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.ICALP.2020.9
URN: urn:nbn:de:0030-drops-124163
URL: https://drops.dagstuhl.de/opus/volltexte/2020/12416/
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Bassilakis, Andrew ; Drucker, Andrew ; GΓΆΓΆs, Mika ; Hu, Lunjia ; Ma, Weiyun ; Tan, Li-Yang

The Power of Many Samples in Query Complexity

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LIPIcs-ICALP-2020-9.pdf (0.6 MB)

Abstract

The randomized query complexity 𝖱(f) of a boolean function f: {0,1}ⁿ β†’ {0,1} is famously characterized (via Yao’s minimax) by the least number of queries needed to distinguish a distribution π’Ÿβ‚€ over 0-inputs from a distribution π’Ÿβ‚ over 1-inputs, maximized over all pairs (π’Ÿβ‚€,π’Ÿβ‚). We ask: Does this task become easier if we allow query access to infinitely many samples from either π’Ÿβ‚€ or π’Ÿβ‚? We show the answer is no: There exists a hard pair (π’Ÿβ‚€,π’Ÿβ‚) such that distinguishing π’Ÿβ‚€^∞ from π’Ÿβ‚^∞ requires Θ(𝖱(f)) many queries. As an application, we show that for any composed function f∘g we have 𝖱(f∘g) β‰₯ Ξ©(fbs(f)𝖱(g)) where fbs denotes fractional block sensitivity.

BibTeX - Entry

@InProceedings{bassilakis_et_al:LIPIcs:2020:12416,
  author =	{Andrew Bassilakis and Andrew Drucker and Mika G{\"o}{\"o}s and Lunjia Hu and Weiyun Ma and Li-Yang Tan},
  title =	{{The Power of Many Samples in Query Complexity}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{9:1--9:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-138-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{168},
  editor =	{Artur Czumaj and Anuj Dawar and Emanuela Merelli},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/12416},
  URN =		{urn:nbn:de:0030-drops-124163},
  doi =		{10.4230/LIPIcs.ICALP.2020.9},
  annote =	{Keywords: Query complexity, Composition theorems}
}

Keywords: Query complexity, Composition theorems
Collection: 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)
Issue Date: 2020
Date of publication: 29.06.2020

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