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When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2009.1808
URN: urn:nbn:de:0030-drops-18080
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2009/1808/
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Ueno, Kenya

A Stronger LP Bound for Formula Size Lower Bounds via Clique Constraints

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Abstract

We introduce a new technique proving formula size lower bounds based on the linear programming bound originally introduced by Karchmer, Kushilevitz and Nisan (1995) and the theory of stable set polytope. We apply it to majority functions and prove their formula size lower bounds improved from the classical result of Khrapchenko (1971). Moreover, we introduce a notion of unbalanced recursive ternary majority functions motivated by a decomposition theory of monotone self-dual functions and give integrally matching upper and lower bounds of their formula size. We also show monotone formula size lower bounds of balanced recursive ternary majority functions improved from the quantum adversary bound of Laplante, Lee and Szegedy (2006).

BibTeX - Entry

@InProceedings{ueno:LIPIcs:2009:1808,
  author =	{Kenya Ueno},
  title =	{{A Stronger LP Bound for Formula Size Lower Bounds via Clique Constraints}},
  booktitle =	{26th International Symposium on Theoretical Aspects of Computer Science},
  pages =	{685--696},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-09-5},
  ISSN =	{1868-8969},
  year =	{2009},
  volume =	{3},
  editor =	{Susanne Albers and Jean-Yves Marion},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2009/1808},
  URN =		{urn:nbn:de:0030-drops-18080},
  doi =		{10.4230/LIPIcs.STACS.2009.1808},
  annote =	{Keywords: Computational and structural complexity}
}

Keywords: Computational and structural complexity
Collection: 26th International Symposium on Theoretical Aspects of Computer Science
Issue Date: 2009
Date of publication: 19.02.2009

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