布尔函数

Besides, through the method of concatenation, the upper bound of algebraic immunity and the form of the annihilators of any generalized boolean function were also determined.

此外，还通过级联函数的方法确定了任意广义布尔函数的代数免疫的上界和零化子的形式。

cryptography ; algebraic attack ; Boolean function ; algebraic immune degree

本文研究了具有1型线性结构的布尔函数f的代数免疫阶，揭示了布尔函数的线性结构对其代数免

Software Description: XICalc is an integer calculator program with the following features: multiple precision integers with millions of digits; uses Hartley Transform to speed-up long multiplies; separate input and outputnotation, base 2 to base 36; greatest common divisor function; Modulo arithmetic options; Bernoullinumbers, Euler Numbers; Boolean functions; random number generator; prime factor algorithm using theElliptic Curve Method; number theoretic functions phi, sigma and tau; prime testing and searching using the Adleman function; algebraic notation; if-then-else statement; go-to statement; can run XICalc code from files; hot help from F1 key; and it抯 written in Microsoft Visual C#.

XICalc 是一款带有如下功能的综合性计算器软件：带有百万数位的多精度整数；使用 Hartley Transform 加速长整型多样化计算；以2到36为基数分隔输入和输出符号；最大公约数函数；模数算法选项；Bernoulli 数字；Euler 数字；布尔函数；随机数字生成器；使用圆周曲线算法的主要因素运算法则；π，τ，Σ的数字理论函数；使用 Adleman 函数的最初测试和搜索功能；代数符号；if-then-else 语法结构声明；go-to 语法结构声明；来自于文件的XICalc 代码；F1键的热点帮助；并且该软件是采用适用于 Windows 操作系统的微软 Visual C#。

Several strong results on neural network approximation capability obtained in this dissertation are important in the approximation theory and applications of neural networks.

本文系统地研究了多层神经网络的非线性逼近能力，给出了多层网络可一致逼近有限维空间R〓紧集上的连续函数、无穷维函数空间紧集上的连续泛函和连续算子以及布尔函数的理论证明。

By analyzing the relationship between the algebraic degree and characteristic matrix of a Boolean function,the relationship between the algebraic immunity and characteristic matrix of a Boolean function is obtained.

通过分析布尔函数的代数次数与特征矩阵的关系，得到了布尔函数的代数免疫度与特征矩阵的关系。

Definition and research of disjoint product sum minimization from the point of view of Boolean function coverage, and proof of three theorems as well as putting forward a recurrent formula.

从布尔函数覆盖的角度定义和研究了最小不交化问题，给出并证明了几个有关的定理，并提出一个求布尔函数最小不交积之和的递推计算原理及公式； 3。

If deg f = n, then Rfc is an empty set. For all the functions of degree 2, Rf have at least 2n-1 vectors, when Rf is a linear subspace, the relationships between Rf and Lf are discussed . Boolean functions have no nonezero linear structure if and only if there are n linear independence vectors in f, the correlation of the vectors in ?

证明了，若degf=n，则R_f~c为空集，对于所有的二次布尔函数而言，均有R_f~c中的元素个数大于等于2~(n-1)，给出了R_f构成线性子空间时，R_f和L_f之间的关系，还给出布尔函数不含有非零线性结构的充分必要条件是ζ_f中含有n个线性无关的元素。

To prove that we can construct any boolean function using only NAND gates, we needonly show how to build an inverter, AND gate, and OR gate from a NAND (sincewe can create any boolean function using only AND, NOT, and OR).

为了证明使用NAND门我们能够构造任何布尔函数，我们只需要展示如何从一个NAND建立一个转换，与门，或门（因为我们可以用AND，OR，NOT建立任何布尔函数）。

Through deducing the representation of the nonlinearity part of the symmetric cipher in Boolean function, the equivalence between symmetric cipher design and Boolean function is verified.

通过推导分组密码的非线性部分的布尔函数表达式，验证了对称加密设计与布尔函数构造之间的等价关系。

Then the above results are extended to the general form of quasi monotone decomposition. In conclusion, we give the necessary and sufficient conditi...

最后将上述结果推广到布尔函数拟单调分解的一般形式，给出一个布尔函数可以分解成 k个单调函数的逻辑组合的充分必要条件。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。