On monotonicity testing and boolean isoperimetric-type theorems

Subhash Khot; Dor Minzer; Muli Safra

doi:10.1137/16M1065872

On monotonicity testing and boolean isoperimetric-type theorems

Subhash Khot
, Dor Minzer
, Muli Safra

Tel Aviv University

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

Abstract

We show a directed and robust analogue of a boolean isoperimetric-type theorem of Talagrand [Geom. Funct. Anal., 3 (1993), pp. 295-314]. As an application, we give a monotonicity testing algorithm that makes Õ(√n/ε ² ) nonadaptive queries to a function f : {0, 1} ⁿ 7→ {0, 1}, always accepts a monotone function, and rejects a function that is ε-far from being monotone with constant probability.

Original language	English
Pages (from-to)	2238-2276
Number of pages	39
Journal	SIAM Journal on Computing
Volume	47
Issue number	6
DOIs	https://doi.org/10.1137/16M1065872
State	Published - 2018

Keywords

Boolean functions
Boolean isoperimetry
Monotonicity testing
Property testing

ASJC Scopus subject areas

General Computer Science
General Mathematics

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10.1137/16M1065872

Cite this

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title = "On monotonicity testing and boolean isoperimetric-type theorems",

abstract = " We show a directed and robust analogue of a boolean isoperimetric-type theorem of Talagrand [Geom. Funct. Anal., 3 (1993), pp. 295-314]. As an application, we give a monotonicity testing algorithm that makes {\~O}(√n/ε 2 ) nonadaptive queries to a function f : \{0, 1\} n 7→ \{0, 1\}, always accepts a monotone function, and rejects a function that is ε-far from being monotone with constant probability.",

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AB - We show a directed and robust analogue of a boolean isoperimetric-type theorem of Talagrand [Geom. Funct. Anal., 3 (1993), pp. 295-314]. As an application, we give a monotonicity testing algorithm that makes Õ(√n/ε 2 ) nonadaptive queries to a function f : {0, 1} n 7→ {0, 1}, always accepts a monotone function, and rejects a function that is ε-far from being monotone with constant probability.

KW - Boolean functions

KW - Boolean isoperimetry

KW - Monotonicity testing

KW - Property testing

UR - https://www.scopus.com/pages/publications/85060043685

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DO - 10.1137/16M1065872

M3 - مقالة

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JO - SIAM Journal on Computing

JF - SIAM Journal on Computing

IS - 6

ER -

On monotonicity testing and boolean isoperimetric-type theorems

Abstract

Keywords

ASJC Scopus subject areas

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