{"title":"单调布尔函数的传播准则，其最小向量支持集为 1 或 2 个元素","authors":"Gleb A. Isaev","doi":"10.1515/dma-2024-0006","DOIUrl":null,"url":null,"abstract":"\n The propagation criterion for monotone Boolean functions with least vector support sets consisting of one or two vectors is studied. We obtain necessary and sufficient conditions for the validity of the propagation criterion for a vector in terms of the Hamming weights of vectors in least vector support set depending on whether these vectors share some nonzero components with the given vector. We find the cardinality of the set of vectors satisfying the propagation criterion for such functions.","PeriodicalId":11287,"journal":{"name":"Discrete Mathematics and Applications","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Propagation criterion for monotone Boolean functions with least vector support set of 1 or 2 elements\",\"authors\":\"Gleb A. Isaev\",\"doi\":\"10.1515/dma-2024-0006\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"\\n The propagation criterion for monotone Boolean functions with least vector support sets consisting of one or two vectors is studied. We obtain necessary and sufficient conditions for the validity of the propagation criterion for a vector in terms of the Hamming weights of vectors in least vector support set depending on whether these vectors share some nonzero components with the given vector. We find the cardinality of the set of vectors satisfying the propagation criterion for such functions.\",\"PeriodicalId\":11287,\"journal\":{\"name\":\"Discrete Mathematics and Applications\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2024-04-01\",\"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-2024-0006\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete Mathematics and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/dma-2024-0006","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Propagation criterion for monotone Boolean functions with least vector support set of 1 or 2 elements
The propagation criterion for monotone Boolean functions with least vector support sets consisting of one or two vectors is studied. We obtain necessary and sufficient conditions for the validity of the propagation criterion for a vector in terms of the Hamming weights of vectors in least vector support set depending on whether these vectors share some nonzero components with the given vector. We find the cardinality of the set of vectors satisfying the propagation criterion for such functions.
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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