A Stronger LP Bound for Formula Size Lower Bounds via Clique Constraints - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Conference Papers Year : 2009

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].
Fichier principal
Vignette du fichier
Ueno_new.pdf (217.45 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

inria-00360141 , version 1 (10-02-2009)

Identifiers

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

Cite

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⟩

Collections

STACS2009
87 View
200 Download

Altmetric

Share

Gmail Facebook X LinkedIn More