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DOI: 10.4230/LIPIcs.STACS.2009.1808

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

Authors: Kenya Ueno

Published in: LIPIcs, Volume 3, 26th International Symposium on Theoretical Aspects of Computer Science (2009)

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).

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Kenya Ueno. A Stronger LP Bound for Formula Size Lower Bounds via Clique Constraints. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 685-696, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)

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@InProceedings{ueno:LIPIcs.STACS.2009.1808,
  author =	{Ueno, Kenya},
  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 =	{Albers, Susanne and Marion, Jean-Yves},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2009.1808},
  URN =		{urn:nbn:de:0030-drops-18080},
  doi =		{10.4230/LIPIcs.STACS.2009.1808},
  annote =	{Keywords: Computational and structural complexity}
}

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

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