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When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CCC.2017.26
URN: urn:nbn:de:0030-drops-75283
URL: http://drops.dagstuhl.de/opus/volltexte/2017/7528/
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Chen, Xi ; Servedio, Rocco A. ; Tan, Li-Yang ; Waingarten, Erik ; Xie, Jinyu

Settling the Query Complexity of Non-Adaptive Junta Testing

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LIPIcs-CCC-2017-26.pdf (0.7 MB)


Abstract

We prove that any non-adaptive algorithm that tests whether an unknown Boolean function f is a k-junta or epsilon-far from every k-junta must make ~Omega(k^{3/2}/ epsilon) many queries for a wide range of parameters k and epsilon. Our result dramatically improves previous lower bounds from [BGSMdW13,STW15], and is essentially optimal given Blais's non-adaptive junta tester from [Blais08], which makes ~O(k^{3/2})/epsilon queries. Combined with the adaptive tester of [Blais09] which makes O(k log k + k / epsilon) queries, our result shows that adaptivity enables polynomial savings in query complexity for junta testing.

BibTeX - Entry

@InProceedings{chen_et_al:LIPIcs:2017:7528,
  author =	{Xi Chen and Rocco A. Servedio and Li-Yang Tan and Erik Waingarten and Jinyu Xie},
  title =	{{Settling the Query Complexity of Non-Adaptive Junta Testing}},
  booktitle =	{32nd Computational Complexity Conference (CCC 2017)},
  pages =	{26:1--26:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-040-8},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{79},
  editor =	{Ryan O'Donnell},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/7528},
  URN =		{urn:nbn:de:0030-drops-75283},
  doi =		{10.4230/LIPIcs.CCC.2017.26},
  annote =	{Keywords: property testing, juntas, query complexity}
}

Keywords: property testing, juntas, query complexity
Seminar: 32nd Computational Complexity Conference (CCC 2017)
Issue Date: 2017
Date of publication: 21.07.2017


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