{"title":"关于分离接触电路类中一些初等连接系统的实现","authors":"Elena G. Krasulina","doi":"10.1515/dma-2023-0003","DOIUrl":null,"url":null,"abstract":"Abstract We show that the system of elementary conjunctions Ωn,2k=K0,…,K2k−1 $ \\Omega_{n,2^k} = {K_0,\\ldots,K_{2^{k} -1}} $ such that each conjunction depends essentially on n variables and corresponds to some codeword of a linear (n, k)-code can be implemented by a separating contact circuit of complexity at most 2k+1 +4k(n − k) − 2. We also show that if a contact (1, 2k)-terminal network is separating and implements the system of elementary conjunctions Ωn,2k $ \\Omega_{n,2^k} $ , then the number of contacts in it is at least 2k+1 − 2.","PeriodicalId":11287,"journal":{"name":"Discrete Mathematics and Applications","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"On implementation of some systems of elementary conjunctions in the class of separating contact circuits\",\"authors\":\"Elena G. Krasulina\",\"doi\":\"10.1515/dma-2023-0003\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract We show that the system of elementary conjunctions Ωn,2k=K0,…,K2k−1 $ \\\\Omega_{n,2^k} = {K_0,\\\\ldots,K_{2^{k} -1}} $ such that each conjunction depends essentially on n variables and corresponds to some codeword of a linear (n, k)-code can be implemented by a separating contact circuit of complexity at most 2k+1 +4k(n − k) − 2. We also show that if a contact (1, 2k)-terminal network is separating and implements the system of elementary conjunctions Ωn,2k $ \\\\Omega_{n,2^k} $ , then the number of contacts in it is at least 2k+1 − 2.\",\"PeriodicalId\":11287,\"journal\":{\"name\":\"Discrete Mathematics and Applications\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2023-02-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Discrete Mathematics and Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1515/dma-2023-0003\",\"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-2023-0003","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
On implementation of some systems of elementary conjunctions in the class of separating contact circuits
Abstract We show that the system of elementary conjunctions Ωn,2k=K0,…,K2k−1 $ \Omega_{n,2^k} = {K_0,\ldots,K_{2^{k} -1}} $ such that each conjunction depends essentially on n variables and corresponds to some codeword of a linear (n, k)-code can be implemented by a separating contact circuit of complexity at most 2k+1 +4k(n − k) − 2. We also show that if a contact (1, 2k)-terminal network is separating and implements the system of elementary conjunctions Ωn,2k $ \Omega_{n,2^k} $ , then the number of contacts in it is at least 2k+1 − 2.
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.