# 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 AC^{0}
**Mon 4 Oct:** Barrington's Theorem, NUDFA's over abelian
groups
**Wed 6 Oct:** NUDFA's over S_{3}, lower bounds
**Tue 12 Oct (Monday Schedule):** Descriptive complexity
and AC^{0}
**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 SAC^{1}
**Mon 25 Oct:** Proof of Smolensky's Theorem, dealing with
mod 6
**Wed 27 Oct:** Characterizations of TC^{0} (PCMI A1-5)

Last modified 25 October 2010