CS 880 - Pseudorandomness and Derandomization Spring 2013

Course Description

Pseudorandomness is the study of distributions that can be generated using little randomness but nevertheless look like a truly random distribution to a computationally limited observer. The theory has significance for a number of areas in computer science and mathematics, including computational complexity, algorithms, cryptography, combinatorics, communications, and additive number theory.

Pseudorandom distributions form the canonical tool in derandomization, the construction of efficient deterministic simulations of randomized processes. For decision processes, derandomization is conjectured to be possible at no more than a polynomial cost in running time and a constant-factor cost in memory space.

We start by introducing the notion of a pseudorandom distribution, and focus on constructions that aim to resolve the conjecture in the general setting as well as in more restricted models of computation. Time permitting and depending on the interests of the audience, we study pseudorandom distributions in other areas.

Prerequisites

Familiarity with basic complexity theory, probability theory, and linear algebra.

Lectures

MW 2:30-3:45pm in 1207 CS&S.

Text

There is no required text. Lecture notes will be made available from the course web page.

Course Work

• Scribes
  Write lecture notes for about three lectures. Someone who missed the class should be able to learn the material from the notes. You need to type your notes in LaTeX using the guidelines provided.

• Homework
  There will be 2 to 3 assignments.