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.

• Course Requirements and Grading (not yet)
• Homework Assignment Directory (none so far)
• Questions and Answers on Homework (none so far)
• Syllabus (a work in progress)

Announcements (11 April 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.) (4 April) Aaron presented on Chapter 8. The assignment is 8.1. (11 April) Cullen presented on part of Chapter 10, up to and including Grover's algorithm. The assignment is 10.1.

Last modified 11 April 2025