Comp. Sci. 741 Computational Complexity Spring, 2003

Student Presentations:

May 9: Audrey Lee; George Bissias (Note: Friday not Wednesday class next week)

May 12: Kazu Hirata; Matt Yurkewych

May 14: Martin Allen; Ross Fairgrieve

Projects: The following are a few papers that might interest you as you are deciding what to do your projects on. Dave and I will add a few others over the next few weeks and suggestions and comments are welcome!

HW1, due Wed., 2/12: please do the following exercises from Descriptive Complexity: 1.5, 1.7, 1.8, 1.12, 1.13, and 1.23.

HW2, due Fri, 3/14: please do the following exercises from Descriptive Complexity: 1.31, 2.3, 2.8: [this is the famous space hierarchy theorem. I suggest that you read a proof and understand it well, and then write it up in your own words. You should still of course cite your sources], 2.16, 2.17, 3.4, 3.7.

Meeting Times: MW 10:35 - 11:50, CMPS 140. Note: This time may conflict with some faculty candidate talks. Please keep the same time slot open on Fridays, because when there is a faculty candidate talk on a Monday or Wednesday during class time, we will usually switch that class to Friday so as not to conflict with the candidate's talk. All graduate students are strongly encouraged to come to all faculty candidate talks!

Instructors: David Mix Barrington and Neil Immerman

CMPSCI 741: Office Hours, Fall 2002
Neil Immerman, CompSci Bldg 374, Tues, Wed: 2:30 -- 3:30, and by appointment.
David Mix Barrington, CMPSCI 210 Tues, 9:00 -- 11:30

What this course is about: This is an advance course/seminar in complexity theory. This course is typically taught every other year, and the topics can vary. For spring, 2003, we are planning to concentrate on descriptive complexity, but to include other topics and recent advances in complexity theory.

Descriptive complexity is an approach, based on mathematical logic, to classifying the relative difficulty of computational problems (particularly queries to a database). While traditional complexity theory concentrates on the resources needed to compute the answer to a query, descriptive complexity focuses on the resources needed to describe the query in some logical formalism --- how many variables, how many quantifiers, which forms of induction, and so forth. Surprisingly, computational complexity classes like P and NP have natural characterizations in descriptive complexity, as do all other well-studied complexity classes.

In this course, among other things, we will:

Text: Descriptive Complexity, by Neil Immerman, Springer Graduate Texts in Computer Science, 1999. This will be available at the Jeffrey Amherst College Store in downtown Amherst.

Prerequisite: CMPSCI 601 or permission of at least one of the instructors.