查询词典 complexity of things

To begin with, theory of FCSR and its sequence is summarized and investigated. Furthermore, emphasis is placed on the vaule of 2-adic complexity. A conclusion is drawn that the vaule lies in the relation between 2-adic complexity and lineai complexity of a same seqence. Fact that there exists sequence with high linear complexity but low 2-adic complexity is given and analyzed. The value of 2-adic complexity in cryptanalysis can be directly drawn from the very fact. A series of problems are opened based on the value and discussions are done in various depth. Some good results are obtained in these problems such as the 2-adic complexity distribution of periodic sequences and the stability of 2-adic complexity. The value of FCSR in stream cipher design is discussed at the same time.

首先对FCSR及其序列理论进行了系统的总结和研究，然后重点探讨了2-adic复杂度的流密码意义，通过论证表明，存在线性复杂度较大而2-adic复杂度较小的序列类，从而明确了2-adic复杂度的流密码分析意义，进而提出了一系列相关的研究问题并进行了不同深度的探讨，对其中周期序列的2-adic复杂度分布和2-adic复杂度的稳定性等问题得到了较好的结果；同时对FCSR的流密码设计意义进行了探讨，对其中的问题给出了一些思路或简单结论。

The characters of linear complexity profile of periodic sequences are investigat- ed. The relation between the continued fraction expansion of rational function and its 1- inear complexity profile is established. The expression of linear complexity profite is gi-~~en and a condition estimating the randomness of a sequence is presented. By the linear complexity profile, the bound of sphere complexity is proposed. A formula to record the number of sequences with given linear complexity profile is presented.

研究了周期序列的线性复杂度曲线特性，在周期序列生成函数的连分式展开式与线性复杂度曲线之间建立联系，给出了周期序列线性复杂度曲线的表达式；给出了判断序列随机性好坏的一个条件；利用线性复杂度曲线特性给出周期序列球体复杂度的一个估计；给出了具有给定线性复杂度曲线的序列个数的一个计数公式。

The representation of sequences is very helpful for the research of their linear complexity,so this paper we first research trace representation of periodic sequences,and the trace representation of a New Generalized Cyclotomic Sequence of order two of length pq is given,then for 2~mp~n period binary sequences,where p is an odd prime and 2 is a primitive root modulo p~2,we present a relation-ship between the linear complexity and the minimum value k for which the k-error linear complexity is strictly less than the linear complexity and have the upper bound and lower bound of the value k, finally we discuss the k-error linear complexity of legendre sequences,also have the upper bound and lower bound of the value k,and discusses the situation where the linear complexity drop again for some Legendre sequences.

序列的表达形式对于其线性复杂度的研究是十分有帮助的，本文我们首先研究的是周期序列的迹表示，给出了2阶pq长度的扩展分圆序列的迹表示，然后讨论了周期为2~mp~n(m≥2)序列的线性复杂度与使得线性复杂度变小的最小的k值的关系，给出了k值的上界和下界，这里p为奇素数，2是模p~2的本原根，并通过例子讨论了其线性复杂度的稳定性，最后对Legendre序列k-错线性复杂度进行了分析，也给出了k值的上界和下界，并对某些Legendre序列讨论了线性复杂度再次下降的情况。

The disorder contained can only cause the complexity in the organization, disorder outside organization has the influence to organization complexity, but it cannot cause the organization the complexity, only if it is absorbed and in the organization, can the disorder constitute the complexity; all nature of the complexity is produced because of the disorder in the organization, if there is no the disorder, the organization has no nature such as fortuitousness, randomness, multiplicity and non-linearity, and it is impossible to appear the perturbation, the fluctuation, emerges with phenomenon such as branch, and cannot change suddenly and evolve.

无序只有包含于组织中才能够导致复杂性，组织外的无序对组织的复杂性产生影响，但它不能导致组织的复杂性，只有被组织吸收，成为组织内的无序，才能构成复杂性。复杂性的所有性质都因包含于组织中的无序而产生。没有无序，组织就没有偶然性、随机性、多样性和非线性等性质，就不可能出现扰动、涨落、涌现和分岔等现象，就不能突变和进化。

The dissertation will study some problems in stream ciphers. The main results that the author obtained are as follows:(1) The concept of fuzzy linear complexity is presented initially. The estimation problem of the fuzzy linear complexity of the random vector is studied, and a lot of upper bounds are given. The limit properties of fuzzy linear complexity of random vector are studied, and the limit theorem and the limit of variance of the fuzzy linear complexity of random vector are given.(2) The concept of fuzzy nonlinear complexity is presented initially.

本文在前人工作的基础上对序列密码中的一些问题进行了研究；所取得的主要研究成果综述如下：（1）首次提出了模糊线性复杂度的概念，对随机向量的模糊线性复杂度的均值进行了估计，给出了几个上界估计公式，并研究了随机向量模糊线性复杂度的极限性质，给出了随机向量模糊线性复杂度的极限定理及其方差的极限。

With the growing developments of the construction of SS/FH sequence in much wider fields, the well-known complexity measures—the linear complexity, the linear complexity profile and the k-error linear complexity—are widelyused but not sufficient to evaluate the complexities of the sequences available, for instance, the cryptographical sequence and the chaotic sequence families.

针对目前国内外普遍采用的LC、LCP和k-error LC(k-error Linear Complexity)序列复杂度检测理论存在的缺陷，将物理学和信息论中信息熵的概念引入到序列的复杂度检验中，提出了基于近似熵(ApEn：Approximate Entroy)的FH/SS(Frequnecy Hopping/Spread Spectrum)序列复杂度检验理论。

Aiming at the limitation of this algorithm,the universal cut-and-try algorithm is put forward.The complexities of macroscopic traffic volume and GDP time series are calculated,respectively.The results show:the complexity of GDP has a positive correlation with the complexity of freight traffic volume;the influence of the complexity of GDP on the complexity of macroscopic traffic volume is long-term with lagged effect;and the correlation between GDP and macroscopic traffic volume has an uncertain relation with the correlation between their complexities.

通过计算宏观交通量与GDP时间序列的复杂度，得到简单结论：GDP复杂度与货运交通量复杂度具有较强的正相关关系；GDP复杂度对宏观交通量复杂度的影响是长期的，具有滞后效应；GDP与宏观交通量现象的相关程度与二者复杂度的相关程度没有必然的联系。

Through review historical cognitions on relations between complexity and randomicity, bring forth and analyzing immediate relationships between randomicity and Kolmogorov complexity from computer science, this paper tries to peel off some errors understanding on this relations and to return real relations about the them, and analyzing Gell Mann effective complexity concept, argument that two relations between complexity and randomicity, and three random instances.

本文通过对历史上复杂性与随机性关系的认识回顾，展示和分析了起源于计算机科学领域的Kolmogorov复杂性与随机性的直接关联，分析了盖尔曼的有效复杂性概念，论证了两种复杂性与随机性的关系，以及随机性的不同情况，力图剥离混合在复杂性与随机性相互关系上的一些误读和误解，还复杂性与随机性一种客观的本真关系。

Halford et al. proposed a theory of relational complexity to interpret the essence of task difficulty. To be exact, the difficulty of task can be determined by the number of argument or dimension related, which is called the re?鄄lational complexity. The relational complexity is increased with the processing demand. We can adopt such mech?鄄anisms as conceptual chunking and segmentation to reduce the complexity.

哈尔福德等人提出了评估任务难度的关系复杂性理论，认为任务难度可由相关的变量数量即关系复杂性来确定；关系复杂性越大加工要求也越高，这时可采取概念组块和分解机制来减少复杂性；认知发展阶段可归因于随着年龄的增长能够加工的关系复杂性的增加。

In this paper, the relationship between the linear complexity and the 2-adic complexity is investigated based on the Chinese Remainder Theorem and some other related theories in the number theory, and the existence of N-periodic sequences that simultaneously achieve the maximum 2-adic complexity and a great k-error 2-adic complexity is proved.

文中借助数论中的中国剩余定理等相关理论研究了二元序列的2-adic复杂度与线性复杂度的关系，证明了具有最大2-adic复杂度以及较大k错2-adic复杂度的N周期序列的存在性，给出了具有这种性质的周期序列的数目的下界。

More direct, directer ; most direct, directest

径直的，笔直的

Do you know how to use a chain saw?

你知道如何使用链锯吗？