CS 225: Pseudorandomness
Spring 2004


Description | Topics | Prerequisites | Grading | Readings | Related Courses

Course meetings:  Tue-Thu 1-2:30, Pierce Hall 209 (29 Oxford Street)

Lecturer: Salil Vadhan
Office: Maxwell-Dworkin 337
Shopping period office hours: Thu 2/5 2:30-3:30 PM, Fri 2/6 2-5 PM (will be away Mon 2/9-Wed 2/11)
Tentative office hours starting 2/10: Tue 4-5, Thu 10-11, or by appointment

Teaching Fellow: Minh Nguyen
Office: Maxwell-Dworkin 138
Tentative office hours: Fri  4:30-6:30

E-mail address for questions: cs225@eecs.harvard.edu
E-mail address for submitting homeworks: cs225-hw@eecs.harvard.edu
Course website: http://www.courses.fas.harvard.edu/~cs225/

Course Description

Over the past few decades, randomization has become one of the most pervasive paradigms in computer science.  Its widespread use includes: So randomness appears to be extremely useful in these settings, but we still do not know to what extent it is really necessary.  Thus, in this course we will ask:

Main Question: Can we reduce or even eliminate the need for randomness in the above settings?

Why do we want to do this?    First, essentially all of the applications of randomness assume we have a source of perfect randomness ­ one that gives "coin tosses" that are completely unbiased and independent of each other.  It is unclear whether physical sources of perfect randomness exist and are inexpensive to access.  Second, randomized constructions of objects such as error-correcting codes and expander graphs often do not provide us with efficient algorithms for using them; indeed, even writing down a description of a randomly selected object can be infeasible.  Finally, and most fundamentally, our understanding of computation would be incomplete without understanding the power that randomness provides.

In this course, we will address the Main Question via a powerful paradigm known as pseudorandomness.  This is the theory of efficiently generating objects that "look random", despite being constructed using little or no randomness.  Specifically, we will study several kinds of "pseudorandom" objects, such as:

Each of the above objects has been the center of a large and beautiful body of research, and until recently these corpora were largely distinct. An exciting recent development has been the realization that all four of these objects are almost the same when interpreted appropriately.  Their intimate connections will be a major focus of the course, tying together the variety of constructions and applications of these objects we will cover.

The course will reach the cutting-edge of current research in this area, covering some results from within the last year.  At the same time, the concepts we will cover are general and useful enough that hopefully anyone with an interest in the theory of computation or combinatorics could find the material appealing.

Some Possible Topics


This is an advanced graduate course, so I will be assuming that you have general "mathematical maturity" and a good undergraduate background in the theory of computation.  One concrete guideline is that you should have had a minimum of two other courses in the theory of computation, including at least one graduate course.  If you have particularly strong math background, then there can be a bit more flexibility with this.  But if you haven't had a prior graduate course in the theory of computation (numbered CS 22x at Harvard), you must come speak to me at office hours before registering for the class.

In terms of topics, I will be assuming familiarity with the following.  In all cases (especially complexity theory), the more background you have, the better.

Grading & Problem Sets

The requirements of the course: The biweekly problem sets will typically be due on Mondays by 5 PM.  Your problem set solutions must be typed and submitted electronically to cs225-hw@eecs.harvard.edu. You are allowed 12 late days for the semester, of which at most 7 can be used on any individual problem set. (1 late day = 24 hours exactly).

The problem sets will be challenging, so be sure to start them early.  You are encouraged to discuss the course material and the homework problems with each other in small groups (2-3 people).   Discussion of homework problems may include brainstorming and verbally walking through possible solutions, but should not include one person telling the others how to solve the problem.  In addition, each person must write up their solutions independently, and these write-ups should not be checked against each other or passed around.


There is no required text for the course.  Indeed, much of the material we will be covering is not written in any textbook.  However, you may find the following references useful.  Most of them should be in the libraries, on reserve.

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