Fall 2025 | T Th 12:30-2 | JGB 2.202 |
Instructor: Dana Moshkovitz
TA: Michael Jaber
Lectures:
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|
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 |
|
|
13 |
Tuesday,
October 7 |
Probabilistically Checkable Proofs and its equivalence to hardness of approximation. |
Chapters 11.1-11.3 |
|
14 |
Thursday,
October 9 |
Linearity testing |
Chapter 11.5.1 +lecture notes |
|
15 |
Tuesday,
October 14 |
Proof of NP in PCP[polyn,O(1)]. Gap quadratic equations. Quadratic testing. |
Chapter 11.5 |
|
16 |
Thursday,
October 16 |
Parallel repetition. Two prover games. Non-interactive agreement. Simple analysis of parallel repetition via fortification. |
|
|
17 |
Tuesday,
October 21 |
IP=PSPACE. Sum check and a simple IP for #SAT |
Chapter 8.3 |
|
18 |
Thursday,
October 23 |
AC0 lower bound (Furst-Saxe-Sipser) |
Chapter 14.1 |
|
19 |
Tuesday,
October 28 |
AC0[3] lower bound (Razborov-Smolensky) |
Chapter 14.2 |
|
20 |
Thursday,
October 30 |
Monotone circuits lower bound (Razborov) |
Chapter 14.3 |
|
21 |
Tuesday,
November 4 |
Natural proofs, cryptographic pseudorandom generators |
Chapter 23 |
|
22 |
Thursday,
November 6 |
Talking about Teaching (towards students presentations) |
|
|
23 |
Tuesday,
November 11 |
Oracle separations, Baker-Gill-Solovay, algebraization |
Chapter 3.4 |
|
24 |
Thursday,
November 13 |
Dry-runs for student presentations |
|
|
25 |
Tuesday,
November 18 |
Student presentations I: reachability in log-space, random walks, expanders, pairwise independence |
|
|
26 |
Thursday,
November 20 |
Student presentations II: Circuit lower bounds, proof complexity (Haken) |
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