Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

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

Duration: This information is not available in the database

Location: OAT S15/S16/S17

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.

Upcoming talks     |     All previous talks     |     Talks by speaker     |     Upcoming talks in iCal format (beta version!)

Previous talks by year:   2024  2023  2022  2021  2020  2019  2018  2017  2016  2015  2014  2013  2012  2011  2010  2009  2008  2007  2006  2005  2004  2003  2002  2001  2000  1999  1998  1997  1996  

Information for students and suggested topics for student talks

Automatic MiSe System Software Version 1.4803M   |   admin login