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.FSTTCS.2017.10
URN: urn:nbn:de:0030-drops-83967
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/8396/
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Anshu, Anurag ; Gavinsky, Dmitry ; Jain, Rahul ; Kundu, Srijita ; Lee, Troy ; Mukhopadhyay, Priyanka ; Santha, Miklos ; Sanyal, Swagato

A Composition Theorem for Randomized Query Complexity

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Abstract

Let the randomized query complexity of a relation for error probability epsilon be denoted by R_epsilon(). We prove that for any relation f contained in {0,1}^n times R and Boolean function g:{0,1}^m -> {0,1}, R_{1/3}(f o g^n) = Omega(R_{4/9}(f).R_{1/2-1/n^4}(g)), where f o g^n is the relation obtained by composing f and g. We also show using an XOR lemma that R_{1/3}(f o (g^{xor}_{O(log n)})^n) = Omega(log n . R_{4/9}(f) . R_{1/3}(g))$, where g^{xor}_{O(log n)} is the function obtained by composing the XOR function on O(log n) bits and g.

BibTeX - Entry

@InProceedings{anshu_et_al:LIPIcs:2018:8396,
  author =	{Anurag Anshu and Dmitry Gavinsky and Rahul Jain and Srijita Kundu and Troy Lee and Priyanka Mukhopadhyay and Miklos Santha and Swagato Sanyal},
  title =	{{A Composition Theorem for Randomized Query Complexity}},
  booktitle =	{37th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2017)},
  pages =	{10:1--10:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-055-2},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{93},
  editor =	{Satya Lokam and R. Ramanujam},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/8396},
  URN =		{urn:nbn:de:0030-drops-83967},
  doi =		{10.4230/LIPIcs.FSTTCS.2017.10},
  annote =	{Keywords: Query algorithms and complexity, Decision trees, Composition theorem, XOR lemma, Hardness amplification}
}

Keywords: Query algorithms and complexity, Decision trees, Composition theorem, XOR lemma, Hardness amplification
Collection: 37th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2017)
Issue Date: 2018
Date of publication: 12.02.2018

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