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

共 50 条

[1] Exact hyperplane covers for subsets of the hypercube
Aaronson, James
Groenland, Carla
Grzesik, Andrzej
Johnston, Tom
Kielak, Bartlomiej
DISCRETE MATHEMATICS, 2021, 344 (09)
[2] EXACT LOWER BOUNDS ON THE EXPONENTIAL MOMENTS OF TRUNCATED RANDOM VARIABLES
Pinelis, Iosif
JOURNAL OF APPLIED PROBABILITY, 2011, 48 (02) : 547 - 560
[3] Explicit rank bounds for cyclic covers
DeBlois, Jason
ALGEBRAIC AND GEOMETRIC TOPOLOGY, 2016, 16 (03): : 1343 - 1371
[4] Lower Bounds for Transversal Covers
Stevens B.
Moura L.
Mendelsohn E.
Designs, Codes and Cryptography, 1998, 15 (3) : 279 - 299
[5] EXACT BOUNDS FOR EXPONENTIAL MOMENTS
PINELIS, IF
UTEV, SA
THEORY OF PROBABILITY AND ITS APPLICATIONS, 1987, 31 (01) : 161 - 162
[6] Explicit bounds of complex exponential frames
Zhong, Hualiang
Boivin, Andre
Peters, Terry M.
JOURNAL OF INEQUALITIES AND APPLICATIONS, 2006, 2006 (1)
[7] Explicit bounds of complex exponential frames
Hualiang Zhong
André Boivin
Terry M. Peters
Journal of Inequalities and Applications, 2006
[8] On lower bounds of exponential frames
Lindner, AM
JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 1999, 5 (2-3) : 185 - 192
[9] Lower bounds of exponential sums
Michel, P
DUKE MATHEMATICAL JOURNAL, 1998, 95 (02) : 227 - 240
[10] Exponential Lower Bounds via Exponential Sums
Chennai Mathematical Institute, India
不详
不详
Leibniz Int. Proc. Informatics, LIPIcs,

← 1 2 3 4 5 →