Generating transition probabilities to support model‐based software testing

Markov chain usage models support test planning, test automation, and analysis of test results. In practice, transition probabilities for Markov chain usage models are often specified using a cycle of assigning, verifying, and revising specific values for individual transition probabilities. For large systems, such an approach can be difficult for a variety of reasons. We describe an improved approach that represents transition probabilities by explicitly preserving the information concerning test objectives and the relationships between transition probabilities in a format that is easy to maintain and easy to analyze. Using mathematical programming, transition probabilities are automatically generated to satisfy test management objectives and constraints. A more mathematical treatment of this approach is given in References [ 1 ] (Poore JH, Walton GH, Whittaker JA. A constraint‐based approach to the representation of software usage models. Information and SoftwareTechnology 2000; at press) and [ 2 ] (Walton GH. Generating transition probabilities for Markov chain usage models. PhD Thesis, University of Tennessee, Knoxville, TN, May 1995.). In contrast, this paper is targeted at the software engineering practitioner, software development manager, and test manager. This paper also adds to the published literature on Markov chain usage modeling and model‐based testing by describing and illustrating an iterative process for usage model development and optimization and by providing some recommendations for embedding model‐based testing activities within an incremental development process. Copyright © 2000 John Wiley & Sons, Ltd.     

基于重要抽样的软件统计测试加速

本文提出一种基于重要抽样的软件统计测试加速方法,该方法通过调整软件Markov链使用模型的迁移概率,在根据统计测试结果得到软件可靠性无偏估计的前提下,可以有效提高安全攸关软件的测试效率,部分解决了安全攸关软件统计测试时间和费用开销过大的问题。同时,本文给出了计算优化迁移概率的模拟退火算法。实验仿真结果表明,该方法可以有效地提高安全攸关软件统计测试的效率。     

基于UML的软件Markov链使用模型构造研究

软件统计测试要求基于软件使用模型产生测试例对软件系统进行测试,并根据测试结果评价软件可靠性,是高可靠软件测试的重要组成部分.由于统一建模语言(unified modeling language,简称UML)已经成为事实上的面向对象标准建模语言,因此,从软件UML模型构造软件使用模型就成为面向对象软件统计测试的关键.为此,定义了加入统计测试约束的UML用例图、序列图以及用例执行顺序关系,为基于UML的软件统计测试提供了一个形式化描述基础.在此基础上,给出一个从软件UML模型构造软件Markov链使用模型的算法,并给出了自动化支持工具UMGen的类图结构,基于一个卫星控制系统,说明了所提出方法的有效性.     

基于UML的软件Markov链使用模型的构建

构建软件的使用模型是进行软件可靠性测试及软件可靠性评估的基础.近年来,如何由软件的UML模型构造软件的使用模型成为研究热点.对于大型的软件系统来说,应用现有方法构建的软件Markov链使用模型的状态空间过于庞大,模型描述困难,不利于测试用例的自动生成及软件可靠性评估.针对以上问题,提出了一种由UML模型构建Markov链使用模型的方法.该方法将场景的前置条件和后置条件作为Markov链使用模型的状态,将场景的执行及执行概率作为状态之间的转移及转移概率.与现有方法相比,新方法构建的Markov链使用模型的状态空间小且无需人为干预,而且可以很方便地生成测试输入从而进行可靠性测试.针对UML模型的有效性,提出了经过可靠性评估扩展的UML模型生成Markov链使用模型的验证算法.最后通过一个卫星控制系统的实例对新方法的性能进行了验证.     

安全关键系统的软件可靠性评估方法

基于统计测试的Markov使用链模型对安全关键系统的可靠性估计提出了一种有效的方法。该方法利用重要抽样技术在保证佑计的无偏性条件下,以可靠性估计的方差最小为目的,通过Ali-Silvey距离度量两个分布之间的差异,调整各个状态之间的转移概率分布,修正测试剖面,增加关键操作的遍历概率。最后给出了软件可靠性估计的最优测试剖面生成迭代算法。仿真结果表明,该方法能明显降低估计方差,在提高估计精度的同时能有效地加速统计测试。     

基于使用模型的嵌入式软件测试用例生成研究

基于Markov链使用模型的软件统计测试是产生高效测试用例,实现软件可靠性定量评估的有效方法。介绍了基于使用模型的统计测试方法,论述了使用模型的概念和特点,以及从使用模型中可以计算出的静态参数和它们在统计测试和软件开发中所起的作用。提出Markov链使用模型用于嵌入式软件的测试,从理论上得到嵌入式软件的可靠性。具体阐述了嵌入式软件的Markov链使用模,型自动生成测试模型的方法。同时使用改进的Kullback判别式探讨测试的可靠性问题,从理论上证明了测试链到使用链收敛的必然性。理论分析和初步的实例证明该方法是可行的和有前途的。     

Review of several stochastic speech unit models

Hidden Markov models are commonly used for speech unit modelling. This type of model is composed of a non-observable or “hidden” process, representing the temporal structure of the speech unit, and an observation process linking the hidden process with the acoustic parameters extracted from the speech signal.Different types of hidden processes (Markov chain, semi-Markov chain, “expanded-state” Markov chain) as well as different types of observation processes (discrete, continuous, semi-continuous—multiple processes) are reviewed, showing their relationships. The maximum likelihood estimation of two-stage stochastic process parameters is presented in an a posteriori probability formalism. An intepretation of the expectation-maximization algorithm is proposed and the practical learning algorithms for hidden Markov models and hidden semi-Markov models are compared in terms of computation structure, probabilistic justification and complexity.This presentation is illustrated by experiments on a multi-speaker 130 isolated word recognition system. The implementation techniques are detailed and the different combinations of state occupancy modelling techniques and observation modelling techniques are studied from a practical point of view.     

NHPP models with Markov switching for software reliability

We describe the use of a latent Markov process governing the parameters of a nonhomogeneous Poisson process (NHPP) model for characterizing the software development defect discovery process. Use of a Markov switching process allows us to characterize non-smooth variations in the rate at which defects are found, better reflecting the industrial software development environment in practice. Additionally, we propose a multivariate model for characterizing changes in the distribution of defect types that are found over time, conditional on the total number of defects. A latent Markov chain governs the evolution of probabilities of the different types. Bayesian methods via Markov chain Monte Carlo facilitate inference. We illustrate the efficacy of the methods using simulated data, then apply them to model reliability growth in a large operating system software component-based on defects discovered during the system testing phase of development.     

Markov random field-based statistical character structure modeling for handwritten Chinese character recognition

This paper proposes a statistical-structural character modeling method based on Markov random fields (MRFs) for handwritten Chinese character recognition (HCCR). The stroke relationships of a Chinese character reflect its structure, which can be statistically represented by the neighborhood system and clique potentials within the MRF framework. Based on the prior knowledge of character structures, we design the neighborhood system that accounts for the most important stroke relationships. We penalize the structurally mismatched stroke relationships with MRFs using the prior clique potentials, and derive the likelihood clique potentials from Gaussian mixture models, which encode the large variations of stroke relationships statistically. In the proposed HCCR system, we use the single-site likelihood clique potentials to extract many candidate strokes from character images, and use the pairsite clique potentials to determine the best structural match between the input candidate strokes and the MRF-based character models by relaxation labeling. The experiments on the KAIST character database demonstrate that MRFs can statistically model character structures, and work well in the HCCR system.     

基于UML的软件使用模型的研究及工具实现*

改进了文献［2］中提出的一种由软件的UML模型转换得到软件的Markov链使用模型的方法。采用Java语言实现了一个从软件的UML模型获得软件使用模型的工具。     

Introducing probabilities in Statecharts to specify reactive systems for performance analysis

Statecharts are expressed in a graphical language to specify complex reactive systems. They are extension of state-transition diagrams to which notions of hierarchy and orthogonality have been added. Recently, they have been suggested to represent performance models and in this regard a software package has been developed. In these performance models, the behavior of a system under study is considered to be probabilistic. Therefore, the inclusion of probabilities in Statecharts formalism will be studied. The proposed extension considers that a modeled system reacts probabilistically to events. In order to deal with these models, an analytical computational method based on constructing a Continuous-Time Markov Chain that is equivalent to the Statecharts model is proposed. The aspect of generating a Continuous-Time Markov Chain from Statecharts representation along with the solution to include probabilities among the transitions will be covered in this paper.     

基于Markov链路径使用模型的软件统计测试

探讨了建立基于路径使用的Markov链模型来分析模块内部代码结构的统计测试方法的可能性。提出将统计理论用于软件的结构测试，从理论上得出软件的结构可靠性结论。提出具有有限状态、离散时间序列的Markov链作为程序的使用模型和测试模型，使用Kullback判别式作为测试链收敛到使用链的判断准则，从理论上证明了测试链到使用链收敛的必然性。理论分析和初步的实验证明该方法是可行和有前途的。     

The least-squares Padé method for model simplification of multivariable systems

This paper is concerned with the simplification of multivariable systems in the frequency domain. Whereas the original model can be represented in either the time or frequency domains, the simplified model will be a transfer matrix. Dominant poles of the original system are retained in the simplified model and thereby the stablity of the latter is guaranteed. The matrices comprising the numerator of the simplified mode! are determined by imposing a number of constraints which is larger than the number of unknowns, and the resulting set of equations is solved in a least squares sense. This usually enables the determination of models which are more accurate over the range of midfrequencies. The contraints used are the approximate retention of Padé and Markov matrices. To apply least-squares techniques, a new formulation is suggested for the matrices of Padé and Markov parameters. By varying the total number of Padé and Markov constraints a family of simplified models is easily obtained, and performance criteria can be used to select the best model. The new algorithm is illustrated using the model or a real power system     

Measuring complexity and coverage of software specifications

Coverage testing in the context of Markov chain usage models refers to coverage of a model of the specification and profile of intended use, rather than coverage of the code that implements the specification. A new measure of specification complexity based on the number of statistically typical paths through the model of the specification is derived. Formulae are presented to compute bounds on the expected number of test cases required to achieve state and arc coverage. Formulae are presented to compare different usage models with respect to the amount of testing required to achieve coverage of typical paths. Convexity properties are established for these formulae to facilitate their use in optimization calculations that are used to generate transition probabilities for the usage models.     

The optimal robust control policy for uncertain semi-Markov control processes

The optimization problems of Markov control processes (MCPs) with exact knowledge of system parameters, in the form of transition probabilities or infinitesimal transition rates, can be solved by using the concept of Markov performance potential which plays an important role in the sensitivity analysis of MCPs. In this paper, by using an equivalent infinitesimal generator, we first introduce a definition of discounted Poisson equations for semi-Markov control processes (SMCPs), which is similar to that for MCPs, and the performance potentials of SMCPs are defined as solution of the equation. Some related optimization techniques based on performance potentials for MCPs may be extended to the optimization of SMCPs if the system parameters are known with certainty. Unfortunately, exact values of the distributions of the sojourn times at some states or the transition probabilities of the embedded Markov chain for a large-scale SMCP are generally difficult or impossible to obtain, which leads to the uncertainty of the semi-Markov kernel, and thereby to the uncertainty of equivalent infinitesimal transition rates. Similar to the optimization of uncertain MCPs, a potential-based policy iteration method is proposed in this work to search for the optimal robust control policy for SMCPs with uncertain infinitesimal transition rates that are represented as compact sets. In addition, convergence of the algorithm is discussed.     

面向复杂UML的Markov建模方法研究

软件可靠性测试技术是保证软件质量的重要研究内容,尤其是对航空航天、金融机构等高信度复杂软件尤为重要。在现有研究的基础上,针对复杂软件UML模型场景消息粒度过大导致构建的Markov链使用模型描述软件的真实度不够的问题,提出了一种基于多层嵌套组合片段UML模型的Markov链使用模型的构建方法,最后结合实例对研究提出的模型构建方法做出应用分析,说明了算法的可行性,为更有效地构建Markov链使用模型提供了指导。     

基于受控Markov链的软件自适应测试策略

基于简化的受控Markov链软件自适应测试模型大多是研究如何以最小的期望成本检测并移除所有的缺陷,并在构建模型时对部分条件进行特殊化和理想化处理.针对受控Markov链软件测试模型适用范围小、效率低的缺陷,在软件控制论思想基础上,对制约条件进行了一系列新的转换,提出一种改进的、资源约束的受控Markov链模型,该模型能够在高效性、复杂性和适用性3方面达到一个平衡.根据该模型设计一种新的软件缺陷优化测试策略,再通过参数估计对优化测试策略进行在线调整的方法,以构造软件自适应测试策略.为了证明其有效,利用该模型得到的新的软件自适应测试策略进行仿真实验,进一步得到了有效结果.     

Information integration via hierarchical and hybrid bayesian networks

A collaboration scheme for information integration among multiple agencies (and/or various divisions within a single agency) is designed using hierarchical and hybrid Bayesian networks (HHBNs). In this scheme, raw information is represented by transactions (e.g., communication, travel, and financing) and information entities to be integrated are modeled as random variables (e.g., an event occurs, an effect exists, or an action is undertaken). Each random variable has certain states with probabilities assigned to them. Hierarchical is in terms of the model structure and hybrid stems from our usage of both general Bayesian networks (BNs) and hidden Markov models (HMMs, a special form of dynamic BNs). The general BNs are adopted in the top (decision) layer to address global assessment for a specific question (e.g., "Is target A under terrorist threat?" in the context of counterterrorism). HMMs function in the bottom (observation) layer to report processed evidence to the upper layer BN based on the local information available to a particular agency or a division. A software tool, termed the adaptive safety analysis and monitoring (ASAM) system, is developed to implement HHBNs for information integration either in a centralized or in a distributed fashion. As an example, a terrorist attack scenario gleaned from open sources is modeled and analyzed to illustrate the functionality of the proposed framework.     

基于软件层次化模型的软件测试数据生成

针对基于Markov链模型的软件测试技术在测试数据生成时不考虑软件的结构信息,生成的测试数据集对代码路径的覆盖能力以及缺陷检测能力都较低的问题,将统计测试与基于Markov链模型的测试相结合,提出了一种新的软件测试模型——软件层次化模型。该模型涵盖了软件与外部环境之间的交互,同时描述了软件内部结构信息。还给出了该模型测试数据集的生成算法：首先生成符合使用情况的测试序列,然后为测试序列生成覆盖软件内部结构的输入数据。通过针对示例软件的实验结果表明,与基于Markov链模型的测试方法对比,基于软件层次化模型的测试在满足软件测试充分性要求的同时,提高了测试数据集的代码路径覆盖能力和缺陷检测能力。