On monotonicity testing and boolean isoperimetric-type theorems

Subhash Khot, Dor Minzer, Muli Safra

Research output: Contribution to journalArticle

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/ε2) 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 languageEnglish (US)
Pages (from-to)2238-2276
Number of pages39
JournalSIAM Journal on Computing
Volume47
Issue number6
DOIs
StatePublished - Jan 1 2018

Fingerprint

Isoperimetric
Monotonicity
Testing
Monotone Function
Theorem
Monotone
Query
Analogue

Keywords

  • Boolean functions
  • Boolean isoperimetry
  • Monotonicity testing
  • Property testing

ASJC Scopus subject areas

  • Computer Science(all)
  • Mathematics(all)

Cite this

On monotonicity testing and boolean isoperimetric-type theorems. / Khot, Subhash; Minzer, Dor; Safra, Muli.

In: SIAM Journal on Computing, Vol. 47, No. 6, 01.01.2018, p. 2238-2276.

Research output: Contribution to journalArticle

Khot, Subhash ; Minzer, Dor ; Safra, Muli. / On monotonicity testing and boolean isoperimetric-type theorems. In: SIAM Journal on Computing. 2018 ; Vol. 47, No. 6. pp. 2238-2276.
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