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

Abstract : We introduce a new technique proving formula size lower bounds based on the linear programming bound originally introduced by Karchmer, Kushilevitz and Nisan [11] 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 [13]. 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 [15].
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Communication dans un congrès
Susanne Albers and Jean-Yves Marion. 26th International Symposium on Theoretical Aspects of Computer Science - STACS 2009, Feb 2009, Freiburg, Germany. IBFI Schloss Dagstuhl, pp.685-696, 2009, Proceedings of the 26th Annual Symposium on the Theoretical Aspects of Computer Science
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Soumis le : mardi 10 février 2009 - 14:14:42
Dernière modification le : vendredi 13 février 2009 - 09:56:37
Document(s) archivé(s) le : mardi 8 juin 2010 - 22:10:46

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  • HAL Id : inria-00360141, version 1
  • ARXIV : 0902.2146

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Kenya Ueno. A Stronger LP Bound for Formula Size Lower Bounds via Clique Constraints. Susanne Albers and Jean-Yves Marion. 26th International Symposium on Theoretical Aspects of Computer Science - STACS 2009, Feb 2009, Freiburg, Germany. IBFI Schloss Dagstuhl, pp.685-696, 2009, Proceedings of the 26th Annual Symposium on the Theoretical Aspects of Computer Science. 〈inria-00360141〉

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