@inproceedings{f0757d5a408c42b5b63e7606aaacd256,

title = "The list-decoding size of Fourier-sparse Boolean functions",

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).",

keywords = "Fourier-sparse functions, Learning theory, List-decoding, Property testing",

author = "Ishay Haviv and Oded Regev",

year = "2015",

month = jun,

day = "1",

doi = "10.4230/LIPIcs.CCC.2015.58",

language = "English (US)",

series = "Leibniz International Proceedings in Informatics, LIPIcs",

publisher = "Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing",

pages = "58--71",

editor = "David Zuckerman",

booktitle = "30th Conference on Computational Complexity, CCC 2015",

note = "30th Conference on Computational Complexity, CCC 2015 ; Conference date: 17-06-2015 Through 19-06-2015",

}