5元1-弹性函数的代数免疫阶

首先给出了最优代数免疫布尔函数弹性阶的一个上界,并且证明了一类5元1阶弹性函数不是最优代数免疫函数,得到了最优代数免疫函数具有一阶弹性时可能的结构形式;在此基础上,给出了布尔函数代数免疫阶和弹性阶随着变元个数变化的一些结果,最后给出了一个5元1阶弹性的最优代数免疫布尔函数。     

Bent函数与其变元的相关特性

本文利用Ｗａｌｓｈ谱研究了Ｂｅｎｔ函数与其变元的非线性组合之间的相关特性，得到了相关系数比文献［１］中的界更紧的界。同时给出了求布尔函数与其变元的布尔组合之间的相关系的一个算法。     

一种多值逻辑函数化简方法——决策树法

将决策树应用于多值逻辑函数的化简，提出了一种新的多值逻辑函数的化简方法，该方法易于编程和上机操作，特别适用于化简多变量的多值逻辑函数。     

多值逻辑函数组构成置换的一个充要条件

本文给出了一组多值逻辑函数构成置换的一个充要条件。     

关于多值逻辑函数的仿射逼近

该文给出了利用函数f的谱来计算新函数afb的谱的计算公式,讨论了多值逻辑函数的仿射逼近问题.     

复合多输出前馈函数的密码学特性

该文讨论复合多输出前馈函数和退化的多输出前馈函数,给出了复合多输出前馈函数和退化的多输出前馈函数的一些密码学性质。     

多值逻辑函数Chrestenson谱的性质

类似于布尔函数Walsh谱的性质，本文得到了两个多值逻辑函数的和函数的Chrestenson循环谱等于这两个多值逻辑函数的Chrestenson循环谱的和的充分必要条件，以及两个多值逻辑函数的和函数的Chrestenson线性谱等于这两个多值逻辑函数的Chrestenson线性谱的和的充分条件。     

关于多值逻辑函数的仿射逼近

该文给出了利用函数ｆ的谱来计算新函数αｆ＋ｂ的谱计算公式，讨论了多值逻辑函数的仿射逼近问题。     

开关函数的一个特性

在开关网络(包括移位寄存器)的分析和综合,数字系统的故障检测等问题中都要涉及开关函数与某一变元无关的条件,关于这个问题文章〔1〕〔2〕都给出一些判别条件。本文通过实例指出开关函数的一个特性,给出开关函数与某一变量无关的一个新的条件,并给出这结论的数学证明,在证明中对充分性给出两种方法。设f(x_1,x_2…,X_n)是定义在V_n(F_2)=GTF(2)×G_1F(2)×…G_1F(2)X…上的一个开关函数。称f(x_1,x_2,…,x_n)与x无关,如果f(x_1…,x_(i-1),o,x_(i 1),…,x_n)=f(x_1,…,x_(i-),1,x_(i ),…,x_i)Ax_1,…,x_(i-1),x_( 1),…,x_n,EGF_((2))我们定义f(x_1,x_2,…,x_n)的重量W_((f))为     

基于多值逻辑的模糊逻辑函数分析与综合

本文首先提出了模糊逻辑和多值逻辑的相似性，并从开关信号理论出发建立了多值逻辑阈运算和模糊函数取值区间有限等级的对应关系，进而提出了利用多值逻辑阈运算实现模糊逻辑函数分析与综合的算法，并用该算法对几个模糊逻辑函数实例进行了分析与综合，实例操作表明，该算法具有操作简单，规范，方便快捷的特点，是分析和综合模糊逻辑函数的有效方法。     

SPECTRAL ANALYSIS OF SOME INDEPENDENCES OF MULTIPLE-VALUED LOGICAL FUNCTIONS ON THEIR VARIABLES

There are many kinds of special relationships between multiple-valued logical func-tions and their variables, and they are difficult to be judged from their expressions. In thispaper, some sufficient and necessary conditions of the independence and statistical independenceof multiple-valued logical functions on their variables are given. Some conditions of algebraicindependence of multiple-valued logical functions on some of their variables and the way to de-generate a function to the greatest extent are proposed, and some applications of these resultsare indicated. All the results are studied by using Chrestenson spectral techniques.     

Spectral analysis of some independences on multiple-valued logical functions on their variables

There are many kinds of special relationships between multiple-valued logical functions and their variables, and they are difficult to be judged from their expressions. In this paper, some sufficient and necessary conditions of the independence and statistical independence of multiple-valued logical functions on their variables are given. Some conditions of algebraic independence of multiple-valued logical functions on some of their variables and the way to degenerate a function to the greatest extent are proposed, and some applications of these results are indicated. All the results are studied by using Chrestenson spectral techniques.     

Introducing disjoint spectral translation in spectral multiple-valued logic design

A new form of expansion of multiple-valued logical functions in generalised Fourier series in terms of the Chrestenson functions is presented. It is shown that this expansion exhibits the property of `disjoint spectral translation? known in binary spectral logic design. This allows extending the possibility of low complexity realisation to a large class of multiple-valued logical functions.     

Using decision trees for the minimization of multiple-valued functions

This paper presents a simple procedure for the approximate minimization of multiple-valued functions using multiple-valued decision trees. The proposed procedure is compared with a near-absolute procedure, using for the test four-valued functions of four variables. The results show a great advantage for our procedure with respect to the CPU time needed.     

基于模代数的真值向量计算及其在多值逻辑综合中的应用

本文提出了由函数的真值向量计算Reed-Muller展式的简捷方法,由此可判定函数能否线性分解或部分线性分解。用典型例子演示了其在多值逻辑综合中的应用,结果表明该方法行之有效。     

时序险象基本判据

本文利用几个定义和限制,得到了一外部激励x,n个状态变量电位异步时序电路的任一状态的一般逻辑表达式特性方程.将此方程与状态表结合,导出了产生时序险象时的状态变量数和稳定状态数所满足的条件;给出了对时序险象研究特别有用的基本判定法则.     

环Zm上随机变量联合分布的一种分解式及其应用

本文给出了ｍ值随机变量联合分布的分解式,考察了一类ｍ值（ｍ为正整数,ｍ≥２）逻辑函数Ｃｈｒｅｓｔｅｎｓｏｎ谱的“分解式”,并据此分解式给出了相关免疫ｍ值逻辑函数的一些新的构造法。     

Blind separation using convex functions

In this paper, the problem of how to conveniently estimate independence from observations is addressed. Random variables (RVs) are transformed by their respective distribution functions and quantized. Then, the uniformity of the joint probability of the obtained discrete RVs is evaluated using a strictly convex function. An infinite class of new independence measures, named quasientropy (QE), is thus proposed. Unbiased estimates of the values of the distribution functions at the observations are directly utilized in estimating QE. The linear instantaneous blind source separation (BSS) algorithm based on QE can separate signals with arbitrary continuous distributions.     

CIRCUIT TESTABLE DESIGN AND UNIVERSAL TEST SETS FOR MULTIPLE-VALUED LOGIC FUNCTIONS

The circuit testable realizations of multiple-valued functions are studied in this letter. First of all, it is shown that one vector detects all skew faults in multiplication modulo circuits or in addition modulo circuits, and n＋1 vectors detect all skew faults in the circuit realization of multiplevalued functions with n inputs. Secondly, min（max） bridging fault test sets with n＋2 vectors are presented for the circuit realizations of multiple-valued logic functions. Finally, a tree structure is used instead of cascade structure to reduce the delay in the circuit realization, it is shown that three vectors are sufficient to detect all single stuck-at faults in the tree structure realization of multiplevalued logic functions.