{"title":"Single diagnostic tests for inversion faults of gates in circuits over arbitrary bases","authors":"Iľya G. Liubich, Dmitriy S. Romanov","doi":"10.1515/dma-2022-0001","DOIUrl":null,"url":null,"abstract":"Abstract We prove that an arbitrary Boolean function may be implemented by an irredundant Boolean circuit over an arbitrary finite complete basis so that the circuit admits a single diagnostic test of length at most 4 with respect to inversion faults at gate outputs.","PeriodicalId":11287,"journal":{"name":"Discrete Mathematics and Applications","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2022-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete Mathematics and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/dma-2022-0001","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
Abstract We prove that an arbitrary Boolean function may be implemented by an irredundant Boolean circuit over an arbitrary finite complete basis so that the circuit admits a single diagnostic test of length at most 4 with respect to inversion faults at gate outputs.
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.
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