最小项

The logical function was expressed in terms of cubic notation andthe logical operation was carried out cubically through intersection,compatibility and sharp product.

采用立方符号表述逻辑函数，把逻辑运算表示为立方的相交、相容及锐积运算，提出用判断最小项来完成对给定程序的判断和校正，进而实现了计算机辅助逻辑综合，得到了最优的逻辑设计结果，并将此应用于计算机辅助气动系统设计中取得了良好的效果

Based on the definition of Boolean function on set and positive extension, The sufficient and necessary condition of PBF is proven. At last, an algorithm of generating MSP expression of stack filter positive Boolean function is presented taking advantage of Hasse diagram.

通过定义布尔函数开、闭集和最小项正、负扩展，证明了布尔函数具有层叠性的充要条件是布尔函数开集的正扩展或闭集的负扩展具有不变性，在此基础上，提出了一种通过Hasse图确定层叠滤波器最简正布尔函数的算法。

Based on the definition of Boolean function on set and positive extension, The sufficient and necessary condition of PBF is proven. At last,an algorithm of generating MSP expression of stack filter positive Boolean function ispresented taking advantage of Hasse diagram.

通过定义布尔函数开、闭集和最小项正、负扩展，证明了布尔函数具有层叠性的充要条件是布尔函数开集的正扩展或闭集的负扩展具有不变性，在此基础上，提出了一种通过Hasse图确定层叠滤波器最简正布尔函数的算法。

Multi-output combinational logic functions are located on the Karnaugh map and the common parts of each function overlap on this map, which makes it easier to find congener common miniterms and merge them.

该化简法要求用一张卡诺图表示多输出逻辑函数，使得它们的共享部分在几何上相互重叠，为辨识同类共享最小项和合并提供了方便。

Using the concept of Boolean functions and combinatorics theory comprehensively, we investigate the construction on annihilators of Boolean functions and the algebraic immunity of symmetric Boolean functions in cryptography:Firstly, we introduce two methods of constructing the annihilators of Boolean functions, Construction I makes annihilators based on the minor term expression of Boolean function, meanwhile we get a way to judge whether a Boolean function has low degree annihilators by feature matrix. In Construction II, we use the subfunctions to construct annihilators, we also apply Construction II to LILI-128 and Toyocrypt, and the attacking complexity is reduced greatly. We study the algebraic immunitiy of (5,1,3,12) rotation symmetric staturated best functions and a type of constructed functions, then we prove that a new class of functions are invariants of algebraic attacks, and this property is generalized in the end.Secondly, we present a construction on symmetric annihilators of symmetric Boolean functions.

本文主要利用布尔函数的相关概念并结合组合论的相关知识，对密码学中布尔函数的零化子构造问题以及对称布尔函数代数免疫性进行了研究，主要包括以下两方面的内容：首先，给出两种布尔函数零化子的构造方法，构造Ⅰ利用布尔函数的小项表示构造零化子，得到求布尔函数f代数次数≤d的零化子的算法，同时得到通过布尔函数的特征矩阵判断零化子的存在性：构造Ⅱ利用布尔函数退化后的子函数构造零化子，将此构造方法应用于LILI-128，Toyocrypt等流密码体制中，使得攻击的复杂度大大降低；通过研究(5，1，3，12)旋转对称饱和最优函数的代数免疫和一类构造函数的代数免疫，证明了一类函数为代数攻击不变量，并对此性质作了进一步推广。

This article analyses the Vector Space Model based on Algebra, and expands the model: expresses the index terms with minterm in order to reflect the relationship between terms, uses singular value decomposition to present the semantic structure of documents.

本文分析了代数理论的向量空间模型，并对该模型进行了扩展：用最小项标引词以反映词与词之间的关系，用奇异值分解来捕捉文献的语义结构；最后对这三种模型进行了比较。

I didn't watch TV last night, because it .

昨晚我没有看电视，因为电视机坏了。

Since this year, in a lot of villages of Beijing, TV of elevator liquid crystal was removed.

今年以来，在北京的很多小区里，电梯液晶电视被撤了下来。