EECS 395/495-0-22: Kolmogorov Complexity
Fall 2008
Lecturer:
Lance Fortnow
Lectures: MWF 10:00-10:50 in Annenberg 101
Description:
This course will study the Kolmogorov complexity of finite strings
which measures the information content (or randomness) of a string by
the size of the smallest program that generates it. This simple idea
has a surprisingly deep theory with many exciting applications to
logic and computer science. We cover the basic relationships
of Kolmogorov complexity, applications with an emphasis in connections
with computational complexity. Topics include: Basic Properties of the
Kolmogorov function, Symmetry of Information, The Incompressibility
Method, Resource-Bounded complexity.
This course is designed for graduate students or advanced
undergraduates. We will assume familiarity with mathematical proofs
but no previous knowledge of Turing machines or computational
complexity.
Textbook: An
Introduction to Kolmogorov Complexity and Its Applications
by Ming Li and Paul Vitanyi.
Assignments
- Assignment 1, due Wednesday, October 8.
- Assignment 2, due Wednesday, October 15.
- Assignment 3, due Wednesday, October 29.
- Assignment 4, due Friday, November 7.
- Assignment 5, due Friday, November 14.
- Assignment 6, due Wednesday, November 26..
Handouts
You may need to be inside Northwestern or use
VPN to download the papers.
- L. Fortnow and
S. Laplante.
Circuit lower bounds a
la Kolmogorov.
Information and Compuation, 123(1):121-126, 1995.
- Lecture
Notes on Entropy by David McAllester.
- Inequalities
for Shannon Entropy and Kolmogorov Complexity by Daniel Hammer,
Andrei Romashchenko, Alexander Shen and Nikolai Vereshchagin.
- Resource-Bounded
Kolmogorov Complexity Revisited by Buhrman, Fortnow and
Laplante. Has results on sizes of sets and applications of extactors
for Kolmogorov complexity.
- Extractors:
Optimal up to Constant Factors, Lu, Reingold, Vadhan and Wigderson,
- Extracting
Randomness Using Few Independent Sources, Barak, Impagliazzo and
Wigderson
- Simulating
independence: new constructions of condensers, ramsey graphs,
dispersers, and extractors, Barak, Kindler, Shaltiel, Sudakov
and Wigderson
- Kolmogorov's
Structure Function and Model Selection, Vereshchagin and Vitanyi.