Fall 2025 | T Th 12:30-2 | JGB 2.202 |
Instructor: Dana Moshkovitz
TA: Michael Jaber
Lectures:
|
|
Date |
Topic |
Reading |
|
1 |
Tuesday,
August 26 |
Turing Machines, complexity classes, hierarchy theorems |
Chapters 1, 3.1 |
|
2 |
Thursday, August
28 |
The polynomial hierarchy, padding arguments, time-space lower bounds |
Chapter 5.1-5.4 |
|
3 |
Tuesday,
September 2 |
Boolean circuits, S3 requires max circuit size |
Chapters 6.1-6.5 |
|
4 |
Thursday,
September 4 |
S2 requires max circuit size |
|
|
5 |
Tuesday,
September 9 |
Randomized Computation, Polynomial Identity testing, Markov inequality, ZPP=RPÇcoRP, |
Chapters 7.1-7.3 |
|
6 |
Thursday,
September 11 |
Amplification of BPP, Chernoff bound, BPPÍP/poly, BPPÍS2 |
Chapters 7.4-7.5 |
|
7 |
Tuesday,
September 16 |
Applications of polynomial identity testing: perfect matchings, communication complexity, error correcting codes |
Chapter 19.2 (error correcting codes) |
|
8 |
Thursday,
September 18 |
Local decoding, univariate poly identity testing requires quadratic time? |
Chapter 19.4.2+Paper |
|
9 |
Tuesday,
September 23 |
One-symbol pseudorandom generator, worst-case to average-case and the connection to locally decodable codes |
Chapter 19.6 |
|
10 |
Thursday,
September 25 |
Nisan-Wigderson (pseudorandom generators with large output), designs |
Chapter 20.2 |
|
11 |
Tuesday,
September 30 |
Space bounded computation (L, BPL, NL). Branching programs. Prob Method argument for PRGs. PRGs for length-2 branching programs. |
Chapter 21.6 + lecture notes |
|
12 |
Thursday,
October 2 |
Impagliazzo-Nisan-Wigderon PRG continued |