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....

Celý popis

Uložené v:
Podrobná bibliografia
Vydané v:Discrete mathematics Ročník 347; číslo 6; s. 113954
Hlavný autor: Byramji, Farzan
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Elsevier B.V 01.06.2024
Predmet:
Boolean cube
Query complexity
Slice
Slice
Query complexity
Boolean cube
ISSN:0012-365X, 1872-681X
On-line prístup:Získať plný text
Tagy: Pridať tag
Žiadne tagy, Buďte prvý, kto otaguje tento záznam!
Popis
Shrnutí: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