Query complexity of Boolean functions on slices

The kth slice ([n]k) of the Boolean cube {0,1}n is the set of all n-bit strings with Hamming weight k. We study the deterministic query complexity of Boolean functions on slices of the Boolean cube. We show that there exists a function on the balanced slice ([n]n/2) requiring n−O(log⁡log⁡n) queries....

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Bibliographic Details
Published in:Discrete mathematics Vol. 347; no. 6; p. 113954
Main Author: Byramji, Farzan
Format: Journal Article
Language:English
Published: Elsevier B.V 01.06.2024
Subjects:
Boolean cube
Query complexity
Slice
Slice
Query complexity
Boolean cube
ISSN:0012-365X, 1872-681X
Online Access:Get full text
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Summary:The kth slice ([n]k) of the Boolean cube {0,1}n is the set of all n-bit strings with Hamming weight k. We study the deterministic query complexity of Boolean functions on slices of the Boolean cube. We show that there exists a function on the balanced slice ([n]n/2) requiring n−O(log⁡log⁡n) queries. We observe that there is an explicit function on the balanced slice requiring n−O(log⁡n) queries based on independent sets in Johnson graphs. We also consider the maximum query complexity on constant-weight slices and how it relates to Ramsey theorems.
ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2024.113954