__Math 267C - Mathematical Logic - Course Homepage
Topics: Bounded Arithmetic and Complexity
__Instructor: Sam Buss

Spring 2003, Univ. of California, San Diego

**Instructor: Sam Buss. **
Email: sbuss@ucsd.edu. Phone: 534-6455.
Office: APM 6210.

**Organizational meeting:** Monday, March 31, 10:00 am. In
room York 3050B.

**If you cannot make the organizational meeting, please email me before hand
with what meeting times would be good for you. We hope to change the
meeting time from its currently scheduled time.**

Emailed Course Announcement

Instructor: Sam Buss

Topics: Bounded Arithmetic and Complexity

Math 267C

Spring 2003

Meeting Time: York 3050B 10:00-10:50 MWF, but this is likely to change

Organizational meeting: Monday, March 31, 10:00.

Please email ahead of time if you cannot attend the meeting.

This course is an introduction to bounded arithmetic and its

relationships with complexity. Topics include theories of bounded arithmetic

and especially the connections to proof complexity and computational

complexity.

Likely Topics, as time permits:

First order theories S^i_2, T^i_2 and polynomial time hierarchy

Second order theories U^i_2 V^i_2 and polynomial space

and exponential time

Finite axiomatizability and the possible collapse of the polynomial

time hierarchy. (Krajicek-Pudlak-Takeuti, Buss, Zambella)

The Paris-Wilkie translation and the Cook translation to

propositional proofs. Constant depth propositional proofs. Polynomial size
propositional proofs.

Natural proofs and interpolation. [Razborov, Pudlak, Krajicek, etc.]

Relationships with cryptographic protocols.

Low complexity classes and weaker fragments of bounded arithmetic

Counting in fragments of arithmetic.

No prior knowledge of bounded arithmetic will be presumed.

Basic results of proof theory will be introduced as needed

(e.g., cut elimination). Prior knowledge of computation classes

including P, NP, PSPACE, ALOGTIME, NC would be helpful.

No textbook, but we will use a variety of sources including

Buss(1985), Krajicek's text book, and course notes by Steve Cook,

and of course papers from the literature.