Pseudorandomness
[draft survey/monograph]

 

Salil Vadhan


Abstract

This is a survey of pseudorandomness, the theory of efficiently generating objects that ``look random'' despite being constructed using little or no randomness. This theory has significance for a number of areas in computer science and mathematics, including computational complexity, algorithms, cryptography, combinatorics, communications, and additive number theory. Our treatment places particular emphasis on the intimate connections that have been discovered between a variety of fundamental "pseudorandom objects" that at first seem very different in nature: expander graphs, randomness extractors, list-decodable error-correcting codes, samplers, and pseudorandom generators.
The structure of the presentation is meant to be suitable for teaching in a graduate-level course, with exercises accompanying each chapter.


Draft version for Foundations and Trends in Theoretical Computer Science (now publishers)

Comments Welcome!

  • Full text as of August 2012 (220 pages) [pdf]
  • Frontmatter [pdf]
  • Chapter 1: Introduction [pdf]
  • Chapter 2: The Power of Randomness [pdf]
  • Chapter 3: Basic Derandomization Techniques [pdf]
  • Chapter 4: Expander Graphs [pdf]
  • Chapter 5: List-Decodable Codes [pdf]
  • Chapter 6: Randomness Extractors (missing references) [pdf]
  • Chapter 7: Pseudorandom Generators (missing references & exercises) [pdf]
  • Chapter 8: Conclusions [pdf]
  • References [pdf][bib]
  • April 2011 version [pdf]
  • August 2010 version [pdf]

See also



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