关于包含所有多项式的部分k值逻辑中的闭类

IF 0.3 Q4 MATHEMATICS, APPLIED

Discrete Mathematics and Applications Pub Date : 2021-08-01 DOI:10.1515/dma-2021-0020

V. Alekseev

{"title":"关于包含所有多项式的部分k值逻辑中的闭类","authors":"V. Alekseev","doi":"10.1515/dma-2021-0020","DOIUrl":null,"url":null,"abstract":"Abstract Let Polk be the set of all functions of k-valued logic representable by a polynomial modulo k, and let Int (Polk) be the family of all closed classes (with respect to superposition) in the partial k-valued logic containing Polk and consisting only of functions extendable to some function from Polk. Previously the author showed that if k is the product of two different primes, then the family Int (Polk) consists of 7 closed classes. In this paper, it is proved that if k has at least 3 different prime divisors, then the family Int (Polk) contains an infinitely decreasing (with respect to inclusion) chain of different closed classes.","PeriodicalId":11287,"journal":{"name":"Discrete Mathematics and Applications","volume":"31 1","pages":"231 - 240"},"PeriodicalIF":0.3000,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"On closed classes in partial k-valued logic that contain all polynomials\",\"authors\":\"V. Alekseev\",\"doi\":\"10.1515/dma-2021-0020\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract Let Polk be the set of all functions of k-valued logic representable by a polynomial modulo k, and let Int (Polk) be the family of all closed classes (with respect to superposition) in the partial k-valued logic containing Polk and consisting only of functions extendable to some function from Polk. Previously the author showed that if k is the product of two different primes, then the family Int (Polk) consists of 7 closed classes. In this paper, it is proved that if k has at least 3 different prime divisors, then the family Int (Polk) contains an infinitely decreasing (with respect to inclusion) chain of different closed classes.\",\"PeriodicalId\":11287,\"journal\":{\"name\":\"Discrete Mathematics and Applications\",\"volume\":\"31 1\",\"pages\":\"231 - 240\"},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2021-08-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Discrete Mathematics and Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1515/dma-2021-0020\",\"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-2021-0020","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: 2

摘要

摘要设Polk是可由多项式模k表示的k值逻辑的所有函数的集合，并且设Int（Polk）是包含Polk并且仅由可从Polk扩展到某个函数的函数组成的部分k值逻辑中的所有闭类（关于叠加）的族。先前作者证明，如果k是两个不同素数的乘积，那么Int（Polk）族由7个闭类组成。本文证明了如果k至少有3个不同的素数，则族Int（Polk）包含一个不同闭类的无限递减（关于包含）链。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

On closed classes in partial k-valued logic that contain all polynomials

Abstract Let Polk be the set of all functions of k-valued logic representable by a polynomial modulo k, and let Int (Polk) be the family of all closed classes (with respect to superposition) in the partial k-valued logic containing Polk and consisting only of functions extendable to some function from Polk. Previously the author showed that if k is the product of two different primes, then the family Int (Polk) consists of 7 closed classes. In this paper, it is proved that if k has at least 3 different prime divisors, then the family Int (Polk) contains an infinitely decreasing (with respect to inclusion) chain of different closed classes.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

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.