Proclaiming dictators and juntas or testing boolean formulae

Michal Parnas, Dana Ron, Alex Samorodnitsky

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

7 Scopus citations

Abstract

We consider the problem of determining whether a given function f: {0, 1}n → {0, 1} belongs to a certain class of Boolean functions F or whether it is far from the class. More precisely, given query access to the function f and given a distance parameter ϵ, we wou ld like to decide whether f∈F or whether it differs from every g ∈F on more than an ϵ -fraction of the domain elements. The classes of functions we consider are singleton (“dictatorship”) functions, monomials, and monotone DNF functions with a bounded number of terms. In all cases we provide algorithms whose query complexity is independent of n (the number of function variables), and polynomial in the other relevant parameters.

Original languageEnglish
Title of host publicationApproximation, Randomization, and Combinatorial Optimization
Subtitle of host publicationAlgorithms and Techniques - 4th International Workshop on Approximation, Algorithms for Combinatorial Optimization Problems, APPROX 2001 and 5th International Workshop on Randomization and Approximation Techniques in Computer Science, RANDOM 2001, Proceedings
EditorsMichel Goemans, Klaus Jansen, Jose D. P. Rolim, Luca Trevisan
Place of PublicationBerlin Heidelberg
PublisherSpringer Verlag
Pages273-285
Number of pages13
ISBN (Electronic)3540424709, 78-3-540-44666-8
ISBN (Print)978-3-540-42470-3
DOIs
StatePublished - 2001
Event4th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2001 and 5th International Workshop on Randomization and Approximation Techniques in Computer Science, RANDOM 2001 - Berkeley, United States
Duration: 18 Aug 200120 Aug 2001

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume2129
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference4th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2001 and 5th International Workshop on Randomization and Approximation Techniques in Computer Science, RANDOM 2001
Country/TerritoryUnited States
CityBerkeley
Period18/08/0120/08/01

Funding

FundersFunder number
Israel Science Foundation32/00-1
National Science FoundationCCR-9987845

    Keywords

    • Learning algorithms
    • boolean function
    • parity function
    • query complexity
    • testing algorithm

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