Junta threshold for low degree Boolean functions on the slice

Yuval Filmus

doi:https://doi.org/10.37236/11115

Junta threshold for low degree Boolean functions on the slice

Yuval Filmus

Computer Science

Technion - Israel Institute of Technology

Research output: Contribution to journal › Article › peer-review

Abstract

We show that a Boolean degree d function on the slice (Formula presented) is a junta if k ≥ 2d, and that this bound is sharp. We prove a similar result for A-valued degree d functions for arbitrary finite A, and for functions on an infinite analog of the slice.

Original language	English
Article number	P1.55
Pages (from-to)	1-55
Number of pages	55
Journal	Electronic Journal of Combinatorics
Volume	30
Issue number	1
DOIs	https://doi.org/10.37236/11115
State	Published - 2023

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Geometry and Topology
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics
Applied Mathematics

Access to Document

https://doi.org/10.37236/11115

Cite this

@article{5137db570ed74344b6c9ab688111d9d1,

title = "Junta threshold for low degree Boolean functions on the slice",

abstract = "We show that a Boolean degree d function on the slice (Formula presented) is a junta if k ≥ 2d, and that this bound is sharp. We prove a similar result for A-valued degree d functions for arbitrary finite A, and for functions on an infinite analog of the slice.",

author = "Yuval Filmus",

note = "Publisher Copyright: {\textcopyright} The author.",

year = "2023",

doi = "https://doi.org/10.37236/11115",

language = "الإنجليزيّة",

volume = "30",

pages = "1--55",

journal = "Electronic Journal of Combinatorics",

issn = "1077-8926",

publisher = "Electronic Journal of Combinatorics",

number = "1",

}

TY - JOUR

T1 - Junta threshold for low degree Boolean functions on the slice

AU - Filmus, Yuval

N1 - Publisher Copyright: © The author.

PY - 2023

Y1 - 2023

N2 - We show that a Boolean degree d function on the slice (Formula presented) is a junta if k ≥ 2d, and that this bound is sharp. We prove a similar result for A-valued degree d functions for arbitrary finite A, and for functions on an infinite analog of the slice.

AB - We show that a Boolean degree d function on the slice (Formula presented) is a junta if k ≥ 2d, and that this bound is sharp. We prove a similar result for A-valued degree d functions for arbitrary finite A, and for functions on an infinite analog of the slice.

UR - http://www.scopus.com/inward/record.url?scp=85150663802&partnerID=8YFLogxK

U2 - https://doi.org/10.37236/11115

DO - https://doi.org/10.37236/11115

M3 - مقالة

SN - 1077-8926

VL - 30

SP - 1

EP - 55

JO - Electronic Journal of Combinatorics

JF - Electronic Journal of Combinatorics

IS - 1

M1 - P1.55

ER -

Junta threshold for low degree Boolean functions on the slice

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this