The list-decoding size of Fourier-sparse Boolean functions

Ishay Haviv, Oded Regev

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

A function defined on the Boolean hypercube is k-Fourier-sparse if it has at most k nonzero Fourier coefficients. For a function f: Fn2→ ℝ and parameters k and d, we prove a strong upper bound on the number of k-Fourier-sparse Boolean functions that disagree with f on at most d inputs. Our bound implies that the number of uniform and independent random samples needed for learning the class of k-Fourier-sparse Boolean functions on n variables exactly is at most O(n · k log k). As an application, we prove an upper bound on the query complexity of testing Booleanity of Fourier-sparse functions. Our bound is tight up to a logarithmic factor and quadratically improves on a result due to Gur and Tamuz (Chicago J. Theor. Comput. Sci., 2013).

Original languageEnglish (US)
Title of host publication30th Conference on Computational Complexity, CCC 2015
EditorsDavid Zuckerman
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Pages58-71
Number of pages14
ISBN (Electronic)9783939897811
DOIs
StatePublished - Jun 1 2015
Event30th Conference on Computational Complexity, CCC 2015 - Portland, United States
Duration: Jun 17 2015Jun 19 2015

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume33
ISSN (Print)1868-8969

Other

Other30th Conference on Computational Complexity, CCC 2015
CountryUnited States
CityPortland
Period6/17/156/19/15

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Keywords

  • Fourier-sparse functions
  • Learning theory
  • List-decoding
  • Property testing

ASJC Scopus subject areas

  • Software

Cite this

Haviv, I., & Regev, O. (2015). The list-decoding size of Fourier-sparse Boolean functions. In D. Zuckerman (Ed.), 30th Conference on Computational Complexity, CCC 2015 (pp. 58-71). (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 33). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.CCC.2015.58