R_0代数的可证等价类

讨论了R0代数的滤子以及相应的可证等价类.在R0代数里给出了一些滤子的具体例子,得到:F是R0代数M的超滤当且仅当F是M的固执滤子;当F是R0代数的蕴涵滤子时,M/F是布尔代数;当F是R0代数的极大布尔滤子时,M/F是只有两个元的布尔代数.     

R0-代数与BL-代数中的素滤子定理

R1-代数与BL-代数在模糊逻辑的研究中有重要作用,这与布尔代数在经典逻辑中的作用类似。本文通过一个特殊集x^-1F分别给出Ro-代数及BL-代数素滤子的一个等价条件,并给出BL-代数的一个新性质。应用这些结果分别得到Ro-代数与BL-代数的素滤子定理。     

R0-代数上的同余关系

研究了Ro-代数上的同余关系,首先通过探讨一类Ro-代数,建立起滤子与同余关系之间的联系,进而深入到其乘积上,最后以模糊滤子为工具定义R0－代数上的同余关系,讨论了滤子与模糊滤子之间的联系,并给出了由同余诱导的商R0－代数。     

三角代数的模糊滤子

引入三角代数和三角代数中滤子的概念,研究三角代数中滤子的性质.给出了三角代数中模糊滤子的概念,进一步给出三角代数模糊滤子的等价刻画;研究了三角代数中滤子与模糊滤子之间的关系,并证明由滤子可以诱导出模糊滤子,反之,由模糊滤子也可以诱导出滤子.     

R0代数的对偶代数

对于R0代数，给出了它的一个等价形式，并建立了它的对偶代数，从此刻划了R0代数内部结构的特征，也为从语义的角度进一步研究模糊逻辑系统提供了一个新的途径。     

对称布尔函数的代数免疫性

在流密码和分组密码的加密体制中,需要构作具有各种密码学性质的布尔函数,用来作为密钥,以抵抗已有的各种有效攻击方法。近年来,人们提出了代数攻击方法,为了抵抗这种攻击方式,构作代数免疫度很大的布尔函数,成为近五年来信息安全领域一个研究热点。本文综述布尔函数代数免疫性方面的重要问题和主要进展,其中包括中国学者在对称布尔函数代数免疫性的研究成果。     

R0代数的注记

讨论了R0代数与MV代数的关系，给出了R0代数的一种根。     

MTL代数的蕴涵滤子与正蕴涵滤子

在MTL代数M上引入了蕴涵滤子、正蕴涵滤子的概念,研究了它们的性质,给出了M的非空子集成为蕴涵滤子及正蕴涵滤子的充要条件和M的蕴涵滤子成为正蕴涵滤子的充要条件.讨论了蕴涵滤子与正蕴涵滤子的关系,得到了M的每一个正蕴涵滤子都是蕴涵滤子,但反之不真.     

BR0-代数的无序表示形式及WBR0-代数性质

对BR0-逻辑代数进行了进一步研究,得到了BR0-逻辑代数的一种无序表示形式,使得BR0-代数中的序关系蕴涵于BR0-代数的基本运算⊕和→之中,并根据BR0-代数的无序表示形式提出了WBR0-代数理论,初步地讨论了其中的性质.     

关于形式系统(L)*的强完备性

进一步讨论了形式系统L^*中的一般演绎推理及强完备性问题。对于任意的公式集Γ,引入一种新的代数结构—R0(Γ)代数,利用子代数结构,代数滤子理论及次直积分解理论等代数工具,证明了系统L^*的强完备性定理。     

关于密码体制中布尔置换的构造

布尔置换在密码体制的设计中有着重要的应用。本文讨论了布尔置换的构造，给出了两种构造方法。     

Construction of a Fuzzy and Boolean Logic Gates Based on DNA

Logic gates are devices that can perform logical operations by transforming a set of inputs into a predictable single detectable output. The hybridization properties, structure, and function of nucleic acids can be used to make DNA‐based logic gates. These devices are important modules in molecular computing and biosensing. The ideal logic gate system should provide a wide selection of logical operations, and be integrable in multiple copies into more complex structures. Here we show the successful construction of a small DNA‐based logic gate complex that produces fluorescent outputs corresponding to the operation of the six Boolean logic gates AND, NAND, OR, NOR, XOR, and XNOR. The logic gate complex is shown to work also when implemented in a three‐dimensional DNA origami box structure, where it controlled the position of the lid in a closed or open position. Implementation of multiple microRNA sensitive DNA locks on one DNA origami box structure enabled fuzzy logical operation that allows biosensing of complex molecular signals. Integrating logic gates with DNA origami systems opens a vast avenue to applications in the fields of nanomedicine for diagnostics and therapeutics.     

基于布尔逻辑的测试选择算法

提出了一种基于布尔逻辑运算的测试选择新方法.首先建立布尔关联矩阵来描述系统中故障与测试的相关关系;然后依据关联矩阵,分别定义描述故障检测用测试集和故障隔离用测试集的布尔逻辑函数;再根据布尔运算定律对逻辑函数进行展开和化简处理,并根据计算结果得到最优测试集.通过案例验证了该方法的正确性,并指出了该方法的优势及其在计算复杂性方面存在的不足.     

密码学中的布尔函数研究综述

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．     

Boolean functions with two distinct Walsh coefficients

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.     

A transformation from a Boolean equation control specification to a Petri net

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.     

Boolean AND and OR logic for cell signalling gateways: a communication perspective

Cell signalling plays a vital role in development, sustaining, differentiation, and reproduction of cells. Pathways involved in signalling networks are quite interwoven and complex. Complexity encountered in understanding these pathways is often reduced with the help of Boolean circuit representation. In this study, the authors provide communication aspect of the signalling pathways that have two input Boolean logic AND/OR implemented at the rear effector protein. Communication is assumed to be taking place in extracellular and intracellular environment. The two environments are connected using a receptor protein acting as relay between a molecular source and effector protein. Each relay detects molecules from outside environment and stimulates the production of signals in the intracellular space. These signals/molecules further activate the effector protein which acts as a Boolean switch driven by AND/OR logic. Assuming Poisson reception at the relay as well as at the receiver, the authors provide probability of error of the AND and OR Boolean logic communication systems. Furthermore, reliability and some capacity bounds are deduced for the given Boolean communication system.Inspec keywords: cellular biophysics, integrated circuit modelling, stochastic processes, probability, cellular transport, proteins, molecular biophysics, Boolean functions, biochemistryOther keywords: cell signalling, communication perspective, signalling networks, Boolean circuit representation, communication aspect, signalling pathways, input Boolean logic, rear effector protein, extracellular environment, intracellular environment, receptor protein, relay, stimulates, signals/molecules, Boolean switch, Boolean logic communication systems, given Boolean communication system     

Optical programmable Boolean logic unit

Logic units are the building blocks of many important computational operations likes arithmetic, multiplexer-demultiplexer, radix conversion, parity checker cum generator, etc. Multifunctional logic operation is very much essential in this respect. Here a programmable Boolean logic unit is proposed that can perform 16 Boolean logical operations from a single optical input according to the programming input without changing the circuit design. This circuit has two outputs. One output is complementary to the other. Hence no loss of data can occur. The circuit is basically designed by a 2×2 polarization independent optical cross bar switch. Performance of the proposed circuit has been achieved by doing numerical simulations. The binary logical states (0,1) are represented by the absence of light (null) and presence of light, respectively.