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.ITCS.2017.28
URN: urn:nbn:de:0030-drops-81869
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/8186/
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Ben-David, Shalev ; Hatami, Pooya ; Tal, Avishay

Low-Sensitivity Functions from Unambiguous Certificates

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LIPIcs-ITCS-2017-28.pdf (0.7 MB)

Abstract

We provide new query complexity separations against sensitivity for total Boolean functions: a power 3 separation between deterministic (and even randomized or quantum) query complexity and sensitivity, and a power 2.22 separation between certificate complexity and sensitivity. We get these separations by using a new connection between sensitivity and a seemingly unrelated measure called one-sided unambiguous certificate complexity. We also show that one-sided unambiguous certificate complexity is lower-bounded by fractional block sensitivity, which means we cannot use these techniques to get a super-quadratic separation between block sensitivity and sensitivity.

Along the way, we give a power 1.22 separation between certificate complexity and one-sided unambiguous certificate complexity, improving the power 1.128 separation due to Goos [FOCS 2015]. As a consequence, we obtain an improved lower-bound on the co-nondeterministic communication complexity of the Clique vs. Independent Set problem.

BibTeX - Entry

@InProceedings{bendavid_et_al:LIPIcs:2017:8186,
  author =	{Shalev Ben-David and Pooya Hatami and Avishay Tal},
  title =	{{Low-Sensitivity Functions from Unambiguous Certificates}},
  booktitle =	{8th Innovations in Theoretical Computer Science Conference (ITCS 2017)},
  pages =	{28:1--28:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-029-3},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{67},
  editor =	{Christos H. Papadimitriou},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/8186},
  URN =		{urn:nbn:de:0030-drops-81869},
  doi =		{10.4230/LIPIcs.ITCS.2017.28},
  annote =	{Keywords: Boolean functions, decision tree complexity, query complexity, sensitivity conjecture}
}

Keywords: Boolean functions, decision tree complexity, query complexity, sensitivity conjecture
Collection: 8th Innovations in Theoretical Computer Science Conference (ITCS 2017)
Issue Date: 2017
Date of publication: 28.11.2017

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