ECS 220 (Theory of Computation) Winter 2015, Prof. Franklin

Time and Location: TuTh 10:30am-11:50am (1062 Bainer)

Office Hours (Kemper 3021): Tues 1pm-3pm

TA: Minseung Kim (msgkim@ucdavis.edu)

TA Office Hours (Kemper 55): Mon 9-11am, Wed 9-11am, Fri 9-10am.

Final Exam: Wed 18 March 3:30pm-5:30pm

The midterm is

Textbook: Arora and Barak, Computational Complexity: A Modern Approach.

Note that we msy use material from these other sources, but in all cases I will provide handouts in class.

Grade: closed-book midterm (35%), closed-book final (65%). The midterm is tentatively scheduled for Tues Feb 10. Turing Machines, Arora-Barak, Chapt 1 (all except 1.5.2, 1.7)

Mostly review: TM model and variants, universal TM, halting problem, P, Church-Turing thesis

NP, and NP completeness, Arora-Barak, Chapt 2 (all)

Mostly review: NP, NP-completeness, Cook-Levin Thm, web of reductions, coNP, EXP, NEXP

Diagonalization, Arora-Barak, Chapt 3 (all except 3.4.1)

Time Hierarchy Thms, Ladner's Thm, Baker-Gill-Solovay Thm

Space Complexity, Arora-Barak, Chapt 4 (all except 4.3)

PSPACE, NSPACE, L, NL, PSPACE-Completeness, Savitch's Theorem

Polynomial Hierarchy, Arora-Barak, Chapt 5 (5.1, 5.2 only)

standard def, properties

Boolean Circuits, Arora-Barak, Chapt 6 (all except 6.2.1, 6.7.2, 6.8)

standard def, TM with advice def, P/poly, P-uniform, Karp-Lipton Thm, lower bounds, NC, AC

Randomized Computation, Arora-Barak, Chapt 7 (7.1. 7.3, 7.4 only)

probabilistic TM's, BPP, RP, ZPP, robustness of defs

PCP Theorem and Hardness of Approximation, Arora-Barak, Chapt 11 (all).

approximation algorithms, two views of PCP theorem, proof of weaker PCP theorem.

If time remains: interactive proofs and zero knowledge (Moore-Mertens, "Nature of Computation", 11.1.1, 11.1.3, 11.2).