A granularity model for balancing the structural complexity of manufacturing systems equipment and layout

The structural complexity of a manufacturing system results primarily from the complexity of its equipment and their layout. The balance between both complexity sources can be achieved by searching for the best system granularity level, which yields a manufacturing system with the least overall structural complexity. A new system granularity complexity index is developed to sum up and normalize the complexity resulting from the system layout complexity and the equipment structural complexity. A previously developed layout complexity index together with a code-based structural complexity assessment are used to determine the structural complexity of standalone pieces of equipment and to arrive at a balance between the two sources of complexity. Cladistics analysis is used to hierarchically cluster required pieces of equipment and bundle them into more integrated equipment and machines and demonstrate the possible different system granularity levels. The new developed model is a useful tool to create specific system configuration and layout alternatives based on system components adjacency, and then select the system design with the least overall structural complexity among those alternatives. The results of the presented case study clearly demonstrated this trade-off where decomposing manufacturing systems into a highly granular configuration with standalone machines maximizes system layout complexity and minimizes equipment complexity, while at a low level of granularity pieces of equipment are bundled into complex integrated machines, lines or cells but with a very simple system layout.     

信息系统体系结构复杂性度量方法研究*

体系结构技术是进行信息系统设计的重要技术,其复杂性直接决定着建设信息系统的复杂性。研究了程序复杂性的度量方法,在复杂性概念研究的基础上,提出了将体系结构复杂性分为动态复杂性和结构复杂性分开进行度量的方法,并提出基于熵的动态复杂性和结构复杂性评估方法。通过对体系结构复杂性度量方法的研究,可以有效地度量体系结构的复杂性,为项目开发与决策提供有力的依据。     

Measuring dynamic program complexity

A relative complexity technique that combines the features of many complexity metrics to predict performance and reliability of a computer program is presented. Relative complexity aggregates many similar metrics into a linear compound metric that describes a program. Since relative complexity is a static measure, it is expanded by measuring relative complexity over time to find a program's functional complexity. It is shown that relative complexity gives feedback on the same complexity domains that many other metrics do. Thus, developers can save time by choosing one metric to do the work of many     

Shape complexity

The complexity of 3D shapes that are represented in digital form and processed in CAD/CAM/CAE, entertainment, biomedical, and other applications has increased considerably. Much research was focused on coping with or on reducing shape complexity. However, what exactly is shape complexity? We discuss several complexity measures and the corresponding complexity reduction techniques. Algebraic complexity measures the degree of polynomials needed to represent the shape exactly in its implicit or parametric form. Topological complexity measures the number of handles and components or the existence of non-manifold singularities, non-regularized components, holes or self-intersections. Morphological complexity measures smoothness and feature size. Combinatorial complexity measures the vertex count in polygonal meshes. Representational complexity measures the footprint and ease-of-use of a data structure, or the storage size of a compressed model. The latter three vary as a function of accuracy.     

Evaluating code complexity triggers,use of complexity measures and the influence of code complexity on maintenance time

Code complexity has been studied intensively over the past decades because it is a quintessential characterizer of code’s internal quality. Previously, much emphasis has been put on creating code complexity measures and applying these measures in practical contexts. To date, most measures are created based on theoretical frameworks, which determine the expected properties that a code complexity measure should fulfil. Fulfilling the necessary properties, however, does not guarantee that the measure characterizes the code complexity that is experienced by software engineers. Subsequently, code complexity measures often turn out to provide rather superficial insights into code complexity. This paper supports the discipline of code complexity measurement by providing empirical insights into the code characteristics that trigger complexity, the use of code complexity measures in industry, and the influence of code complexity on maintenance time. Results of an online survey, conducted in seven companies and two universities with a total of 100 respondents, show that among several code characteristics, two substantially increase code complexity, which subsequently have a major influence on the maintenance time of code. Notably, existing code complexity measures are poorly used in industry.     

A Complexity Measure

This paper describes a graph-theoretic complexity measure and illustrates how it can be used to manage and control program complexity. The paper first explains how the graph-theory concepts apply and gives an intuitive explanation of the graph concepts in programming terms. The control graphs of several actual Fortran programs are then presented to illustrate the correlation between intuitive complexity and the graph-theoretic complexity. Several properties of the graph-theoretic complexity are then proved which show, for example, that complexity is independent of physical size (adding or subtracting functional statements leaves complexity unchanged) and complexity depends only on the decision structure of a program.     

面向对象类的复杂性的度量方法

简要分析了已有的几种面向对象软件复杂性度量方法,指出了这些方法在反映类复杂性方面存在的不足,运用软件复杂性分解的思想,提出了一种新的类复杂性度量方法。该方法将类复杂性分解为类成员复杂性、类成员关系复杂性和封装复杂性三个复杂性分量,对各分量分别度量,进而得出总复杂性。其中,类成员复杂性采用类所实现的成员的复杂性SIMC、类接口复杂性之和SCIC反映;类成员关系复杂性通过对文中提出的伪二部图进行分析反映;封装复杂性采用成员可见率反映。最后,通过实例验证了该方法的有效性和可行性。     

Kolmogorov-Chaitin Complexity of Digital Controller Implementations

The complexity of linear, fixed-point arithmetic digital controllers is investigated from a Kolmogorov-Chaitin perspective. Based on the idea of Kolmogorov-Chaitin complexity, practical measures of complexity are developed for state-space realizations, parallel and cascade realizations, and for a newly proposed generalized implicit state-space realization. The complexity of solutions to a restricted complexity controller benchmark problem is investigated using this measure. The results show that from a Kolmogorov-Chaitin viewpoint, higher-order controllers with a shorter word-length may have lower complexity and better performance, than lower-order controllers with longer word-length.     

若干二元周期序列的紧错线性复杂度

综合线性复杂度、k错线性复杂度、k错线性复杂度曲线和最小错误minerror（S）的概念,提出m紧错线性复杂度的概念。 序列S的m紧错线性复杂度是一个二元组（km,LCm）。序列S的k错线性复杂度曲线的第m个跃变点对应的km值和对应km错线性复杂度LCm,称为序列S的m紧错线性复杂度。通过使用简洁的cost二维结构,给出了周期为2n的二元序列的紧错线性复杂度算法,并证明具有Stamp-Martin模式的线性复杂度算法均可以简单地推广为求紧错线性复杂度的算法。与现有k错线性复杂度算法不同,该算法中省去了原来序列元素的运算。在王-张-肖算法基础上,通过使用cost二维结构,给出了周期为pn的二元序列的紧错线性复杂度算法,其中p是一个素数,2是一个模p2的本原根。     

数值计算程序的存储复杂性分析

由于越来越多的技术用于缩小处理器与存储器之间的日益加大的速度差距,计算机的存储系统变得日趋复杂．现在,任何一个程序设计者,尤其是数值计算程序的设计者,若不考虑其所用计算平台存储系统的特点是很难获取高性能的．因此公用传统的算法评价方法,从时间复杂性和空间复杂性着手来解释一个算法的不同实现在同一计算平台上很大的性能差异,显然是不够的．计算平台存储系统的特点必须在分析算法的复杂性时加以考虑．孙家昶１９９     

构件软件的回归测试复杂性度量

基于构件的软件构建方法目前被广泛使用在软件开发中,用于减少软件开发的工程成本和加快软件开发进度.在软件维护过程中,由于构件更新或者新版本的发布,基于构件的系统会受到影响,需要进行回归测试.对于指定的软件修改需求,维护者可以实施不同的修改手段.不同的修改手段会导致不同的回归测试复杂性,这种复杂性是软件维护成本和有效性的重要因素.目前的研究没有强调构件软件的回归测试复杂性问题.基于修改影响复杂性模型和度量,提出一种回归测试的复杂性度量框架.该度量框架包括两个部分:基于图的模型和形式化度量计算.该度量可以有效表示构件软件分别在构件和系统层面的回归测试复杂性因素,可视化地体现复杂性变化.然后根据模型,提出具体的度量计算方式.最后,通过实验研究,针对同一个构件软件的相同修改需求,利用若干个实验组进行独立修改实施,然后比较回归测试的复杂性.实验结果表明,所提出的度量方式是可行和有效的.     

一种基于相对海明距离的地图复杂性度量

提出一种适用于分层路径搜索算法的地图复杂性度量方法。针对不同规模的地图,将其实际复杂度与可达到的最大复杂度之比作为相对复杂度,提出基于相对海明距离的度量方法,并引入地图区域间方差,从而更好地计算障碍物分布不均匀地图的复杂度。实验结果证明,该方法能准确地反映不同规模与障碍物分布不均的地图复杂程度,并与HPA*算法的搜索效率有较强关联性。     

基于熵的信息系统业务模型复杂性度量

业务模型的复杂度决定企业信息系统的复杂度,也对信息系统的重构性能具有很大程度的影响。目前研究多侧重于代码级软件的复杂度度量,而对业务模型的复杂度则关注较少。本文首先给出了企业业务模型的分层体系结构,依据模型实体之间的依赖关系与分解关系将业务模型分解为一组基本模型单元。然后重点提出一种基于熵的模型复杂性度量方法,使用信息熵来描述业务模型的复杂性,通过计算基本模型单元的复杂度递归得到各模型实体、依赖关系的复杂性,进而综合得到模型的复杂性。最后通过实际案例验证了此方法的可行性。该方法为信息系统的设计与构造过程提供了有效的参考与决策依据。     

Producing maintainable software

The increasing cost of software maintenance has resulted in greater emphasis on the production of maintainable software. One method used to enhance the development of maintainable software is to employ complexity metrics as a technique for controlling software complexity. In order to control complexity, it is imperative to plan for increases in complexity levels from code generation to code implementation. This paper presents a study of complexity increases during the testing and debugging phases of the software life cycle. The metrics used to measure complexity are lines of code, unique operators, unique operands, data difficulty, Halstead's effort and cyclomatic complexity.     

图像复杂度研究综述

图像相关复杂度的研究领域很广泛,除了计算机科学领域,还延伸到医学、认知心理学等研究领域。在以上应用领域,与图像相关的复杂度的定义有很多,包括图像复杂度、视觉复杂度、场景复杂度,其中图像复杂度又可以进一步细分为颜色复杂度、纹理复杂度和形状复杂度。文中对以上这些复杂度的应用、定义和计算方法进行了归纳总结,并依据组成论中相关复杂度的定义,提出了一种研究图像复杂度的思路,即从图像组成元素的角度来研究图像复杂度。这种图像复杂度的定义只与图像本身所包含的元素、内容有关系,与图像处理任务和算法无关。同时,这种图像复杂度的定义符合一般意义下人对图像复杂性的感受和理解。图像元素可以分为颜色、形状、纹理三大类,它们又可以进一步用一些特征来表示。根据组成论,文中给出了定义这3种特征的广义集的方法。后续研究将进一步给出图像复杂度的计算算法,并通过与人工实验的相关性分析来验证计算结果是否与人的感受相一致。     

On The Randomness Complexity of Property Testing

We initiate a general study of the randomness complexity of property testing, aimed at reducing the randomness complexity of testers without (significantly) increasing their query complexity. One concrete motivation for this study is provided by the observation that the product of the randomness and query complexity of a tester determine the actual query complexity of implementing a version of this tester that utilizes a weak source of randomness (through a randomness-extractor). We present rather generic upper and lower bounds on the randomness complexity of property testing and study in depth the special case of testing bipartiteness in two standard property testing models.     

Kolmogorov Complexity for Possibly Infinite Computations

In this paper we study the Kolmogorov complexity for non-effective computations, that is, either halting or non-halting computations on Turing machines. This complexity function is defined as the length of the shortest input that produce a desired output via a possibly non-halting computation. Clearly this function gives a lower bound of the classical Kolmogorov complexity. In particular, if the machine is allowed to overwrite its output, this complexity coincides with the classical Kolmogorov complexity for halting computations relative to the first jump of the halting problem. However, on machines that cannot erase their output –called monotone machines–, we prove that our complexity for non effective computations and the classical Kolmogorov complexity separate as much as we want. We also consider the prefix-free complexity for possibly infinite computations. We study several properties of the graph of these complexity functions and specially their oscillations with respect to the complexities for effective computations.     

Software complexity and its impact on software reliability

To produce reliable software, its complexity must be controlled by suitably decomposing the software system into smaller subsystems. A software complexity metric is developed that includes both the internal and external complexity of a module. This allows analysis of a software system during its development and provides a guide to system decomposition. The basis of this complexity metric is in the development of an external complexity measure that characterizes module interaction     

Identifying step-level complexity in procedures: Integration of natural language processing into the Complexity Index for Procedures—Step level (CIPS)

Task complexity plays an important role in performance and procedure adherence. While studies have attempted to assess the contribution of different aspects of task complexity and their relationship to workers’ performance and procedure adherence, only a few have focused on application-specific measurement of task complexity. Further, generalizable methods of operationalizing task complexity that are used to both write and evaluate a wide range of routine or non-routine procedures is largely absent. This paper introduces a novel framework to quantify the step-level complexity of written procedures based on attributes such as decision complexity, need for judgment, interdependency of instructions, multiplicity of instructions, and excess information. This framework was incorporated with natural language processing and artificial intelligence to create a tool for procedure writers for identifying complex elements in procedures steps. The proposed technique has been illustrated through examples as well as an application to a tool for procedure writers. This method can be used both to support writers when constructing procedures as well as to examine the complexity of existing procedures. Further, the complexity index is applicable across several high-risk industries in which written procedures are prevalent, improving the linguistic complexity of the procedures and thus reducing the likelihood of human errors with procedures associated with complexity.