# Mittagsseminar (in cooperation with M. Ghaffari, A. Steger and B. Sudakov)

__Mittagsseminar Talk Information__ | |

**Date and Time**: Tuesday, February 24, 2009, 12:15 pm

**Duration**: This information is not available in the database

**Location**: CAB G51

**Speaker**: Kenya Ueno (The Univ. of Tokyo)

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

A formula is a binary tree with leaves labeled by literals and internal nodes
labeled by AND and OR. Formula size is defined as the number of leaves.
Proving formula size lower bounds is a fundamental problem in complexity theory.
Karchmer, Kushilevitz and Nisan [SIAM J.DM95] formulate the formula
size problem as an integer programming problem and devise a technique called the LP
bound.

It shows a lower bound by giving a feasible solution for the dual problem of the LP-relaxation.
At the same time, they also showed that it cannot prove a lower bound
larger than 4n^2. Recently, Laplante, Lee and Szegedy [CCC05] and Lee [STACS07] have
shown that the LP bound subsumes several known techniques proving formula size
lower bounds.

In this study, we devise a stronger version of the LP bound by utilizing
the theory of stable set polytope, especially clique constraints.
It tightens the integrality gap which causes the limit of the original
technique. To show the relative strength, we apply it to some families of Boolean
functions.

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