COMPSCI 741: Complexity Theory

David Mix Barrington

Fall, 2019

This is the syllabus, such that it is, for COMPSCI 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. (Thus some of this syllabus will be filled in after the fact.)

Chapter/lecture numbers are from the PCMI notes (A, B).

• Tue 3 Sept: TM and Circuit Definitions and Examples (B1, B2)

• Thu 5 Sept: Nondeterminism, NP, NL (B3, B4)

• Tue 10 Sept: Basic Classes, Reductions, NP-Completeness (B5-B7)

• Thu 12 Sept: Other Complete Problems, Hierarchy (B8, B9)

• Tue 17 Sept: Smolensky's Theorem (B10)

• Thu 19 Sept: Proofs, Games, Alternation (B11) (HW#1 Due)

• Tue 24 Sept: Randomization and Interaction (B12, B13)

• Thu 26 Sept: IP = PSPACE (B14)

• Tue 1 Oct: A Brief Look at PCP (B15)

• Thu 3 Oct: Three Ways to Express Problems (A1)

• Tue 8 Oct: Connecting the Three Models (A2)

• Thu 10 Oct: Algebra and Languages (A3)

• Tue 15 Oct: NO CLASS (Monday Schedule)

• Thu 17 Oct: Non-Regular Languages and Uniformity (A4)

• Tue 22 Oct: Boolean Formulas, NC^1, and M-Programs (A5)

• Thu 24 Oct: Arithmetic and Threshold Circuits (A6)

• Tue 29 Oct: More Arithmetic, Fun With Primes (A7)

• Thu 31 Oct: Chinese Remainder Representation (A8)

• Tue 5 Nov: Towards Logspace Division (A9)

• Thu 7 Nov: Logspace Division and Consequences (A10)

• Tue 12 Nov : Log-Time Uniform TC^0 Division (HAB paper)

• Thu 14 Nov: Selected topics

• Tue 19 Nov: Selected topics

• Thu 21 Nov: Selected topics

• (THANKSGIVING BREAK)

• Tue 3 Dec: Selected topics

• Thu 5 Dec: In-Class Presentations

• Tue 10 Dec: In-Class Presentations

Last modified 10 September 2019