CMPSCI 741: Complexity Theory

David Mix Barrington

Fall, 2010

This is the syllabus, such that it is, for CMPSCI 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 Vollmer (V) or the PCMI notes (A, B).

• Wed 8 Sept: Introduction, circuit definitions

• Mon 13 Sept: Uniformity, P = PSIZE, CVP is P-complete

• Wed 15 Sept: Addition and iterated addition, cd-Reductions (V1.4)

• Mon 20 Sept: Iterated multiplication in P-uniform TC^o (V 1.4)

• Wed 22 Sept: Asympotic size complexity of worst-case functions (V1.5)

• Mon 27 Sept: Introduction to algebraic automata theory

• Wed 29 Sept: Non-uniform automata, starfree languages, programs over aperiodics equal non-uniform AC⁰

• Mon 4 Oct: Barrington's Theorem, NUDFA's over abelian groups

• Wed 6 Oct: NUDFA's over S₃, lower bounds

• Tue 12 Oct (Monday Schedule): Descriptive complexity and AC⁰

• Wed 13 Oct: BIS characterization of circuit classes (with log-time uniformity)

• Mon 18 Oct: Begin Alternation/Circuit Theorem

• Wed 20 Oct: Finish Alternation/Circuit Theorem, CFL's in SAC¹

• Mon 25 Oct: Proof of Smolensky's Theorem, dealing with mod 6

• Wed 27 Oct: Characterizations of TC⁰ (PCMI A1-5)

Last modified 25 October 2010