Mittagsseminar (in cooperation with J. Lengler, A. Steger, and D. Steurer)

Date and Time: Thursday, June 06, 2013, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Timon Hertli

Strong ETH Holds for Regular Resolution

The Exponential Time Hypothesis (ETH) conjectures that algorithms for k-SAT run in time at least 2^s_kn, for s_k>0. The Strong ETH furthermore states that s_k goes to 1 as k goes to infinity. That is, for large k, brute-force search is close to optimal.

I will present a very recent result by C. Beck and R. Impagliazzo [STOC 13] that gives Strong ETH lower bounds for a large class of SAT algorithms. They showed that k-CNF formulas exist for which regular resolution needs almost 2ⁿ steps. Such lower bounds were previously only known for the weaker tree-like resolution. They also give a (3/2)ⁿ lower bound for full resolution.

The construction is based on a random system of linear equations over a finite field GF(p). This system is converted into a k-CNF, where each variable in GF(p) corresponds to the sum of Θ(p) Boolean variables. Using expansion properties of the equations, the claimed lower bound is first shown for tree-like resolution and then for regular resolution.

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