Propagation criterion for monotone Boolean functions with least vector support set of 1 or 2 elements

IF 0.3 Q4 MATHEMATICS, APPLIED

Discrete Mathematics and Applications Pub Date : 2024-04-01 DOI:10.1515/dma-2024-0006

Gleb A. Isaev

引用次数: 0

Abstract

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.

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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

本文研究了单调布尔函数的传播准则，该函数的最小向量支持集由一个或两个向量组成。我们根据最小矢量支持集中矢量的汉明权重（取决于这些矢量是否与给定矢量共享一些非零分量），得到了矢量传播准则有效性的必要条件和充分条件。我们找到了满足此类函数传播准则的向量集合的万有引力。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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.