Cutset Analysis of Networks Using Basic Minimal Paths and Network Decomposition

The concept of basic minimal paths has been introduced, and its use in deducing the node cutsets of a network was described. This 3 paper deals with two important aspects of basic minimal paths: 1) the deduction of link cutsets from node cutsets, and 2) reduction of computational requirements in deducing the basic minimal paths using network decomposition.     

对AES算法的S盒布尔函数分析

分组密码的安全性很大程度上取决于分组密码中唯一的非线性结构S盒。论文对AES的S盒的代数性质进行分析,采用布尔函数的方法,先得到S盒的真值表,再求解S盒的布尔函数表达式,根据布尔函数表达式计算得出S盒的平衡性、正交性、线性性、差分均匀性质、鲁棒性、非线性性等代数性质,说明AES的S盒的安全性。     

Boolean Functions, Projection Operators, and Quantum Error Correcting Codes

This paper describes a fundamental correspondence between Boolean functions and projection operators in Hilbert space. The correspondence is widely applicable, and it is used in this paper to provide a common mathematical framework for the design of both additive and nonadditive quantum error correcting codes. The new framework leads to the construction of a variety of codes including an infinite class of codes that extend the original ((5, 6, 2)) code found by Rains It also extends to operator quantum error correcting codes.     

布尔函数的对偶性和线性点

本文主要讨论了部分自对偶和部分反自对偶函数、部分线性函数以及具有线性点的函数的性质。     

Realization of Boolean Functions via CNN: Mathematical Theory, LSBF and Template Design

As a paradigm for nonlinear spatial-temporal processing, cellular nonlinear networks (CNN) are biologically inspired systems where computation emerges from a collection of simple locally coupled nonlinear cells. Our investigation is an exploration of an important and difficult aspect of implementing arbitrary Boolean functions by using CNN. A typical class of basic key Boolean functions is the class of linearly separable ones. In this paper, we focus on establishing a complete set of mathematical theories for the linearly separable Boolean functions (LSBF) that are identical to a class of uncoupled CNN. First, we obtain an essential relationship between the template and the offset levels as well as the basis of the binary input vector set in the uncoupled CNN. More precisely, we construct a neat binary input–output truth table and some interesting properties of the offset levels of the uncoupled CNN, and develop a practical design formula for the class of CNN template. Especially, we found a criterion for LSBF, which depends only on symbolic relations between a Boolean function's outputs. Furthermore, we develop a method for representing any linearly nonseparable Boolean function into a logic operation of a sequence of linearly separable ones for a small number of inputs.     

非线性平衡布尔函数及其构造方法

介绍了抗密码分析能力强的布尔函数的两个重要特性:平衡性和非线性,并研究了三种可产生具有高非线性的布尔函数的方法,即链接、分裂、修改序列。最后指出通过修改序列获得的平衡布尔函数比通过以往任何构造方法获得的具有更高的非线性。     

System Reliability Evaluation for a Multistate Supply Chain Network With Failure Nodes Using Minimal Paths

This work devotes to the application of network methods for the reliability of a complex supply chain system, which is a set of several factories with supply-demand relationship. Two characters are considered in the proposed network: 1) nodes, and arcs all have multiple possible capacities, and may fail; and 2) the capacity weight varies with arcs, nodes, and types of commodity. The purpose of this paper is to study the systems reliability, in this case the possibility that a given quantity $(d_{1},d_{2})$ of two types of commodities can be transmitted from the source factory to the destination factory simultaneously. Such a possibility can be treated as a performance index to measure the quality level of a supply chain network. The flow model is constructed by flow assignments, and capacity vectors. The $(d_{1},d_{2})$ -MP, which represents the capacity of each arc/node, is a minimal capacity vector meeting the demand constraint. A simple algorithm in terms of minimal paths is first proposed to generate all $(d_{1},d_{2})$-MP. The system reliability can then be calculated efficiently in terms of $(d_{1},d_{2})$-MP. Time complexity of the proposed algorithm is also analyzed.      

一类布尔函数的性质及其应用

讨论了不重复齐次k次布尔函数的密码性质,给出了这类函数所满足非线性准则;研究了这类函数在非线性组合函数的构造中的应用,得到了几个基于这类函的构造定理。     

Minimizing Great-Circle Distance Ratios of Undesired and Desired Signal Paths on a Spherical Earth

Preventing interference among mobile radio (MR) nets often requires spectrum managers to observe channel-assignment rules based on minimum ratios of the great-circle distances traversed by desired and undesired (potentially interfering) signals. Finding the true minimum values of these ratios, rather than the simply computed worst-case estimates, is necessary to utilize the spectrum efficiently. This paper provides an analysis of the case where the MRs operate in or above circular service areas on the surface of a spherical Earth. The analysis provides an accurate and efficient way, which is less complicated than performing the calculations on the sphere, to compute true minimum distance ratios. The method uses stereographic projection to transform the original minimization problem into a simpler problem of minimizing a ratio of Euclidean distances, which is expressed as a function of a single real variable, over the boundaries of discs (i.e., circles) in the complex plane. In a large, complicated problem, this methodology has been shown to reduce the computational time by two thirds.      

An Efficient Algorithm for Deducing the Minimal Cuts and Reliability Indices of a General Network Configuration

The paper describes an efficient algorithm for evaluating the minimal cut sets of any general network. The algorithm is based on Boolean algebra and set theory, and contains many important improvements. The four most important features are 1. only one set of topological input data is required to evaluate the minimal cuts and reliability indices of every output node; 2. a mix of undirectional, bidirectional and multi ended components can be included very simply; 3. any number of input nodes may be specified; 4. a new concept of overall system reliability permits different, large, and complex systems to be compared. The computational efficiency of the algorithm is clearly indicated by the fact that the time required to analyse Example 1 on a CDC7600 was 0.7 sec. The storage required with the appropriate arrays dimensioned for a system having 100 components and up to 125 minimal cut sets per output node is 15 k-words. These times and storage include the overall system reliability analysis.     

2阶相关免疫函数的构造与计数

本文讨论２阶相关免疫函数的构造与计数问题，构造出了一大类重量为２的方幂的２阶相关免疫函数，首次给出了２阶相关免疫函数个数的下界。     

A New Decomposition Algorithm for Threshold Synthesis and Generalization of Boolean Functions

A new algorithm for obtaining efficient architectures composed of threshold gates that implement arbitrary Boolean functions is introduced. The method reduces the complexity of a given target function by splitting the function according to the variable with the highest influence. The procedure is iteratively applied until a set of threshold functions is obtained, leading to reduced depth architectures, in which the obtained threshold functions form the nodes and a and or or function is the output of the architecture. The algorithm is tested on a large set of benchmark functions and the results compared to previous existing solutions, showing a considerable reduction on the number of gates and levels of the obtained architectures. An extension of the method for partially defined functions is also introduced and the generalization ability of the method is analyzed.      

Ternary Walsh Transform and Its Operations for Completely and Incompletely Specified Boolean Functions

The new ternary Walsh transform is considered in this paper. Such a ternary Walsh transform can be used in a similar manner as the standard Walsh transform for binary logic functions as shown here. It is based on the Kronecker product as well as the Galois field and new ternary operations. The same hardware implementation can be used for both forward and inverse ternary Walsh transforms based on its fast algorithms and properties. The ternary Walsh transform is suitable for processing both completely and incompletely specified Boolean functions. Its properties for the decomposition and symmetry detections of the Boolean functions are shown.     

广义严格雪崩准则及满足它的布尔函数性质

本文从实际出发减弱了Ｗｅｂｓｔｅｒ和Ｔａｖａｒｅｓ给出的严格雪崩准则（ＳＡＣ）的限制条件，定义了广义严格雪崩准则，并在不作出实质性“牺牲”的前提下避免了严格雪崩准则的阶数与非线性阶之间的折衷。同时，讨论了满足广义严格雪崩准则的布尔函数性质，结果表明满足严格雪崩准则的布尔函数具有的良好性质得到了很好的继承。     

Noncoherent MIMO Communication: Grassmannian Constellations and Efficient Detection

This paper considers the design of both a transmitter and a receiver for noncoherent communication over a frequency-flat, richly scattered multiple-input multiple-output (MIMO) channel. The design is guided by the fact that at high signal-to-noise ratios (SNRs), the ergodic capacity of the channel can be achieved by input signals that are isotropically distributed on the (compact) Grassmann manifold. The first part of the paper considers the design of Grassmannian constellations that mimic the isotropic distribution. A subspace perturbation analysis is used to determine an appropriate metric for the distance between Grassmannian constellation points, and using this metric, greedy, direct and rotation-based techniques for designing constellations are proposed. These techniques offer different tradeoffs between the minimum distance of the constellation and the design complexity. In addition, the rotation-based technique results in constellations that have lower storage requirements and admit a natural “quasi-set-partitioning” binary labeling.      

电视台播出系统通路技术指标的测试与分析

本文根据河北省《广播电视播出系统通路技术指标等级暂行标准》和行业标准《VHF电视发射通道运行技术测量方法》,结合我台现有条件,对电视台播出系统通路技术指标测试进行分析和探讨。     

构建基因调控布尔网络及其动态分析

利用互信息理论和布尔网络共同建立基因调控网络模型,并且通过举例说明该方法,用此方法相应地可推导出多个基因决定某个或多个基因的表达值的逻辑规则,根据得到的逻辑规则建立基因电路网络,再对得到的基因逻辑电路网络依据分析逻辑电路网络的方法建立基因调控网络动态转换,从而分析基因间的调控关系.     

一阶相关免疫函数计数下界的改进

本文构造了一大类相关免疫布尔函数，给出了一阶相关免疫函数个数的新的下界，从而大大改进了相关免疫函数的计数公式。     

Symbol Error Probabilities for M-ary CPFSK: Coherent and Noncoherent Detection

Continuous-phase frequency shift keying (CPFSK) is discussed and theoretical predictions for symbol error probabilities are derived, where the memory inherent in the phase continuity is used to improve performance. Previously known results concluded that binary CPFSK can outperform coherently detected PSK at high SNR. New results presented here show thatM-ary CPFSK outperforms more tranditionally usedM-ary modulation systems. Specifically, coherently detected quaternary CPFSK with a five-symbol interval decision can outperform coherent QPSK by 3.5 dB, and octal coherent CPFSK with a three- symbol decision can outperform octal orthogonal signaling by 2.6 dB at high SNR. Results for coherently detected and noncoherently detected CPFSK are derived. These performance improvements are estimates derived from symbol error probability upper bounds. Monte Carlo simulation was performed which then verified the results.     

Modularizing, Minimizing, and Interpreting the K&H Fault-Tree

The verification by Worrell & Stack (W&S) of results previously obtained by Kumamoto & Henley (K&H) for a fault tree of an s-noncoherent system and its inverse and their correction of the three errors in the tree makes it possible to simplify the analysis by forming modules; this facilitates Boolean algebraic operations, so that both sets are described economically in their minimal forms, a subset of the prime implicants (p.i.'s). Quine's consensus operation is used to minimize and to find the p.i.'s. Corresponding to the MOCUS output for the inverse reported by K&H, which is neither minimal nor the set of p.i.'s, instead of 32 terms, there are 15 in the modularized set. Instead of the 42 p.i.'s obtained by both K&H and W&S, we have 17; 13 of these are a unique minimal form. Instead of 352 p.i.'s for the tree per both K&H and W&S, we have a 15-term minimal form, identical to the list of p.i.'s. The results are further analyzed as a contribution to the continuing discussion of the utility of minimal forms vis-a-vis the p.i.'s and of the consensus method.