On Monotonicity Testing and Boolean Isoperimetric Type Theorems

Subhash Khot; Dor Minzer; Muli Safra

doi:10.1109/FOCS.2015.13

On Monotonicity Testing and Boolean Isoperimetric Type Theorems

Subhash Khot, Dor Minzer, Muli Safra

New York University

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

40 Scopus citations

Abstract

We show a directed and robust analogue of a boolean isoperimetric type theorem of Talagrand. As an application, we give a monotonicity testing algorithm that makes, up to polylog factors, (square root of n)/∈2 non-adaptive queries to a function f:0, 1n -> 0, 1, always accepts a monotone function and rejects a function that is ∈-far from being monotone with constant probability.

Original language	English
Title of host publication	Proceedings - 2015 IEEE 56th Annual Symposium on Foundations of Computer Science, FOCS 2015
Publisher	IEEE Computer Society
Pages	52-58
Number of pages	7
ISBN (Electronic)	9781467381918
DOIs	https://doi.org/10.1109/FOCS.2015.13
State	Published - 11 Dec 2015
Event	56th IEEE Annual Symposium on Foundations of Computer Science, FOCS 2015 - Berkeley, United States Duration: 17 Oct 2015 → 20 Oct 2015

Publication series

Name	Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
Volume	2015-December
ISSN (Print)	0272-5428

Conference

Conference	56th IEEE Annual Symposium on Foundations of Computer Science, FOCS 2015
Country/Territory	United States
City	Berkeley
Period	17/10/15 → 20/10/15

Keywords

Boolean functions
isoperimetry
monotone functions
property testing

Access to Document

10.1109/FOCS.2015.13

Cite this

Khot, S., Minzer, D., & Safra, M. (2015). On Monotonicity Testing and Boolean Isoperimetric Type Theorems. In Proceedings - 2015 IEEE 56th Annual Symposium on Foundations of Computer Science, FOCS 2015 (pp. 52-58). Article 7354387 (Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS; Vol. 2015-December). IEEE Computer Society. https://doi.org/10.1109/FOCS.2015.13

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abstract = "We show a directed and robust analogue of a boolean isoperimetric type theorem of Talagrand. As an application, we give a monotonicity testing algorithm that makes, up to polylog factors, (square root of n)/∈2 non-adaptive queries to a function f:0, 1n -> 0, 1, always accepts a monotone function and rejects a function that is ∈-far from being monotone with constant probability.",

keywords = "Boolean functions, isoperimetry, monotone functions, property testing",

author = "Subhash Khot and Dor Minzer and Muli Safra",

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Khot, S, Minzer, D & Safra, M 2015, On Monotonicity Testing and Boolean Isoperimetric Type Theorems. in Proceedings - 2015 IEEE 56th Annual Symposium on Foundations of Computer Science, FOCS 2015., 7354387, Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS, vol. 2015-December, IEEE Computer Society, pp. 52-58, 56th IEEE Annual Symposium on Foundations of Computer Science, FOCS 2015, Berkeley, United States, 17/10/15. https://doi.org/10.1109/FOCS.2015.13

On Monotonicity Testing and Boolean Isoperimetric Type Theorems. / Khot, Subhash; Minzer, Dor; Safra, Muli.
Proceedings - 2015 IEEE 56th Annual Symposium on Foundations of Computer Science, FOCS 2015. IEEE Computer Society, 2015. p. 52-58 7354387 (Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS; Vol. 2015-December).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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On Monotonicity Testing and Boolean Isoperimetric Type Theorems

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Keywords

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