Advanced Complexity Theory

Lecture Notes

The students in this class usually transcribe the lecture notes. Professor Moshkovitz selected notes from various years for the 2016 class. All student notes are used with permission. Some students agreed to publish their names along with their scribed notes, while others chose to publish anonymously.

In addition, there are notes and readings from other sources.

LEC #	LECTURE NOTES
1	PH Time-Space Tradeoffs (PDF) (Courtesy of anonymous MIT student. Used with permission.)
2	Relativization (PDF) (Courtesy of Di Liu. Used with permission.)
3	Circuits and Karp-Lipton (PDF) (Courtesy of anonymous MIT student. Used with permission.)
4	Unique-SAT, Parity-SAT, and Approximate Counting (PDF) (Courtesy of anonymous MIT student. Used with permission.)
5	Toda’s Theorem (PDF) (Courtesy of Ilya Razenshteyn. Used with permission.)
6	AC0 Lower Bounds and Switching Lemma (PDF) (Courtesy of Ilya Razenshteyn. Used with permission.)
7	Razborov-Smolensky (PDF) (Courtesy of Brian Chen. Used with permission.)
8–9	NEXP vs ACC0 (Addendum to Arora-Barak) (PDF)
10–11	Communication Complexity 1 (PDF) Lower Bounds for Deterministic Communication (PDF)
12	Randomized Communication (PDF) (Courtesy of Andrew He. Used with permission.)
13	Karcher-Wigderson Games and KRW <Lecture notes not available>
14	Intro to PCP (PDF)
15	PCP Theorem Recap and FGLSS Reduction <Lecture notes not available>
16	Linearity Testing (PDF) (Courtesy of anonymous MIT student. Used with permission.) Exponential Sized PCP (PDF) (Courtesy of Haoran Xu. Used with permission.)
17	PCP with Polylogarithmic Queries and Sum Check (PDF) (Courtesy of Michael Forbes. Used with permission.)
18	Unique Games Conjecture and Hardness for MAX-2LIN (PDF) (Courtesy of anonymous MIT student. Used with permission.)
19	Parallel Repetition from Fortification <Lecture notes not available>
20	P vs BPP 1 (PDF) (Courtesy of anonymous MIT student. Used with permission.)
21	P vs BPP 2 (PDF) (Courtesy of anonymous MIT student. Used with permission.)
22	Derandomization Implies Circuit Lower Bounds (PDF) (Courtesy of anonymous MIT student. Used with permission.)
23	Natural Proofs <Lecture notes not available>