For some lectures we will follow Lectures in Computational Complexity of Jin-Yi Cai (LC below), the book Computational Complexity: A Modern Approach of Sanjeev Arora and Boaz Barak (MA below), and the book Communication Complexity of Anup Rao and Amir Yehudayoff (CC below). TC denotes the Sipser book.
Date |
Topic |
Readings |
Homework |
|---|---|---|---|
| Sep 11 | Introduction; Review: Turing machines, Time Complexity, P vs NP; Hierarchy theorems. | Sec 2.1, 2.1, 2.2 of LC (also 3.1, 9.1 of TC) | |
| Sep 18 | Polynomial hierarchy and Oracle Turing Machines; Σ2P = NPSAT | Sec 2.3, 2.4, 2.5 of LC | |
| Sep 25 | Space Complexity: Classes L, NL, PSPACE; NL=coNL; PSPACE=NPSPACE | Chapter 8 of TC (also Chap 4 of MA) | HW1 Due 10/01 11:59pm |
| Oct 2 | Space Complexity cont'd, Catalytic Space | Chapter 8 of TC (also Chap 4 of MA) | |
| Oct 9 | Quiz 1. | ||
| Catalytic Space, Cook-Mertz and William's algorithms | Simulating time in sqrt-space (R.Williams) | HW2 Due 10/15 11:59pm | |
| Oct 16 | Randomized algorithms: Classes RP, BPP; BPP in Σ2P; hardness vs. randomness, randomness in cryptography | Sec 5.1.1, 5.1.2, 5.1.3, 5.4, 5.5 of LC (also Chap 7 of MA) | |
| Oct 23 | Midterm | ||
| Oct 30 | Interactive Proofs; #SAT in IP, IP=PSPACE | Sec 10.4 of TC (also Chap 8 of MA) | |
| Nov 6 | PCP Theorem, Hardness of Approximation | Sec 18.1, 18.2 of MA | HW3 Due 11/12 11:59pm |
| Nov 13 | Intro Communication Complexity, Deterministic, Rank, Randomized CC | Pages 15-37 of CC | |
| Nov 20 | Communication Complexity: Randomized Communication, Set Disjointness | Chapter 3 of CC, Sec 2.1-2.4 of Notes (S. Lovett) | |
| Nov 27 | Holiday (no class) | ||
| Dec 4 | Quiz 2. | ||
| Intro Circuit Complexity, Karp-Lipton Theorem | Sec 4.1, 4.2 of LC (also Chap 6 of MA) | HW4 Due 12/10 11:59pm | |
| Dec 11 | Monotone circuit depth lower bounds, TFNP and proof complexity | Pages 97-101 of CC |