Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar Talk Information |

**Date and Time**: Thursday, February 24, 2011, 12:15 pm

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

**Location**: CAB G51

**Speaker**: Dominik Scheder

For a language L over {0,1}^*, its count function c(n) is the number of words in L of size at most n. For example, if L is the language of palindromes, then c(n) is approximately 2^(n/2). A language is sparse if its count function c(n) is bounded by some polynomial p(n).

There are sparse languages that are undecidable, and there are decidable sparse languages with arbitrarily high time complexity. However, Mahaney's Theorem states that if there is an NP-complete sparse language L, then P=NP. The proof is constructive, i.e., gives an algorithm quickly solving SAT. The challenge is that the algorithm cannot make any membership queries to L, since, as said, L might even be undecidable.

Mahaney's Theorem is a classic, and may be older than many people in the audience (it dates back to 1982). Its proof is fun and nicely highlights the weird ways in which you often have to think in complexity theory.

References:

Sparse complete sets for NP: Solution of a conjecture of Berman and Hartmanis by Steve Mahaney, JCSS 1982.

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

Previous talks by year: 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