CMPSCI 741: Complexity Theory
David Mix Barrington
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
I generally answer my email fairly
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