CS 388T: Theory of Computation

Spring 2020 | MW 3:30-5 | GDC 2.210 |

 

Instructor:         Dana Moshkovitz

TA:                     Ruizhe Zhang

Course Information

Text Book:

Sanjeev Arora and Boaz Barak, Computational Complexity – A Modern Approach, Cambridge University Press, 2009.

 

Lectures:

 

 

Date

Topic

Reading

1

Wednesday,

January 22

The polynomial hierarchy and time-space lower bounds

Chapter 5.4

 

2

Monday,

January 27

approximate counting

Chapters 17.4.1-17.4.4

3

Wednesday, January 29

Toda’s Theorem

Chapter 17.4.5

4

Monday, February 3

Relativization and its limits; Baker-Gill-Solovay

 

Chapters 3.1- 3.4

 

 

5

Wednesday, February 5

lower bounds from counting, S2ËSIZE(nk)

Chapters 6.1-6.5

6

Monday,

February 10,

AC0 and switching lemma

Chapter 14.1

7

Wednesday,

February 12,

Razborov-Smolensky

Chapter 14.3

8

Monday,

February 17,

Communication Complexity and depth lower bounds

Madhu’s notes

9

Wednesday,

February 19

Randomization and derandomization

Avi’s book

Chapter 21.1

10

Monday, February 24

Pseudorandom generators

Chapters 19, 20.1-20.2

11

Wednesday, February 26

GradFest

 

12

Monday, March 2

From worst-case hardness to average-case hardness

Chapters 19, 20.1-20.2

13

Wednesday, March 4

Derandomization of space-bounded computation

 

14

Monday, March 9

Derandomization requires circuit lower bounds

Chapter 20.4

15

Wednesday, March 11

Natural Proofs

Chapter 23

 

 

Spring break

 

 

 

 

 

 

 

 

 

16

Monday, March 30

ACC0 vs. NEXP – from SAT algorithms to lower bounds

Web addendum

19

Wednesday, April 1

The easy witness Lemma

Web addendum

+ Chapter 20

20

Monday, April 6

SAT algorithm for ACC0

Web addendum

21

Wednesday, April 8

Project proposals presentations

 

22

Monday, April 13

PCP, 2-prover games and hardness of approximation

Chapters 11.1-11.3

23

Wednesday, April 15

Linearity testing

 

24

Monday, April 20

PCP from linearity testing

Chapter 11.5

25

Wednesday, April 22

Parallel repetition

 

26

Monday,

April 27

Optimal hardness of approximation

Chapters 22.4,22.9.3-22.9.5

27

Wednesday,

April 29

Project presentations

 

28

Monday, May 4

Project presentations

 

29

Wednesday, May 6

Project presentations