关于有限集上多仿射谓词的性质

IF 0.3 Q4 MATHEMATICS, APPLIED

Discrete Mathematics and Applications Pub Date : 2023-08-01 DOI:10.1515/dma-2023-0023

S. Selezneva

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引用次数: 0

摘要

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。

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On properties of multiaffine predicates on a finite set

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.

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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.