CMPSCI 741: Complexity Theory

David Mix Barrington

Fall, 2010

This is the home page for CMPSCI 741. CMPSCI 741 is an advanced graduate course in computational complexity theory, with a focus on circuit complexity and its connections to automata theory and logic. The exact subject matter treated will depend somewhat on the interests of the students.

Instructor Contact Info: David Mix Barrington, 210 CMPSCI building, 545-4329, office hours Monday 11-12 (but not 14 Sept), Thursday 2-3:30. I generally answer my email fairly reliably.

The course will meet for two lecture meetings a week, Monday and Wednesday 2:05-3:20, in room 142 of the Computer Science building. (This room is ridiculously large for such a small class and will probably be changed at some point.)

The expected background is a graduate course in the theory of computation, such as our own CMPSCI 601 which I taught last spring. This background can be obtained from a variety of textbooks, such as those by Arora-Barak, Papadimitriou, or Sipser.

The required textbook is Introduction to Circuit Complexity by Heribert Vollmer. We will cover most of the material in this book, and also read some research papers. Each student will prepare a presentation of some topic related to the course, in the last couple of weeks of the term. That presentation, and some problem sets during the term, will be the basis for grading the course.

Announcements (25 October 2010):

(25 Oct) I have updated the syllabus through this week.

(3 Oct) I have updated the syllabus for the next two weeks, though what we actually do may depend on how quickly things go and how much you remember from previous courses.

(19 Sept) I am putting up a draft syllabus of a sort today. This week we will deal with the remainder of Vollmer 1.4 (using Chinese remaindering to put iterated multiplication and other problems in P-uniform TC⁰) and maybe Vollmer 1.5 (asymptotic bounds on the size necessary to compute worst-case or random functions with circuits).

(9 Sept) In our first class we did most of those basic definitions and left you with a problem -- to show that the Circuit Value Problem (CVP), which is to input a circuit C and an input x and calculate C(x), is (a) in P, and (b) hard for P under log-space reductions. On Monday we will start into Vollmer's treatment of addition and iterated addition in his Chapter 1.

(6 Sept) I am just putting up the preliminary web page, as I would like to find out more about the student body of the course before fixing the syllabus in more detail. We will begin on Wednesday with a review of the basic definitions of circuit complexity from CMPSCI 601 or an equivalent course: size, depth, uniformity, polynomial size and polynomial time, and several examples of algorithms implemented by circuits.

Last modified 25 October 2010