蕴涵项的扩展算法

本文提出了一个把逻辑函数的积项扩展为本源蕴涵项的算法。用此算法得到的本源蕴涵项集合通过去冗过程产生的最后结果最接近绝对最小化的解。     

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.     

逻辑函数的卡诺图化简法

从卡诺图化简法与公式化简法的比较入手,说明卡诺图化简法的优点及适用范围,阐述了卡诺图的特点、最小项的定义和性质、用卡诺图化简逻辑函数的基本原理以及化简是否达到最简形式的判定标准。然后给出了具体实例来诠释卡诺图化简法并给出其应用的一般步骤。最后总结出卡诺图化简法易出错的几种情况,从而得出用卡诺图化简逻辑函数的一般方法。     

化简组合逻辑网络的一种无冗余算法

本文探讨组合逻辑二级化简课题.作者对N.Necula求无冗余解的算法做了改进和修正——提出了布尔函数的全小项码表示法,修正了原算法中选拔质蕴含项的规则2,从而使得算法比较节省存储和运算时间,并同样能得到接近最小价格的解.本文算法以及原Necula算法均在NOVA3/D机上用FORTRAN IV实现并做了时效比较.     

关于多变量开关函数化简的问题

本文提出n维立方体及顶点编号方法的模型,应用它可以解决多变量开关函数化简问题。该模型能全面准确地揭示出n维空间中2~n个多变量开关函数每个最小项之间相邻的数学关系,相邻单元的组合关系,并给出合并最小项的差值合并定理及系统化简方法,方法简单直观,可获得最简表达式。这对大规模集成电路设计和计算机辅助开关电路设计具有十分重要的意义。     

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。     

逻辑函数求补算法及其改进

逻辑函数求补算法存在的主要问题是时间开销大及需要的存储空间过大。该文在对递归裂变求补算法和基于最小项求补算法进行分析研究的基础上,提出了积项输入、邻项合并、积项输出的无冗余覆盖的逻辑函数求补算法。该求补算法的时间、空间的需求将大大缩小。     

基于近似计算与多数覆盖技术的电路面积优化

针对基于最小项的近似计算技术不适合解决大规模电路面积优化问题,提出一种采用乘积项和逻辑覆盖的电路面积近似计算技术优化算法.利用基于乘积项的多数覆盖技术实现近似逻辑函数搜索,用逻辑覆盖不相交运算实现近似函数错误率计算,可以有效地避免因输入变量增加和最小项数量激增导致算法效率低下甚至无法工作的问题.文中算法用C编程并经MC...     

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:     

基于改进NB分类方法的网络异常检测模型

在神经网络的数字VLSI实现中,激活函数及乘累加等计算部件是设计中的难点.区别于使用乘法器及加法器的传统方法,该文提出的LMN方法基于查找表(即函数真值表),使用逻辑最小项化简提炼出函数最简逻辑表达式后,可直接生成结构规整的门级电路,除线延时外,电路只有数个门级延时.以非线性函数为例对该方法进行了介绍,结果表明当定点数位数较少时,算法在速度及误差方面具有更好的性能.     

Simplification of Switching Functions Involving a very Large Number of ‘Don't Care’ States†

A method of simplification of switching functions involving a very large number of ‘ don't care’ states is suggested in the present paper. First a tabular technique is suggested which generates all the prime implicants starting from the maxterm type expressions of switching functions, avoiding generation of the prime implicants formed of ‘don't care’ states only. The technique presented is simple and iterative. Next it is suggested how the knowledge of the sets of prime implicants thus obtained can be utilized for finding minimal or other irredundant sums of switching functions.     

Simplification of fuzzy switching functions

This paper is concerned with the study of simplification of fuzzy switching functions. A novel algorithm for generating all fuzzy prime implicants is introduced, followed by a new method of simplification of fuzzy switching functions. This algorithm is then reduced to a simple algorithm that produces only those fuzzy prime implicants that are essential. There areonly two other valid techniques for the minimization of fuzzy switching functions in the literature,^(1,2) and those methods are not very suitable for computerized application. Thus, the principal advantages of this technique are the new concept of direct simplification via essential fuzzy prime implicants (without generation of all of the fuzzy prime implicants), and the fact that the algorithm is the first one to be suitable for efficient computer implementation.On leave from the Computer Science Department, New Mexico Institute of Mining and Technology, Socorro, New Mexico.     

On Graphical Studies of PEN-IM Sets of Boolean Functions and their Minimizations. Part I†

The graphs of the sets of all penultimate implicants of certain types of Boolean functions are obtained in this part of the paper. Identification of different C.H. Boolean functions with their graphs are then made and terms are coined to designate these functions for the easy pattern recognition of their graphs. Finally formulae are deduced which give the number of prime implicants that must be present in any minimal cover of these functions.     

基于编码算法的组合逻辑电路最优化软件的设计与实现

在组合电路综合领域,逻辑最小化对电路面积及性能起到至关重要的作用。文章提出了一个新的产生本源蕴涵项的算法,并开发了一个最优化软件MININT,实验表明,它在运算速度和存储性能上都是高效的。     

Useless prime implicants of incompletely specified multiple-output switching functions

In the process of finding a minimal sum representation for an incompletely specified multiple-output switching function, there often occur certain types of prime implicants, referred to as useless, which can be discarded because of the presence of the don't-cares. This paper presents a correction to the definition of useless given by Tison and extends the definition to other notations. A procedure for removing useless prime implicants quickly is presented for the case when multiple-output prime implicants are derived from minterms. The deletion of useless prime implicants can, in many cases, speed up any procedure for finding a minimal sum that begins with the multiple-output prime implicants in both hand calculation and in computer implementation.This work was supported in part by the National Science Foundation under Grant No. MCS-77-09744.     

A method of finding simple disjunctive decomposition with one free variable

Simple disjunctive decomposition with one free variable can be obtained by using the prime implicants of the Boolean function. A function is decomposable with its redundant variable as a free variable. A necessary condition for decomposition with a non-redundant variable as free variable is that the number of minterms in an n variable function be 2^(n?1). A sufficient condition is that the variable remain present, in either true or complemented form, in all the prime implicants of the function.     

Decompositions of four variable Boolean functions

All the decompositions of a Boolean function of four variables can be determined directly from its prime implicants if it is decomposable with one free variable. Decompositions of functions of three variables can be obtained from the column ratio of the variables.     

逻辑函数绝对最小覆盖的改进算法

逻辑函数的绝对最小化算法存在的主要问题是运行时间过长和需要的存储空间过大。本文提出了一个从给定本源蕴涵项集合中抽出一个绝对最小覆盖的算法，而时间、空间的需求被大缩小了。     

Some Further Studies on Determination of all the Minimal Prime Implicant Covers of Switching Functions†

A method of determination of all the minimal prime implicant covers of switching functions by utilizing their connected cover term matrices is suggested in the paper. The method presented is an extension of the technique suggested by the authors in a previous paper (Choudhury and Das 1964). When majority of the prime implicants of a switching function will occur in more than two different columns of the cover table, it is shown that the determination of all the minimal prime implicant covers can often be greatly facilitated by initially dividing the cover table into more than two suitable sub-tables.     

The use of linear programming to select an optimal set of prime implicants

This study shows how the selection of an optimal subset of prime implicants from a prime implicant table, as encountered in digital logic design and similar applications, may be formulated as a linear programming problem in zero-one variables.