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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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Submitted on : Tuesday, February 10, 2009 - 2:14:42 PM
Last modification on : Friday, February 13, 2009 - 9:56:37 AM
Long-term archiving on: : Tuesday, June 8, 2010 - 10:10:46 PM


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



Kenya Ueno. A Stronger LP Bound for Formula Size Lower Bounds via Clique Constraints. 26th International Symposium on Theoretical Aspects of Computer Science - STACS 2009, Feb 2009, Freiburg, Germany. pp.685-696. ⟨inria-00360141⟩



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