Bounds on Shannon functions of lengths of contact closure tests for contact circuits

IF 0.3 Q4 MATHEMATICS, APPLIED

Discrete Mathematics and Applications Pub Date : 2021-06-01 DOI:10.1515/dma-2021-0015

K. A. Popkov

引用次数: 0

Abstract

Abstract We consider the problem of synthesis of irredundant two-pole contact circuits which implement n-place Boolean functions and allow short single fault detection or diagnostic tests of closures of at most k contacts. We prove that the Shannon function of the length of a fault detection test is equal to n for any n and k, and that the Shannon function of the length of a diagnostic test is majorized by n + k(n − 2) for n ⩾ 2.

查看原文本刊更多论文

接触电路接触闭合试验长度Shannon函数的界

摘要我们考虑了无冗余双极接触电路的合成问题，该电路实现n位布尔函数，并允许对最多k个接触的闭合进行短的单故障检测或诊断测试。我们证明了对于任何n和k，故障检测测试长度的Shannon函数等于n，并且对于n⩾2，诊断测试长度的香农函数由n+k（n−2）决定。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Discrete Mathematics and Applications MATHEMATICS, APPLIED-

CiteScore

0.60

自引率

20.00%

发文量

期刊介绍： The aim of this journal is to provide the latest information on the development of discrete mathematics in the former USSR to a world-wide readership. The journal will contain papers from the Russian-language journal Diskretnaya Matematika, the only journal of the Russian Academy of Sciences devoted to this field of mathematics. Discrete Mathematics and Applications will cover various subjects in the fields such as combinatorial analysis, graph theory, functional systems theory, cryptology, coding, probabilistic problems of discrete mathematics, algorithms and their complexity, combinatorial and computational problems of number theory and of algebra.