逻辑函数的立体化简法及其实现

逻辑函数的“立体化简法”是在卡诺图化简法的思想基础上设计的一种新型逻辑函数化简方法.这种方法用逻辑函数立方体代替卡诺图,在三维立体空间进行逻辑函数的化简.卡诺图法可以方便地化简四个变量以内的逻辑函数,而立体化简法可以方便地化简六个变量以内的逻辑函数.使用CubeScape在线网站的功能可以方便地表示逻辑函数立方体,让学生直观地感受逻辑函数最小项的逻辑相邻关系,更好地理解立体化简法化简逻辑函数的原理.     

用于二级优化的有限搜索算法

在计算机辅助逻辑设计理论中,最小项(零多维体)的相邻度是一个基本且十分有用的概念,一系列重要的二级优化算法都是以最小项相邻度概念为基础的.本文把最小项相邻度的概念推广到任意维多维体,定义了多维体方向集概念.并利用方向集概念成功地提出了优于张弛算法的二级优化算法:有限搜索法,即有限搜索法在造价优于张弛法的前提下,求取质蕴涵项的速度比张弛法快一到几个数量级,且有限搜索法扩展了张弛法的适用范围,可以综合输入变量大于20的布尔函数.     

逻辑函数多边形简化法

本文提出一种逻辑函数的多边形简化法。这种方法的要点是:将n 个逻辑变量C_1,C_2,……,C_n 及它们的补(?),(?),……,(?)构成一个2n 边形。将逻辑函数中的每一个最小项看成是2n 边形中的一个n 边形,然后按文中指出的法则读出重边或重点就得到了简化式。     

从三值K图到三值b_i图的图块转换算法

1.引言 逻辑函数有两种基本的规范展开式,一是以Post代数为基础的最小项展开式。n变量、三值逻辑函数的最小项展开式可写成:     

由多维体运算求布尔差分

布尔差分(布尔导数)是对逻辑电路进行动态分析和求故障测试集的有效数学工具,自1968年由Sellers等人提出后被人们广泛采用.如果将逻辑函数的布尔表达式用多维体集合表示,利用自动逻辑综合中所定义的一些运算符和多维体集合之间的一些运算方法可以不需要展开为最小项而求布尔差分,因而占用存储单元较少.n个变量逻辑函数可以表示为:     

多值开关理论

多值开关元件可以像二值开关元件那样用泉设计开关线路。所用的一组开关元件必须能夠实现各种可以由真值表规定的开关函数(即函数的完整性)。对於一组所采用的元件,可以建立一条联系,n个變数函数与n—1个变数函数的展开定理。本文给出了设计线路的方法及例子。从展开定理可以求得实现任何开关函数所需要开关元件数的上限。当采用能实现模代数结合的开关元件时,所得上限为最小。     

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。     

逻辑函数的编码化简法

本文给出了一个通过求最小项编码的相邻码的方法化简逻辑函数的算法,实验证明:本算法运算速度较快,占用存贮空间较小,本文还为该算法建立了一个定理。     

基于粒计算的逻辑函数快速粒约简算法

逻辑函数是描述数字电路中输入变量与输出变量之间逻辑因果关系的重要工具,研究逻辑函数的约简具有重要的理论和实际意义.针对计算机化简逻辑函数普遍存在的算法复杂度高、运算速度慢的问题,将粒计算思想与启发式搜索相结合来约简逻辑函数.首先将逻辑函数转化为最小项之和的表达形式,按照粒度由粗到细的次序,在不同粒度下的知识空间中利用吸收律和最小项之间的统计信息求取信息粒,当所有信息粒对应的最小项覆盖论域时,算法结束.算法由MATLAB编程实现.通过计算实例和算法复杂度分析证明了算法的快速性和有效性.     

用二值逻辑对多值逻辑进行优化

提出以二值多输出逻辑优化软件OPLG为基础，对多值逻辑函数进行逻辑优化的方法．通过对多值变量、多值函数的二进制矢量描述，将多值多维体转换为布尔表达式积项形式，从多值多维体的多值最小项出发，给出计算基本无关集的方法。对多值逻辑函数的优化通过调用二值逻辑优化软件OPLG(允许的最大输入、输出变量之和为300)来实现，二值逻辑优化的结果最终再转换为多值多维体的表示形式。     

一种改进的n维空间递归滤波算法

基于递归运算准则,本文提出了一种n维空间非线性滤波器的改进算法。该算法利用像素点的周边信息完成对噪声点的识别与修复。此n维空间滤波器可以递归地分解到更低一维空间,本文主要分析了这种改进的滤波算法在二维空间信号消噪处理中的性能。仿真结果表明,与中值滤波和Peak-and-Valley滤波算法比较,该算法在信噪比和图像细节保留方面具有更大的优势,并且在有高强度的脉冲噪声时也能达到较为理想的滤波效果。     

Optimal multicast communication in wormhole-routed torus networks

This paper presents efficient algorithms that implement one-to-many, or multicast, communication in wormhole-routed torus networks. By exploiting the properties of the switching technology and the use of virtual channels, a minimum-time multicast algorithm is presented for n-dimensional torus networks that use deterministic, dimension-ordered routing of unicast messages. The algorithm can deliver a multicast message to m-1 destinations in [log₂ m] message-passing steps, while avoiding contention among the constituent unicast messages. Performance results of a simulation study on torus networks with up to 4096 nodes are also given     

Analysis of the n-dimensional quadtree decomposition for arbitraryhyperrectangles

We give a closed-form expression for the average number of n-dimensional quadtree nodes (“pieces” or “blocks”) required by an n-dimensional hyperrectangle aligned with the axes. Our formula includes as special cases the formulae of previous efforts for two-dimensional spaces. It also agrees with theoretical and empirical results that the number of blocks depends on the hypersurface of the hyperrectangle and not on its hypervolume. The practical use of the derived formula is that it allows the estimation of the space requirements of the n-dimensional quadtree decomposition. Quadtrees are used extensively in two-dimensional spaces (geographic information systems and spatial databases in general), as well in higher dimensionality spaces (as oct-trees for three-dimensional spaces, e.g., in graphics, robotics, and three-dimensional medical images). Our formula permits the estimation of the space requirements for data hyperrectangles when stored in an index structure like a (n-dimensional) quadtree, as well as the estimation of the search time for query hyperrectangles, for the so-called linear quadtrees. A theoretical contribution of the paper is the observation that the number of blocks is a piece-wise linear function of the sides of the hyperrectangle     

An optimal multicast algorithm for cube-connected cycles

This paper presents an efficient algorithm that implements one-to-many,or multicast,communication in one-port wormhole-routed cube-connected cycles(CCCs) in the absence of hardware multicast support.By exploiting the propoeries of the switching technology and the use of virtual channels,a minimumtime multicast algorithm is presented for n-dimensional CCCs that use deterministic routing of unicast messages.The algorithm can deliver a multicast message to m-1 destinations in [log2m] message-passing steps,while avoiding contention among the constitutent unicast messages,Performance results of a simulation study on CCCs with up to 10,240 nodes are also given.     

The immersive visualization probe for exploring n-dimensional spaces

A new tool uses two types of dimensional navigation to display continuous 4D subsets of n-dimensional data. Thanks to the tool's embedded coordinate systems, researchers can better understand a model's underlying physical or mathematical process. Here, we describe a new method for visualizing data structure or models defined in higher-dimensional spaces. This technique is suitable for applications in which a scalar function, defined mathematically or procedurally, depends on n variables or parameters. The function's values essentially describe a set of points in n-dimensional space. To visualize these sets, we fix all but three of the parameters and then sample the resulting 4D set (the three parameters and the function's resulting value) on several discrete grids located on planes in the 3D space. We compose the image by using color to represent the fourth dimension (the function's value) at discrete locations on these grids. Interactive control over the way the parameters are fixed results in a highly dynamic system that researchers can easily use to explore the n-dimensional space's structure.     

Diagnosability of crossed cubes under the comparison diagnosismodel

Diagnosability of a multiprocessor system is one important study topic in the parallel processing area. As a hypercube variant, the crossed cube has many attractive properties. The diameter, wide diameter and fault diameter of it are all approximately half of those of the hypercube. The power that the crossed cube simulates trees and cycles is stronger than the hypercube. Because of these advantages of the crossed cube, it has attracted much attention from researchers. We show that the n-dimensional crossed cube is n-diagnosable under a major diagnosis model-the comparison diagnosis model proposed by Malek (1980) and Maeng and Malek (1981) if n⩾4. According to this, the polynomial algorithm presented by Sengupta and Dahbura (1992) may be used to diagnose the n-dimensional crossed cube, provided that the number of the faulty nodes in the n-dimensional crossed cube does not exceed n. The conclusion of this paper also indicates that the diagnosability of the n-dimensional crossed cube is the same as that of the n-dimensional hypercube when n>5 and better than that of the n-dimensional hypercube when n=4     

Conditional Edge-Fault Hamiltonicity of Matching Composition Networks

A graph G is called Hamiltonian if there is a Hamiltonian cycle in G. The conditional edge-fault Hamiltonicity of a Hamiltonian graph G is the largest k such that after removing k faulty edges from G, provided that each node is incident to at least two fault-free edges, the resulting graph contains a Hamiltonian cycle. In this paper, we sketch common properties of a class of networks, called matching composition networks (MCNs), such that the conditional edge-fault hamiltonicity of MCNs can be determined from the found properties. We then apply our technical theorems to determine conditional edge-fault hamiltonicities of several multiprocessor systems, including n-dimensional crossed cubes, n-dimensional twisted cubes, n-dimensional locally twisted cubes, n-dimensional generalized twisted cubes, and n-dimensional hyper Petersen networks. Moreover, we also demonstrate that our technical theorems can be applied to network construction.     

二维hash链在Payword中的应用

由于hash函数的高效安全性，利用hash链构造微支付方案已经成为一个研究热点。在WCC’2005会议上，Quan Son Nguyen提出了基于RSA的多维hash链模型。该文指出了该方案的不可行之处，并对该方案进行了改进，使之满足PayWord的要求。     

A unified approach to reliability and edge fault tolerance of cube-based interconnection networks under three hypotheses

The Journal of Supercomputing - The topological structures of the interconnection networks of some parallel and distributed systems are designed as n-dimensional hypercube $$Q_n$$ or n-dimensional...     

Diagnosability of crossed cubes under the comparison diagnosismodel

Diagnosability of a multiprocessor system is an important study topic in the parallel processing area. As a hypercube variant, the crossed cube has many attractive properties. The diameter, wide diameter and fault diameter of it are all approximately half those of the hypercube. The power with which the crossed cube simulates trees and cycles is stronger than the hypercube. Because of these advantages, the crossed cube has attracted much attention from researchers. In this paper, we show that the n-dimensional crossed cube is n-diagnosable under a major diagnosis model-the comparison diagnosis model proposed by Malek and Maeng (1981) if n ⩾ 4. According to this, the polynomial algorithm presented by Sengupta and Dahbura (1992) may be used to diagnose the n-dimensional crossed cube, provided that the number of the faulty nodes in the n-dimensional crossed cube does not exceed n. The conclusion also indicates that the diagnosability of the n-dimensional crossed cube is the same as that of the n-dimensional hypercube when n ⩾ 5 and better than that of the n-dimensional hypercube when n = 4