多值触发器及其在时序电路设计中的应用

本文对于多值逻辑代数系统中的基本运算和实现这些基本运算的门电路，作了必要的阐述。作者将ＤＹＬ集成线性“与或“门，用来设定多值逻辑电平的基础上，提出了多值Ｄ、Ｔ、ＪＫ等触发器电路，并将这类多值触发器，作为多值逻辑器件，用于时序电路设计。     

一种实现三值逻辑电路的DNA计算模型

近年来,随着生物计算和量子计算研究的深入,多值逻辑电路的各种实现成为一个热门的研究方向.发夹结构是DNA分子一种特殊杂交方式的产物,具有结果稳定、特异性强的优点.本文首次提出了一种利用DNA分子来实现多值逻辑电路的方法,用DNA分子的多发夹结构来表示三值逻辑的值,并给出"与"运算和"或"运算的计算模型,该模型适合应用于大规模的多值逻辑电路.     

任意值数的组合逻辑电路设计

自我国首创的DYL线性集成逻辑门问世后更促进了多值逻辑和连续逻辑理论及其应用的研究。我们经过将近一年的时间在中科院半导体所王守觉教授的指导下,根据多值逻辑代数的基本运算规则,运用DYL线性集成门实现了任意值数的组合逻辑电路设计。本文介绍了多值逻辑代数的基本运算和定律以及多值逻辑组合电路的设计方法。     

基于布尔过程论的层次化延时分析方法

芯片设计的日益复杂化和高速化对电路精确的定时特性提出了越来越高的要求。电路的延时不仅与电路的拓扑结构有关,而且还与电路的逻辑功能及输入都有密切的关系。采用Boole过程论这种统一描述数字电路的逻辑行为和时变行为的代数形式作为理论基础,提出了波形多项式偏导的概念,并用之重新定义了敏化。用偏导定义的敏化改进了解析延时模型,基于最长可敏化通路的延时建立了电路模块或子电路的延时矩阵模型,由延时矩阵模型出发提出了一种精确的电路层次化延时分析方法。最后用实验验证了文中提出的延时分析方法的有效性。     

一种求解多值逻辑函数接近最小覆盖的算法

1.引言 本文研究Allen-Givone多值逻辑代数系统中的“积之和”形式的函数的简化算法。首先,在讨论符合目前多值逻辑函数实现特点的合理代价标准基础上,提出了一种折衷的代价标准,按着这个标准不求所有质蕴涵项集合,直接求解无冗余覆盖。这个算法以减少文字门的个数为依据,在确定某些质蕴涵项和实现文字数较少之间进行权衡,它在一个位     

低功耗CMOS“二值工作三值检测”门电路

1.引言 多值逻辑电路应用于二值逻辑系统以构成自校验系统或简化故障检测是多值逻辑应用的一个方面。文献[1]提出一种方案:用CMOS技术实现一种新型的三值门电路,再用这种门电路构成自校验的二值逻辑系统。这个方案的基本原理是用三值门电路的二个逻辑值作为二值系统的正常工作值,而多余的一个逻辑值作为故障的测试及自校     

一种基于多值逻辑的开放式逻辑软件设计方法

在工业控制系统中，将对逻辑测控过程的表述抽象成象值逻辑是一种准确而又便利的方法，同时，测控过程的多样性又使传统的利用程序设计语言中逻辑语句的软件设计方法很难适应对开放性的要求，本文提出一种适合多值逻辑处理的数据结构和代数系统，并以此为基础，构造逻辑描述式，实现组合多值逻辑和时序多值逻辑的开放式设计。     

CCD多值逻辑电路

作者提出了一种采用电荷耦合器件(CCD)的多值逻辑电路,它输出的数字信息稳定可靠,并可借以实现所需基数值(由二值直到数百值以上)的多值逻辑。文中介绍了CCD器件的有关原理和基本结构,和据此设计的多值逻辑电路,讨论了其性质及几种应用。     

Matlab语言与线性电路的符号仿真

目前的电路仿真软件通常是在电路中所有元件值都是给定的情况下得到一些数值结果，而非解析结果。该文利用Matlab的符号运算功能编程，通过节点列表法，实现了任意线性电路的自动解析求解，为电路分析提供了一个有效的辅助工具。     

多变量三值时序电路综合

本文提出多变量三值时序电路综合基本方法，首先从转移条件推出电路方程，使功能复杂的多变量三值时序电路易于实现，接着本文研究电路状态分配原则和指数运算定理，最后扩展三值非完全描述的概念，用以表达任意型触发器的激盛函数。     

有限布尔代数上的线性自动机

自动机理论是计算机科学理论的重要组成部分。论文研究了布尔代数上的线性自动机,证明了任意一个线性有限自动机是函数布尔代数上的一个内动机。定出了有限布尔代数上的一类可逆线性内动机,给出并证明了有限布尔代数上内动机图型为下向森林的充分必要条件,给出了树型内动机中每一层节点数的计算公式,进而证明了有限布尔代数上的非可逆内动机图型为恰等叉支下向树的充分必要条件。     

Refinement algebra with dual operator

Algebras of imperative programming languages have been successful in reasoning about programs. In general an algebra of programs is an algebraic structure with programs as elements and with program compositions (sequential composition, choice, skip) as algebra operations. Various versions of these algebras were introduced to model partial correctness, total correctness, refinement, demonic choice, and other aspects. We introduce here an algebra which can be used to model total correctness, refinement, demonic and angelic choice. The basic model of our algebra are monotonic Boolean transformers (monotonic functions from a Boolean algebra to itself).     

异步时序电路反馈稳定性判据

本文提出了"含相开关代数"的概念,证明了它与布尔代数是同构的,从而使布尔代数可 用于设计时序电路.文中利用含相开关代数这一概念推导出异步时序电路反馈稳定性判据, 从而能方便地找出全部不稳定转换.     

Maximal contractions in Boolean algebras

In the present paper,the concepts of deductive element and maximal contraction are introduced in Boolean algebras,and corresponding theories of consistency and maximal contractions are studied.An algorithm principle is proposed to compute all maximal contractions for a consistent set with respect to its refutation in Boolean algebras.It is pointed out that the quotient algebra of the first-order language with respect to its provable equivalence relation constitutes a Boolean algebra,and hence the computation of R-contractions for closed formulas in first-order languages can be converted into the one in Boolean algebras proposed in this paper.Furthermore,the concept of basic element is introduced in Boolean algebras,which contributes to the definitions of clause and Horn clause transplanted from logic to a special type of Boolean algebras generated by basic elements.It is also pointed out that the computation of R-contractions for clauses in the classical propositional logic can be converted into the one in Boolean algebras generated by basic elements proposed in this paper.     

Pseudocomplemented lattice effect algebras and existence of states

We prove that in every pseudocomplemented atomic lattice effect algebra the subset of all pseudocomplements is a Boolean algebra including the set of sharp elements as a subalgebra. As an application, we show families of effect algebras for which the existence of a pseudocomplementation implies the existence of states. These states can be obtained by smearing of states existing on the Boolean algebra of sharp elements.     

Robbins algebra: Conditions that make a near-boolean algebra boolean

Some problems posed years ago remain challenging today. In particular, the Robbins problem, which is still open and which is the focus of attention in this paper, offers interesting challenges for attack with the assistance of an automated reasoning program; for the study presented here, we used the program OTTER. For example, when one submits this problem, which asks for a proof that every Robbins algebra is a Boolean algebra, a large number of deduced clauses results. One must, therefore, consider the possibility that there exists a Robbins algebra that is not Boolean; such an algebra would have to be infinite. One can instead search for properties that, if adjoined to those of a Robbins algebra, guarantee that the algebra is Boolean. Here we present a number of such properties, and we show how an automated reasoning program was used to obtain the corresponding proofs. Additional properties have been identified, and we include here examples of using such a program to check that the corresponding hand-proofs are correct. We present the appropriate input for many of the examples and also include the resulting proofs in clause notation.This work was supported by the Applied Mathematical Sciences subprogram of the Office of Energy Research, U.S. Department of Energy, under Contract W-31-109-Eng-38.     

从布尔代数到布尔微积分

布尔函数作为最简单的有限值函数具有特殊的重要性．它在包括信息、控制等许多领域有着广泛的应用．本文综合介绍有关布尔函数的理论基础．包括从布尔代数到布尔微积分的主要理论结果,它们在信息与控制中的一些重要应用,以及其前沿动态与新进展．介绍的一个重点是矩阵半张量积在这些领域的应用．     

An algebra of temporal faults

Faults modelling is essential to anticipate failures in critical systems. Traditionally, Static Fault Trees are employed to this end, but Temporal and Dynamic Fault Trees are gaining evidence due to their enriched power to model and detect intricate propagation of faults that lead to a failure. In previous work, we showed a strategy based on the process algebra CSP and Simulink models to obtain fault traces that lead to a failure. Although that work used Static Fault Trees, it could be used with Temporal or Dynamic Fault Trees. In the present work we define an algebra of temporal faults (with a notion of fault propagation) and prove that it is indeed a Boolean algebra. This allows us to inherit Boolean algebra’s properties, laws and existing reduction techniques, which are very beneficial for faults modelling and analysis. We illustrate our work on a simple but real case study supplied by our industrial partner EMBRAER.     

Algebraic Properties of Cores of Generalized Neurofunctions

This paper considers generalized neural elements and identifies the conditions for implementation of functions of algebra of logic from these elements. We introduce the concept of a modified core of Boolean functions with respect to the system of characters of a group on which functions of algebra of logic are given. The criteria of belonging these functions to the class of generalized neurofunctions are provided. The algebraic structure of cores of Boolean neurofunctions is studied. On the basis of properties of tolerance matrices, a number of necessary conditions for implementation of Boolean functions by one generalized neural element are obtained. The obtained results allow to develop efficient methods of synthesis of integer-valued generalized neural elements with a large number of inputs that can be successfully applied in solving information compression and transmission problems, as well as discrete signal recognition problems.     

Rough 3-valued algebras

Rough set theory is an important tool for dealing with granularity and vagueness in information systems. This paper studies a kind of rough set algebra. The collection of all the rough sets of an approximation space can be made into a 3-valued Lukasiewicz algebra. We call the algebra a rough 3-valued Lukasiewicz algebra. In this paper, we focus on the rough 3-valued Lukasiewicz algebras, which are a special kind of 3-valued Lukasiewicz algebras. Firstly, we examine whether the rough 3-valued Lukasiewicz algebra is an axled 3-valued Lukasiewicz algebra. Secondly, we present the condition under which the rough 3-valued Lukasiewicz algebra is also a 3-valued Post algebra. Then we investigate the 3-valued Post subalgebra problem of the rough 3-valued Lukasiewicz algebra. Finally, this paper studies the relationship between the rough 3-valued Lukasiewicz algebra and the Boolean algebra constructed by all the exact sets of the corresponding approximation space.