COMPSCI 596C: Group Independent Study in Complexity Theory
David Mix Barrington
Spring, 2025
This is the home page for COMPSCI 596C.
COMPSCI 596C is a group independent study course in computational
complexity theory.
Instructor Contact Info:
David Mix Barrington, 210 CMPSCI
building, 545-4329, zoom 459 532 6175, office hours Spring 2025 TBA.
I generally answer my email fairly
reliably.
Until the last few years, CICS has offered COMPSCI 601, a
course in complexity theory following on the material in
COMPSCI 501. After starting this group independent study,
I learned that it will be offered by Hung Le in Fall
2025!
The goal of this course is to provide an opportunity for students who have
done COMPSCI 501 to learn some of this material, using the
Arora-Barak textbook. It is a group independent study
course, with participants rotating to present chapters of the
text. There will be no exams, but we would work through some
of the exercises in the book. Quinn Mayo, the undergraduate
doing an honors thesis with me this year, has learned large
fractions of this material and will be a lead participant.
This would _not_ replace COMPSCI 601 for any graduate requirements --
in factit will not meet any specific undergraduate
requirements, other than three graduation credits.
The course will meet for one lecture meeting a week, Fridays
4:00-5:00
p.m., in room 140 of the Computer Science building.
The expected background is a prior course in computability and
complexity, like our own COMPSCI 501. Anyone may attend the group
meetings,
and students registered in the course are expected to present material.
The required textbook is the Computational Complexity: A Modern
Approach by Sanjeev Arora and Boaz Barak.
Each student will prepare some material from the textbook, to be
decided during the term.
That presentation, and some problem sets during the term, will be the basis
for grading the course.
Announcements (28 March 2025):
- (30 Jan) I am just putting up the preliminary web page,
and we will meet tomorrow. There are now six students registered,
and
I can get more students enrolled if they like. In the first meeting
we
will begin scheduling lectures -- Quinn Mayo will present Chapter 1
of AB on 7 February.
- (1 Feb) We had our first meeting. The tentative plan is to
cover the first six chapters of AB in the next six Fridays. Quinn
will
present Chapter 1 on 7 February and Justin Steinman will present
Chapter
2 on 14 February.
- (7 Feb) Quinn presented on Chapter 1. The problem is 1.15, on
binary versus unary representation of numbers. Exercise: 1.15
- (14 Feb) Justin presented on Chapter 2. The problem is 2.29, that
languages in NP intersect coNP are closed under XOR. Exercise: 2.29.
- (21 Feb) Cullen presented on Chapter 3. This is a ton of material,
and he understandibly chose highlights of the major results. For the
assignment, I'll take either 3.4 on complexity classes being "superior"
to others, or either 3.8 or 3.9 on P vs. NP for different kinds of
random oracles. Either of these would probably require referring to
other sources. Exercise: 3.4 or 3.8 or 3.9
The current plan is for Minh and Aaron, in either order, to present
28 February on Chapter 4 (space complexity) and 7 March on Chapter 5
(PH and alternations). I'll do Chapter 6 (circuits) on 14 March.
- (28 Feb) Aaron presented on Chapter 4. Exercise: 4.8 and
4.10.
- (7 March) Minh presented on Chapter 5. Exercise: 5.9.
- (14 March) I presented on Chapter 6. Exercises 6.8 and 6.10.
- (10 March) Coming attractions:
- 14 March: Dave on Chapter 6
- 28 March: Justin on Chapter 7
- 4 April: Aaron on Chapter 8
- 11 April: Minh or Cullen on Chapter 10
- 18 April: NO CLASS (Monday schedule)
- 25 April: Minh or Cullen on Chapter 10
- 2 May: Quinn on Chapter 14
- 9 May: Dave, maybe on Barrington's Theorem
- (23 March) Updating with the welcome news that Hung Le is
going to offer COMPSCI 601 in Fall 2025. I don't believe
there are any definite decisions about how often it will be
offered going forward (at one point it was offered every two years,
for example).
- (28 March) Justin presented on Chapter 7, assignment is 7.9
and 7.10. (Justin didn't get to probabilistic space classes,
and these two problems concern them.)
Last modified 28 March 2025