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.STACS.2018.8
URN: urn:nbn:de:0030-drops-84953
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/8495/
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Ambainis, Andris ; Kokainis, Martins ; Prusis, Krisjanis ; Vihrovs, Jevgenijs

All Classical Adversary Methods are Equivalent for Total Functions

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LIPIcs-STACS-2018-8.pdf (0.5 MB)

Abstract

We show that all known classical adversary lower bounds on randomized query complexity are equivalent for total functions, and are equal to the fractional block sensitivity fbs(f). That includes the Kolmogorov complexity bound of Laplante and Magniez and the earlier relational adversary bound of Aaronson. For partial functions, we show unbounded separations between fbs(f) and other adversary bounds, as well as between the relational and Kolmogorov complexity bounds.

We also show that, for partial functions, fractional block sensitivity cannot give lower bounds larger than sqrt(n * bs(f)), where n is the number of variables and bs(f) is the block sensitivity. Then we exhibit a partial function f that matches this upper bound, fbs(f) = Omega(sqrt(n * bs(f))).

BibTeX - Entry

@InProceedings{ambainis_et_al:LIPIcs:2018:8495,
  author =	{Andris Ambainis and Martins Kokainis and Krisjanis Prusis and Jevgenijs Vihrovs},
  title =	{{All Classical Adversary Methods are Equivalent for Total Functions}},
  booktitle =	{35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)},
  pages =	{8:1--8:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-062-0},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{96},
  editor =	{Rolf Niedermeier and Brigitte Vall{\'e}e},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/8495},
  URN =		{urn:nbn:de:0030-drops-84953},
  doi =		{10.4230/LIPIcs.STACS.2018.8},
  annote =	{Keywords: Randomized Query Complexity, Lower Bounds, Adversary Bounds, Fractional Block Sensitivity}
}

Keywords: Randomized Query Complexity, Lower Bounds, Adversary Bounds, Fractional Block Sensitivity
Collection: 35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)
Issue Date: 2018
Date of publication: 27.02.2018

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