改进的Q-M逻辑函数化简方法

为进一步提高逻辑函数的化简速度,提出一种改进的Q-M逻辑函数化简方法。在迭代比较过程中设置2个权值以缩减可合并蕴涵项集合的大小,只对满足条件的蕴涵项进行合并处理,得到全部质蕴涵项。构造质蕴涵项与最小项关联图,利用启发式规则得到能蕴涵全部最小项的最少质蕴涵项集合,从而得到逻辑函数的最小覆盖,完成逻辑函数化简。实验结果表明,该算法能降低迭代次数,减少逻辑函数的化简时间。     

一种支持大规模数据逻辑函数优化的改进选拔算法

选拔算法是两级逻辑综合中求解最小化覆盖的经典方法之一,但在输出变量集合和质立方体集合规模较大的情况下,采用选拔法求最小化覆盖存在空间复杂度高、求解时间长等问题。为此,提出了求解多输出函数最小化覆盖的改进选拔算法。利用相交迭代和局部搜索的思想,分别对选拔法的极值运算和分支处理进行了改进。实验结果表明,在现有计算机资源条件下,该算法为大规模数据条件下逻辑函数的优化提供了一种有效的方法。     

求解多输出逻辑函数覆盖问题的覆盖矩阵取补法

本文根据多输出多维体蕴涵的概念,提出构成多输出函数简化覆盖表的方法,将求解单输出函数的覆盖矩阵取补法推广到多输出函数的求解。该方法可求得函数全部有意义的无冗余覆盖(包括最小覆盖)。对于大覆盖表运用修改的锐积运算可只求得唯一一组无冗余覆盖。这个方法同时可用于消除输出冗余连接。覆盖表的产生和求解,只需存储它的某一部分或全部不存。因此本算法很简单,程序实现方便,解覆盖几乎不需要增加内存,并且计算量较小。现已编成程序,试算结果表明适于求解输入、输出变量较多的逻辑函数覆盖问题和其它规模较大的覆盖问题。     

接近最小化积之和式的简化方法

本文介绍一个将任意布尔函数最小化的算法。其方法与先前首先求得全部质蕴涵项然后确定最小覆盖的方法不同。这个算法为了获得接近最小的积之和的实现,运用一组条件来选择质蕴涵项。并把它推广到多输出和不完全规定函数的情况。所提出的算法的主要特点是求解同一问题所化费的机器时间比用其它的算法少。如果只要求结果是较少的乘积项时,MINI算法对于输入、输出数目多的布尔函数可以给出较好的结果。这个算法也适合于寻求内部按积之和实现的大的布尔函数的可编程序阵列(PLA)的解。     

逻辑函数无冗余覆盖选择问题

逻辑函数的最小化算法可以分为两大步骤,产生本源蕴涵项和在这些蕴涵项中选择一个最小覆盖。提出一个适于大变量输入输出逻辑函数的实质项与相对冗余项的识别和选择近似最小覆盖的算法。Benchmark例题测试表明,算法具有理想的处理效果。     

大变量逻辑函数最佳覆盖问题研究

逻辑函数的最佳覆盖，一直是逻辑综合领域的关键环节。尤其是大变量逻辑函数最佳覆盖，对复杂的逻辑综合更为重要，但也更加困难。本文在对逻辑覆盖算法研究的基础上，提出了适合大变量逻辑函数最佳覆盖的Beister改进算法。经过大量算题的测试表明，改进的列覆盖算法在时间复杂度和选择效果方面均优于Beister算法。     

一种求解多值逻辑函数接近最小覆盖的算法

1.引言 本文研究Allen-Givone多值逻辑代数系统中的“积之和”形式的函数的简化算法。首先,在讨论符合目前多值逻辑函数实现特点的合理代价标准基础上,提出了一种折衷的代价标准,按着这个标准不求所有质蕴涵项集合,直接求解无冗余覆盖。这个算法以减少文字门的个数为依据,在确定某些质蕴涵项和实现文字数较少之间进行权衡,它在一个位     

支持大规模变量集的最小覆盖迭代搜索算法

两级逻辑综合中的多输出逻辑电路最小覆盖的求解是一个NP难解问题,在输出变量集合和质蕴含项集合规模较大的情况下,会出现空间需求过大、处理时间太长等问题,影响多输出最小覆盖求解的可行性．在精选法的基础上,提出一种多输出最小覆盖迭代求解算法．将一次性求解最小覆盖的模式转换为多次迭代逼近最优解的过程,使得在有限的时间和空间范围内获得尽可能优化的最小覆盖结果．同时,对影响算法复杂度的单输出到多输出函数的阵列合并、极值的选择这2个主要环节进行了改进,大幅度降低了多输出最小覆盖求解算法的时间和空间复杂度．     

PLA分解与输入变量最小集的求解方法

寻求函数输入变量最小集和函数列阵分解问题,无论对于PLA或门阵列的制版布线及测试设计都是十分重要的。本文将它们统一考虑为用求解质蕴涵项表的覆盖矩阵取补(锐积)法求解。实际上PLA分解需要两次求解覆盖问题。首先求出各子列阵输入变量的全部最小集(或无冗余子集);然后再寻求其输入变量最小集能够覆盖全部子列阵输入变量最小集的一组子列阵,于是便获得函数列阵的分解结果。 本文针对上述这类规模较大的覆盖问题,围绕如何提高速度、节省内存,运用覆盖矩阵取补法构造出寻求输入变量最小集及PLA分解的算法。其特点是规则性强,实现方便,几乎不需另外占用内存便可求解出这些规模较大的覆盖问题。根据这些算法构成的自动逻辑综合软件可用于以寄存器传输级硬件描述语言(如DDL、AHPL等)为输入的计算机设计自动化系统。     

组合函数无冗余覆盖的优算法

本文提出了“相邻点分布密度”及质蕴涵项“生成元”的概念,从而使函数质蕴涵项的生成在选点及方向上,为形成无冗余覆盖有了依据,并进而提出了一个产生函数无冗余覆盖的较优算法,从理论和实践上验证了根据本算法编制的程序条数少、速度快、存储量少。     

一种新的商覆盖立方体生成算法

提出一种的新的商覆盖立方体生成算法GroupDFS,将待计算的基本表先依据各维属性进行Group By运算,再对得到的结果集采用DFS算法计算其上界集,所得结果即为原待计算基本表的商覆盖立方体。GroupDFS算法结合了2^N算法和DFS算法的优点,相对于DFS算法缩短了计算所需的时间。采用weather数据集进行的实验结果表明,采用GroupDFS计算商覆盖立方体所需时间仅为采用DFS算法时的45%。     

测试集问题的集合覆盖贪心算法的深入近似

测试集问题是一个有着广泛应用的NP难问题.集合覆盖贪心算法是测试集问题的一个常用近似算法,其由集合覆盖问题得到的近似比21nn+1能否改进是一个公开的问题.集合覆盖贪心算法的推广被用来求解生物信息学中出现的冗余测试集问题.通过分析条目对被区分次数的分布情况,用去随机方法证明了集合覆盖贪心算法对测试集问题的近似比可以为1.51nn+0.5lnlnn+2,从而缩小了这种算法近似比分析的间隙.另外,给出了集合覆盖贪心算法对冗余度为n-1的加权冗余测试集问题的近似比的紧密下界(2-o(1))lnn-Θ 1).     

A backtracking search tool for constructing combinatorial test suites

Combinatorial testing is an important testing method. It requires the test cases to cover various combinations of parameters of the system under test. The test generation problem for combinatorial testing can be modeled as constructing a matrix which has certain properties. This paper first discusses two combinatorial testing criteria: covering array and orthogonal array, and then proposes a backtracking search algorithm to construct matrices satisfying them. Several search heuristics and symmetry breaking techniques are used to reduce the search time. This paper also introduces some techniques to generate large covering array instances from smaller ones. All the techniques have been implemented in a tool called EXACT (EXhaustive seArch of Combinatorial Test suites). A new optimal covering array is found by this tool.     

Suboptimal minimum cluster volume cover-based method for measuring fractal dimension

A new method for calculating fractal dimension is developed in this paper. The method is based on the box dimension concept; however, it involves direct estimation of a suboptimal covering of the data set of interest. By finding a suboptimal cover, this method is better able to estimate the required number of covering elements for a given cover size than is the standard box counting algorithm. Moreover, any decrease in the error of the covering element count directly increases the accuracy of the fractal dimension estimation. In general, our method represents a mathematical dual to the standard box counting algorithm by not solving for the number of boxes used to cover a data set given the size of the box. Instead, the method chooses the number of covering elements and then proceeds to find the placement of smallest hyperellipsoids that fully covers the data set. This method involves a variant of the Fuzzy-C Means clustering algorithm, as well as the use of the Minimum Cluster Volume clustering algorithm. A variety of fractal dimension estimators using this suboptimal covering method are discussed. Finally, these methods are compared to the standard box counting algorithm and wavelet-decomposition methods for calculating fractal dimension by using one-dimensional cantor dust sets and a set of standard Brownian random fractal images.     

Computing small partial coverings

We study the generalization of covering problems such as the set cover problem to partial covering problems. Here we only want to cover a given number k of elements rather than all elements. For instance, in the k-partial (weighted) set cover problem, we wish to compute a minimum weight collection of sets that covers at least k elements. As a main result, we show that the k-partial set cover problem and its special cases like the k-partial vertex cover problem are all fixed parameter tractable (with parameter k). As a second example, we consider the minimum weight k-partial t-restricted cycle cover problem.     

Canonical Forms and Algorithms for Steiner Trees in Uniform Orientation Metrics

We present some fundamental structural properties for minimum length networks (known as Steiner minimum trees) interconnecting a given set of points in an environment in which edge segments are restricted to λ uniformly oriented directions. We show that the edge segments of any full component of such a tree contain a total of at most four directions if λ is not a multiple of 3, or six directions if λ is a multiple of 3. This result allows us to develop useful canonical forms for these full components. The structural properties of these Steiner minimum trees are then used to resolve an important open problem in the area: does there exist a polynomial time algorithm for constructing a Steiner minimum tree if the topology of the tree is known? We obtain a simple linear time algorithm for constructing a Steiner minimum tree for any given set of points and a given Steiner topology.     

ε-Guarantee of a covering of 2D domains using random-looking curves

The problem of covering a given 2D convex domain D with a C¹ random-looking curve C is considered. C within D is said to cover D up to ϵ > 0 if all points of D are within ϵ distance of C. This problem has applications, for example, in manufacturing, 3D printing, automated spray-painting, polishing, and also in devising a (pseudo) random patrol-path that will visit (i.e. cover) all of D using a sensor of ϵ distance span. Our distance bound approach enumerates the complete set of local distance extrema, enumeration that is used to provide a tight bound on the covering distance. This involves computing bi/tri-normals, or circles tangent to C at two/three different points, etc. A constructive algorithm is then proposed to iteratively refine and modify C until C covers a given convex domain D and examples are given to illustrate the effectiveness of our algorithm.     

基于遗传算法测试用例集极小化研究

提出了一种应用于软件回归测试过程中的基于遗传算法的最小化测试用例集算法模型。该算法针对在软件回归测试过程中,测试套间内的测试用例间往往存在着重复覆盖测试需求的情况,因而测试套间中将存在着大量的冗余测试用例,将测试用例与测试需求之间的覆盖关系模型转化为集覆盖模型。然后利用遗传算法强大的全局搜索能力,优化在极小化的测试用例空间,较低的测试成本条件下,覆盖回归测试需求。并通过对算法的仿真结果进行分析表明,该算法较一般的优优化算法具有更高算法性能与效率。     

An Improved Approximation Algorithm for the Most Points Covering Problem

In this paper we present a polynomial time approximation scheme for the most points covering problem. In the most points covering problem, n points in R ², r>0, and an integer m>0 are given and the goal is to cover the maximum number of points with m disks with radius r. The dual of the most points covering problem is the partial covering problem in which n points in R ² are given, and we try to cover at least p≤n points of these n points with the minimum number of disks. Both these problems are NP-hard. To solve the most points covering problem, we use the solution of the partial covering problem to obtain an upper bound for the problem and then we generate a valid solution for the most points covering problem by a careful modification of the partial covering solution. We first present an improved approximation algorithm for the partial covering problem which has a better running time than the previous algorithm for this problem. Using this algorithm, we attain a \((1 - \frac{{2\varepsilon }}{{1 +\varepsilon }})\)-approximation algorithm for the most points covering problem. The running time of our algorithm is \(O((1+\varepsilon )mn+\epsilon^{-1}n^{4\sqrt{2}\epsilon^{-1}+2}) \) which is polynomial with respect to both m and n, whereas the previously known algorithm for this problem runs in \(O(n \log n +n\epsilon^{-6m+6} \log (\frac{1}{\epsilon}))\) which is exponential regarding m.