用不可靠逻辑门的自校正电路实现线性布尔函数

IF 0.6 4区数学 Q3 MATHEMATICS

Mathematical Notes Pub Date : 2024-04-22 DOI:10.1134/s0001434624010073

K. A. Popkov

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引用次数: 0

摘要

摘要我们证明，如果一个布尔函数本质上至少取决于两个变量，那么它就不能由一个电路来实现，该电路由不可靠门电路组成，每个不可靠门电路最多有两个输入端，并且至少对任意数量门电路的某些故障具有自校正功能。鉴于前面的结果，只需为线性函数建立这一事实即可。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Implementation of Linear Boolean Functions by Self-Correcting Circuits of Unreliable Logic Gates

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Implementation of Linear Boolean Functions by Self-Correcting Circuits of Unreliable Logic Gates

Abstract

We prove that if a Boolean function essentially depends on at least two variables, then it cannot be implemented by a circuit that consists of unreliable gates with at most two inputs each and is self-correcting with respect to at least some faults of an arbitrary number of gates. In view of the previous results, it suffices to establish this fact for linear functions.

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来源期刊

Mathematical Notes 数学-数学

CiteScore

0.90

自引率

16.70%

发文量

179

审稿时长

24 months

期刊介绍： Mathematical Notes is a journal that publishes research papers and review articles in modern algebra, geometry and number theory, functional analysis, logic, set and measure theory, topology, probability and stochastics, differential and noncommutative geometry, operator and group theory, asymptotic and approximation methods, mathematical finance, linear and nonlinear equations, ergodic and spectral theory, operator algebras, and other related theoretical fields. It also presents rigorous results in mathematical physics.