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 3 | Review of Turing machines; Hierarchy theorems. | Sections 3.1 and 9.1 of TC | |
| Sep 8 | Polynomial hierarchy. | Section 2.3 of LC | |
| Sep 10 | Oracle Turing machines; Σ2P = NPSAT | Sections 2.4 and 2.5 of LC | |
| Sep 15 | Circuits and sparse sets; Karp–Lipton theorem | Sections 4.1 and 4.2 of LC | |
| Sep 17 | Mahaney's theorem; PSPACE | Section 4.3 of LC and Section 8.1 of TC | |
| Sep 22 | PSPACE = NPSPACE | Sec 8.1 and 8.2 of TC | |
| Sep 24 | L, NL and coNL | Sec 8.4 and 8.6 of TC | |
| Sep 29 | NL = co-NL and PSPACE-completeness | Sec 8.6 and 8.3 of TC | |
| Oct 1 | NL-completeness and randomized algorithms | Sec 8.5 of TC and 5.2.2 of LC | |
| Oct 6 | Amplification of RP and BPP with tail bounds | Sec 5.1.1, 5.1.2, 5.1.3 and 5.4 of LC | |
| Oct 8 | BPP in Σ2P and Interactive Proof Systems | Sec 5.5 of LC | |
| Oct 13 | #SAT in IP | Sec 10.4 of TC | |
| Oct 15 | IP = PSPACE | Sec 10.4 of TC | |
| Oct 20 | Midterm | ||
| Oct 22 | PCP Theorem | Sec 18.1 of MA | |
| Oct 27 | PCP Theorem | Sec 18.2 of MA | |
| Oct 29 | PCP Theorem | Sec 18.4 of MA | |
| Nov 3 | Academic Holiday | ||
| Nov 5 | PCP Theorem | Sec 18.4 of MA | |
| Nov 10 | Communication complexity | Chapter 1 of CC | |
| Nov 12 | Lower bounds via monochromatic rectangles | Chapter 1 of CC | |
| Nov 17 | CC vs monochromatic partitions; rank | Chapter 1 and Pages 33-37 of CC | |
| Nov 19 | Randomized communication complexity | Sec 2.1, 2.2 and 2.4 of Notes by Shachar Lovett | |
| Nov 24 | Academic Holiday | ||
| Nov 26 | Lower bounds for disjointness | Sec 4.3 of Notes by Shachar Lovett | |
| Dec 1 | Circuit depth and KW games | Pages 97-99 of CC | |
| Dec 3 | Monotone circuit depth lower bounds | Pages 99-101 of CC | |
| Dec 8 | TBA |