共查询到19条相似文献,搜索用时 125 毫秒
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相关免疫布尔函数的一种构造方法 总被引:3,自引:0,他引:3
本文证明了布尔函数的谱分解定理,定义了布尔函数的谱(分解)特征向量,给出相应的充要条件,将全部N元相关免疫布尔函数的构造问题转化为线性方程组的求解问题,为相关免疫布尔函数的构造提供了新的方法。)满足,可求得符合要求的用上述方法我们通过人工计算确定出86个符合要求的谱特征向量,注意到向量中各分量地位的对称性,并注意到定理4,我们得知全部4无相关免疫的非平凡布尔函数共2×324=648个N=4,m=2时,定理6中条件即从后面11个方程可求得联系(Ⅱ)中的第5~14个方和即知在(Ⅲ4)下b1、b2、b3、b4全为1(全为0平凡情况),在(Ⅲ4)下b1、b2、b3、b4中有3个取1、1个取0,由此可得全部4元至少2阶相关免疫的非平凡布尔函数所对应的谱特征向量如下:它们所对应的的布尔函数依次是(此结论与[1]p155上结论相符),因而4元1阶相关免疫的布尔函数共有648-10=638个。一般情况下,在我们的方法里构造全部N元相关免疫布尔函数实质上是在定理6中“约束条件”(1)下去求2N-1个变元、N个方程的方程组(Ⅱ)所有解,构造全部N元至少m(≥2)附相关免疫布尔函数实质上是在定理6中“约束条件,(1)下去解2N- 相似文献
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广义Bent函数的稳定性及其构造 总被引:2,自引:0,他引:2
在p是素数时,用p次本原单位根给出广义Bent函数的谱判别条件,并由此对广义Bent函数的稳定性的概率意义进行了考察,最后,利用谱分解式研究了广义Bent函数的性质和构造,并据此给出了广义Bent函数的一种运算形式更一般的新的构造方法。 相似文献
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概述了目前密码学中布尔函数的研究现状和重要研究方向上的新成果,并对布尔函数的研究进行了展望,指出了一些重要的研究热点问题. 相似文献
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p值逻辑函数最佳仿射逼近的谱特征 总被引:2,自引:0,他引:2
给出了p(正整数p≥2)值逻辑函数与p值仿射函数符合率的Chrestenson谱表示,并用两种Chrestenson谱分别确定了p值逻辑函数的最佳仿射逼近函数。 相似文献
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本文对这个基本不确定度进行了计算机模拟研究,所得模拟曲线与R.G.Dorsch,G.Hausler等人的研究基本一致。此外,还对基本不确定度与表面粗糙度的关系,基本不确定度与成象系统点扩散函数内所包含的相关单元的关系进行了研究。 相似文献
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在平稳随机过程的谱表示基础上,采用随机函数的思想,将谱表达式中的标准正交随机变量表示为基本随机变量的正交函数形式。通过两组随机正交三角函数的构造,实现了非高斯正交随机变量和高斯独立随机变量的随机函数表达。与经典的谱表示方法相比,采用随机函数表达,仅需1~2个基本随机变量即可描述原随机过程的概率特性,而且可以直接由功率谱密度函数生成具有给定概率的非高斯平稳过程和高斯平稳过程的样本函数。最后,结合平稳地震动加速度过程的功率谱密度函数,验证了随机函数-谱表示方法的有效性。 相似文献
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Ziran Tu Dabin Zheng Xiangyong Zeng Lei Hu 《Applicable Algebra in Engineering, Communication and Computing》2011,22(5-6):359-366
Are there other Boolean functions having two distinct Walsh coefficients except affine Boolean functions and maximal nonlinear (i.e. bent) Boolean functions? This paper proves that all Boolean functions with exactly two distinct Walsh coefficients are just the two known classes of affine and bent Boolean functions and the Boolean functions obtained by modifying the value of affine or bent Boolean functions at x?=?0. 相似文献
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本文提出一种新的布尔空间描述方法——语义网络描述,推出了结点与有向链的计算公式。把计算机图解法与语义网络启发式搜索相结合,给出了化简布尔空间的一种全新方法。它比“布尔代数”、“奎尼表”、“卡诺图”等方法具有快速、简洁、实用、直观的优越性。 相似文献
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Radomir S. Stanković Claudio Moraga Jaakko Astola 《Applicable Algebra in Engineering, Communication and Computing》2001,12(3):227-253
Arithmetic expressions for switching functions are introduced through the replacement of Boolean operations with arithmetic
equivalents. In this setting, they can be regarded as the integer counterpart of Reed-Muller expressions for switching functions.
However, arithmetic expressions can be interpreted as series expansions in the space of complex valued functions on finite
dyadic groups in terms of a particular set of basic functions. In this case, arithmetic expressions can be derived from the
Walsh series expansions, which are the Fourier expansions on finite dyadic groups.
In this paper, we extend the arithmetic expressions to non-Abelian groups by the example of quaternion groups. Similar to
the case of finite dyadic groups, the arithmetic expressions on quaternion groups are derived from the Fourier expansions.
Attempts are done to get the related transform matrices with a structure similar to that of the Haar transform matrices, which
ensures efficiency of computation of arithmetic coefficients.
Received: October 5, 1999; revised version: June 14, 2000 相似文献
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F. Oelschlägel 《Forschung im Ingenieurwesen》2000,66(2):94-100
To consider the reliability of systems or products a random variable is based on the variability of the properties of materials, elements (equipment, parts of a product), manufacture and utilization. In practice we often find inaccurate primary data, the statistical analysis of which can be complicated. A possibility to exploit this uncertainty for a quantitative analysis of reliability is the use of interval mathematical methods. Here for the distribution parameters of reliability we assume uniform distributions in order to simplify calculations or to make them possible. The analysis (“find the reliability of a system for given reliabilities of elements”) and synthesis (inverse of analysis) of serial-parallel-forms of Boolean elements are described. Two plain examples (gear, drive system) are enclosed for illustration. 相似文献
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本文介绍了一个小型三维造型系统,着重叙述了作者独立完成的物体拼合以及显示输出子模块中的三维线框模型输出,同时介绍了该软件在制图课教学中的应用。 相似文献
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In this article we present an algorithm to transform a set(s) of Boolean equations into a Petri net(s). Boolean logic provides a mathematical basis for switching control and many other areas. In the case of programmable logic controllers used for the sequential control in manufacturing applications, Boolean equations are fundamental both in programming and in understanding their operation. A major difficulty with Boolean equations is the lack of any type of mathematical theory for the analysis of the systems that are being represented by these equations. Petri nets, on the other hand, possess a mathematical framework to analyze the properties of the system being modeled. Furthermore, Petri nets have been proved to be appropriate models for sequential control. The popularity as well as the generality of Boolean logic, on one hand, and the modeling and analytical capabilities of Petri nets, on the other hand, are the major motivations for this research. 相似文献
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本文采用数字散斑相关法对高能超声法制备的颗粒增强金属基复合材料在拉伸变形过程中颗粒与基体的界面处的位移进行了测量与分析,。实验结果表明,界面处所发生的位移变化要大于颗粒和基体内部所发生的位移,说明在颗粒与基体合金的界面处存在着导致应变集中的缺陷,从而导致了颗粒增强金属基复合材料失效过程中常常出现颗粒与基体在界面处脱粘的损伤形式。 相似文献