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URN: urn:nbn:de:0030-drops-142922
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A Majority Lemma for Randomised Query Complexity

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Abstract

We show that computing the majority of n copies of a boolean function g has randomised query complexity R(Maj∘gⁿ) = Θ(n⋅R ̅_{1/n}(g)). In fact, we show that to obtain a similar result for any composed function f∘gⁿ, it suffices to prove a sufficiently strong form of the result only in the special case g = GapOr.

BibTeX - Entry

@InProceedings{goos_et_al:LIPIcs.CCC.2021.18,
  author =	{G\"{o}\"{o}s, Mika and Maystre, Gilbert},
  title =	{{A Majority Lemma for Randomised Query Complexity}},
  booktitle =	{36th Computational Complexity Conference (CCC 2021)},
  pages =	{18:1--18:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-193-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{200},
  editor =	{Kabanets, Valentine},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/14292},
  URN =		{urn:nbn:de:0030-drops-142922},
  doi =		{10.4230/LIPIcs.CCC.2021.18},
  annote =	{Keywords: Query Complexity, Composition, Majority}
}

Keywords: Query Complexity, Composition, Majority
Seminar: 36th Computational Complexity Conference (CCC 2021)
Issue date: 2021
Date of publication: 08.07.2021


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