Explicit exponential lower bounds for exact hyperplane covers

被引：1

作者：

Diamond, Benjamin E. ^{[1
]}

Yehudayoff, Amir ^{[2
]}

机构：

[1] Coinbase, Appl Cryptog, Santa Monica, CA 90401 USA

[2] Technion IIT, Dept Math, Haifa, Israel

来源：

DISCRETE MATHEMATICS | 2022年 / 345卷 / 11期

基金：

美国国家科学基金会;

关键词：

Exact hyperplane covers; Communication complexity; Lower bounds; LITTLEWOOD; OFFORD;

D O I：

10.1016/j.disc.2022.113114

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We describe an explicit and simple subset of the discrete hypercube which cannot be exactly covered by fewer than exponentially many hyperplanes. The proof exploits a connection to communication complexity, and relies heavily on Razborov's lower bound for disjointness.(c) 2022 Elsevier B.V. All rights reserved.

引用

页数：7

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