reachability, liveness, boundedness. However, the original model fails in representing two important features: complex functional aspects, such as conditions which rule the flow of control, and time. Due to that, two different classes of extensions of Petri nets have been proposed: high-level nets and timed Petri nets. High-level nets allow the representation of functional aspects in full details, but do not provide a means for representing time; on the other hand, timed Petri nets have been thought for time representation, but they do not provide a means for representing detailed functinal aspects. Thus, these two important aspects cannot be mastered together. In particular, it is difficult to express relationships between time and functional aspects.This paper investigates the relationships between high-level nets and timed Petri nets, thus extending a first set of results published in a previous paper, where a unifying Petri net based model for time representation has been proposed. It first recalls how time can be represented in a Petri net extension called ER nets, and assesses its generality. It then investigates the relationships of ER nets with the best known high-level nets. In particular it shows the overall equivalence of ER nets, Colored Petri nets and Predicate/Transition nets, and extends the mechanism for time representation introduced in ER nets to both Colored Petri nets and Predicate/Transition nets. It also shows that these models cannot be simplified without significantly constraining the timing aspects that can be modeled.     

Scheduling and control of real-time systems based on a token player approach

Petri nets are a powerful formalism for the specification and verification of concurrent systems, such as sequential systems and manufacturing systems. To deal with real-time systems whose time issues become essential, different extensions of Petri nets with time have been proposed in the literature. In this paper, a new scheduling and control technique for real-time systems modeled by ordinary P-time Petri nets is proposed. Its goal is to provide a scheduling for a particular firing sequence, without any violation of timing constraints ensuring that no deadline is missed. It is based on the firing instant notion and it consists in determining an inequality system generated for a possible evolution (in terms of a feasible firing sequence for the untimed underlying Petri net) of the model. This system can be used to check reachability problems as well as evaluating the performances of the model considered and determining the associated control for a definite functioning mode and it introduces partial order on the execution of particular events.     

Synthesis a Petri net based control model for a FMS cell

Petri nets have been recognised as a high level formal and graphical specification language for modelling, analysis, and control of concurrent asynchronous distributed systems. This paper presents a PN model, synthesised by an extended version of the knitting synthesis technique. This method, as an incremental design approach, establishes the conditions under which the fundamental behavioural properties of the synthesised systems are fulfilled and preserved. That is, the synthesised models are live, bounded, and reversible (cyclic). A Petri net with the aforementioned properties is called a well-behaved Petri net system which is guaranteed to operate in a deadlock-free, stable, and cyclic fashion. Well-behaved Petri net models, synthesised using the proposed method can be compiled into control codes and implemented as real-time controllers for flexible manufacturing systems. The significance of this paper is due to the application of an extended version of knitting synthesis technique to a real life example of a flexible manufacturing system.     

Distributed control systems simulation using high level Petri nets

To deal with the complexity of the implementation of control systems for flexible manufacturing systems, formal methods of design are needed. In this work the modeling and validation tool selected is high level Petri nets. Based on this approach we have studied the problems that a distributed implementation can introduce. For the evaluation of different strategies of the model implementation and the scheduling of production tasks a simulator has been constructed. This simulator has been written in Ada language.     

Symbolic execution of concurrent systems using Petri nets

Techniques for analyzing sequential programs in order to improve their reliability have been widely studied in the past. Among the most interesting analysis techniques, we consider symbolic execution. However, analysis techniques for concurrent programs, and in particular symbolic execution, are still an open research area. In this paper, we define a method for symbolic execution of concurrent systems, based on an extension of the Petri net formalism, called EF nets. EF nets are a powerful, highly expressive and general formalism. Depending on the level of abstraction of actions and predicates that one associates to the transitions of the net, EF nets can be used as a high-level specification formalism for concurrent systems, or as a lower level internal representation of concurrent programs. Thus, the model is not dependent on a particular concurrent programming language, but it is flexible enough to be the kernel model for the representation of a wide set of systems and programming languages. In the paper, in order to support the analysis of a concurrent system or program, at first a general algorithm for symbolically executing an EF net is defined. Then, a more efficient algorithm is given for the particular, though important, subclass of EF nets, defined as safe EF nets. Such algorithm is proved to significantly help in reducing the amount of information needed to characterize a symbolic execution. Both the modelling power of the EF nets and the usefulness of the concurrent symbolic execution algorithms defined are illustrated by means of a case study.     

Development of context-aware workflow systems based on Petri Net Markup Language

The Petri Net Markup Language (PNML) is originally an XML-based interchange format for Petri nets. Individual companies may specify their process models in Petri nets and exchange the Petri nets with other companies in PNML. This paper aims to demonstrate the capabilities of PNML in the development of applications instead of an industrial interchange format only. In this paper, we apply PNML to develop context-aware workflow systems. In existing literature, different methodologies for the design of context-aware systems have been proposed. However, workflow models have not been considered in these methodologies. Our interests in this paper are to propose a methodology to automatically generate context-aware action lists for users and effectively control resource allocation based on the state of the workflow systems. To achieve these objectives, we first propose Petri net models to describe the workflows. Next, we propose models to capture resource activities. Finally, the interactions between workflows and resources are combined to obtain a model for the whole processes. Based on the combined model, we propose architecture to automatically generate context-aware graphical user interface to guide the users and control resource allocation in workflow systems. We demonstrate our design methodology using a health care example.     

动态描述逻辑动作间关系的Petri网分析方法研究

针对动态描述逻辑动作理论在描述和分析多个动作间关系(尤其并发关系)时能力的不足, 提出对多个动态描述逻辑动作间关系描述和分析的 Petri 网方法. 首先讨论了动态描述逻辑动作的等价 Petri 网描述, 进一步通过对动作描述的推理和各个动作的 Petri 网共享合成操作, 得到多个动态描述逻辑动作的 Petri 网系统. 在此基础上, 应用 Petri 网的相关理论与方法, 如可达图分析方法, 研究了多个动态描述逻辑动作间关系的分析与判定方法, 对动态描述逻辑动作理论的描述和分析能力进行了必要的扩充.     

层次结构的Petri网

Petri网是一个很好地描述与分析并行系统的模型。但在实际应用中,如果系统过大或较复杂时,会遇到结点数过多的问题。介绍了着色网和几种层次结构的Petri网,包括位置/转移精化网、对象网以及开放网等;分析和比较了这几种模型用以减少结点数和引入层次结构的方法,而且从结构上讨论了它们相互之间的关系。     

Knowledge intensive Petri net framework for concurrent intelligent design of automatic assembly systems

The integration of design and planning of flexible assembly system has been recognized as a tool for achieving efficient assembly in a production environment that demands assembly with a high degree of flexibility. This paper proposes a concurrent intelligent approach and framework for the design of robotic flexible assembly systems. The principle of the proposed approach is based on the knowledge Petri net formalisms, incorporating Petri nets with more general problem-solving strategies in AI using knowledge-based system techniques. The complex assembly systems are modeled and analyzed by adopting a formal representation of the system dynamic behaviors through knowledge Petri net modeling from the specifications and the analysis of those models. A template is first defined for a knowledge Petri net model, and then the models for assembly system individuals are established in the form of instances of the template. The design of assembly systems is implemented through a knowledge Petri net-based function–behavior–structure model. The research results show that the proposed knowledge Petri net approach is applicable for design, simulation, analysis and evaluation, and even layout optimization of the flexible assembly system in an integrated intelligent environment. The integration of assembly design and planning process can help reduce the development time of assembly systems.     

基于Petri网的列控系统形式化分析方法

利用原型Petri网对列车控制系统建模难于实现,用带抑止弧的增广Petri网则可以较好地描述问题。将带抑止弧的增广Petri网作为计算模型,对列车控制系统的一些关键问题进行了建模并给出了两个控制子系统：车站调度子系统与区间运行子系统。车站调度子系统实现了对列车请求进入和驶离车站的协调控制,区间运行子系统则实现了闭塞区间的车辆的安全性控制、突发事件时(如遭遇雷击,信号丢失的情况发生等)的安全性处理和公路铁路交叉口的调度等。最后,利用S-不变量对模型的活性、可达性和有界性等给予了形式化的验证。     

基于Petri网的软件测试用例的产生及分析

软件测试不仅要考虑到功能的正确性、覆盖的完整性,也应该考虑到测试用例的可行性。一种常用的产生测试用例的方法是路径覆盖,它是通过分析控制流来产生的,但是这样很可能产生不可行路径。论文运用Petri网来描述程序,并且按照一定的数学规则将此Petri网进行分解,得到独立的段组(Independent Segment Group,ISG)并产生测试用例,最后设计一个算法找到满足覆盖准则的最少测试用例。     

模糊定时高级Petri网的协同设计活动建模和分析

利用模糊定时高级Petri网和工作流技术对协同设计活动进行建模和分析，定义了评估和推理规则，解决了协同设计中对不确定性时间参数的管理，并能够实现对协同设计的时间验证，特别是对协同设计时间的定量分析，最后举例说明了如何建立相应的模糊Petri网模型，并对其性能进行分析推理。     

一种兼顾协议正确性验证和性能评估的Petri网方法

基于Petri网的协议形式化分析方法由于其精炼、简洁和无二义性逐步成为分析协议的一条可靠和准确的途径,但是协议的形式化分析目前研究还不够深入,协议分析的两个重点内容正确性验证和性能评估所需要的模型不同,一种模型只能解决一方面的工作。为了有效地解决这一问题,文中提出了一种用原型Petri网作为协议验证模型的思路和方法,在不改变原型Petri网结构的基础上对变迁赋予发生时延,解决了协议的性能评估问题。本文还给出了协议验证内容与Petri网分析方法的对应关系,并对0-1停止等待协议进行了详细的分析,最后把0-1停止等待协议的原型Petri网模型转化为时延Petri网,对协议的性能进行了评估。     

State equation, controllability, and maximal matchings of petri nets

Petri nets are a versatile modeling device for studying the structure and control of concurrent systems. Petri nets and related graph models have been used for modeling a wide variety of systems from computers to social systems. In order to introduce this interesting modeling device to the researcher in control theory, this paper discusses Petri nets in the context of the state equation for a linear discrete-time system. The controllability concept of dynamic systems is applied to Petri nets for the first time. It is also shown that the controllability and reachability of a Petri net are related to maximal matchings of its bipartite graph.     

不可否认协议的Petri网建模与分析

Petri网是一种描述及分析并发行为的工具,在安全协议的形式化分析中得到了广泛的应用．作为一种特殊的安全协议,不可否认协议虽然已得到了多种形式化方法的分析,但还没有人使用Petri网来分析它们．以一般安全协议的Petri网分析方法为基础,提出了使用Petri网分析不可否认协议的建模及分析方法,该方法可以描述并分析一些其他形式化方法无法描述的协议性质．使用该方法分析Zhou和Gollmann于1996年提出的一个公平不可否认协议,可以发现该协议的一个许多其他形式化方法不能发现的已知缺陷．