License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CCC.2015.264
URN: urn:nbn:de:0030-drops-50663
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Servedio, Rocco A. ; Tan, Li-Yang ; Wright, John

Adaptivity Helps for Testing Juntas

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We give a new lower bound on the query complexity of any non-adaptive algorithm for testing whether an unknown Boolean function is a k-junta versus epsilon-far from every k-junta. Our lower bound is that any non-adaptive algorithm must make Omega(( k * log*(k)) / ( epsilon^c * log(log(k)/epsilon^c))) queries for this testing problem, where c is any absolute constant <1. For suitable values of epsilon this is asymptotically larger than the O(k * log(k) + k/epsilon) query complexity of the best known adaptive algorithm [Blais,STOC'09] for testing juntas, and thus the new lower bound shows that adaptive algorithms are more powerful than non-adaptive algorithms for the junta testing problem.

BibTeX - Entry

  author =	{Rocco A. Servedio and Li-Yang Tan and John Wright},
  title =	{{Adaptivity Helps for Testing Juntas}},
  booktitle =	{30th Conference on Computational Complexity (CCC 2015)},
  pages =	{264--279},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-81-1},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{33},
  editor =	{David Zuckerman},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-50663},
  doi =		{10.4230/LIPIcs.CCC.2015.264},
  annote =	{Keywords: Property testing, juntas, adaptivity}

Keywords: Property testing, juntas, adaptivity
Collection: 30th Conference on Computational Complexity (CCC 2015)
Issue Date: 2015
Date of publication: 06.06.2015

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