On properties of multiaffine predicates on a finite set

IF 0.3 Q4 MATHEMATICS, APPLIED Discrete Mathematics and Applications Pub Date : 2023-08-01 DOI:10.1515/dma-2023-0023
S. Selezneva
{"title":"On properties of multiaffine predicates on a finite set","authors":"S. Selezneva","doi":"10.1515/dma-2023-0023","DOIUrl":null,"url":null,"abstract":"Abstract We consider predicates on a finite set that are invariant with respect to an affine operation fG, where G is some Abelian group. Such predicates are said to be multiaffine for the group G. Special attention is paid to predicates that are affine for a group Gq of addition modulo q=ps, where p is a prime number and s=1. We establish the predicate multiaffinity criterion for a group Gq. Then we introduce disjunctive normal forms (DNF) for predicates on a finite set and obtain properties of DNFs of predicates that are multiaffine for a group Gq. Finally we show how these properties can be used to design a polynomial algorithm that decides satisfiability of a system of predicates which are multiaffine for a group Gq, if predicates are specified by DNF.","PeriodicalId":11287,"journal":{"name":"Discrete Mathematics and Applications","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2023-08-01","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-2023-0023","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 consider predicates on a finite set that are invariant with respect to an affine operation fG, where G is some Abelian group. Such predicates are said to be multiaffine for the group G. Special attention is paid to predicates that are affine for a group Gq of addition modulo q=ps, where p is a prime number and s=1. We establish the predicate multiaffinity criterion for a group Gq. Then we introduce disjunctive normal forms (DNF) for predicates on a finite set and obtain properties of DNFs of predicates that are multiaffine for a group Gq. Finally we show how these properties can be used to design a polynomial algorithm that decides satisfiability of a system of predicates which are multiaffine for a group Gq, if predicates are specified by DNF.
查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
关于有限集上多仿射谓词的性质
摘要考虑有限集合上关于仿射操作fG的不变量谓词,其中G是某个阿贝尔群。这样的谓词被称为群g的多仿射谓词。特别注意的是对加模q=ps的群Gq的仿射谓词,其中p是素数且s=1。我们建立了群Gq的谓词多亲和准则。然后引入有限集合上谓词的析取范式(DNF),得到了群Gq上多仿射谓词的析取范式的性质。最后,我们展示了如何使用这些属性来设计一个多项式算法,该算法决定了一个多仿射的谓词系统对于一个群Gq的可满足性,如果谓词是由DNF指定的。
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 去求助
来源期刊
CiteScore
0.60
自引率
20.00%
发文量
29
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.
期刊最新文献
Asymptotically sharp estimates for the area of multiplexers in the cellular circuit model Propagation criterion for monotone Boolean functions with least vector support set of 1 or 2 elements On the complexity of implementation of a system of three monomials of two variables by composition circuits Inverse homomorphisms of finite groups On the approximation of high-order binary Markov chains by parsimonious models
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1