Seminar: Introduction to Propositional Proof Complexity
Office: APM 6210.
Office phone: 858-534-6455.
Dates: Winter 2014 quarter, Fridays 12:00-1:30
Room: APM 7218
First meeting: Friday, January 10, 12:00pm-1:30pm
Course number: Math 268 (Topics in Logic)
Overview: This seminar will cover topics in propositional proof complexity, especially upper and lower bounds on proof size and other measures of proof complexity. Proof systems to be discussed include: resolution, Res(k), Frege systems, extended Frege systems, mod-k and TC0-Frege, cutting planes, the Nullstellensatz system, and the Polynomial Calculus. Other topics include: switching lemmas, Craig interpolation, natural proofs, cryptographic conjectures, and applications of monotone circuit complexity. If time permits, we may also cover related topics from SAT solvers. Lectures will be mostly presented by the instructor, but it is hoped there will also be some guest lectures.
Propositional proof complexity addresses open problems in computational complexity --- ultimately, the NP vs coNP question --- from the point of view of mathematical logic: This combines questions from computational complexity (about expressibility of propositional properties) with questions about the provability of propositional properties) and brings a range of tools from mathematical logic to bear on the P versus NP problem.
This is an introductory seminar. Although some background in logic or computational complexity would be helpful, there are no particular prerequisites beyond a certain level of mathematical maturity.Handwritten lecture notes (students and instructor) These are rough and unproofread notes, being made available to give an overview of the topics covered.
These are rough handwritten notes intended for Sam's archival storage. Not recommended for anyone else. Click here.