The discovery and study of probabilistic proof systems, such as PCPs and IPs, have had a tremendous impact on theoretical computer science. These proof systems have numerous applications (e.g., to hardness of approximation) but one of their most compelling uses is a direct one: to construct cryptographic protocols that enable super fast verification of long computations. This course will introduce students to the foundations of probabilistic proof systems, covering both classical results as well as modern efficient constructions.
This course requires knowledge of basic algorithms (CS 170) and complexity (CS 172).
Completing the course requires regular attendance/participation, completing occasional homework, scribing (once or twice), and a research project.
This course has no required textbook. We give specific references for each lecture.
This course will be a similar (though not identical) offering to one that I taught in [Spring 2019].
TBA
#  Date  Topic  Reading 

1  2020.08.27  Interactive Proofs 1 

2  2020.09.01  Interactive Proofs 2 

3  2020.09.03  Interactive Proofs 3 

4  2020.09.08  Interactive Proofs 4 

5  2020.09.10  Interactive Proofs 5 

6  2020.09.15  Interactive Proofs 6 

7  2020.09.17  Interactive Proofs 7 

8  2020.09.22  Basic Probabilistic Checking 1 

9  2020.09.24  Basic Probabilistic Checking 2 

10  2020.09.29  Basic Probabilistic Checking 3 

11  2020.10.01  Basic Probabilistic Checking 4 

12  2020.10.06  Basic Probabilistic Checking 5 

13  2020.10.08  PCPs with Sublinear Verification 1 

14  2020.10.13  PCPs with Sublinear Verification 2 

15  2020.10.15  Hardness of Approximation 1 

16  2020.10.20  Hardness of Approximation 2 

17  2020.10.22  Reducing Query Complexity 1 

18  2020.10.27  Reducing Query Complexity 2 

19  2020.10.29  Reducing Query Complexity 3 

20  2020.11.03  Parallel Repetition 1 

21  2020.11.05  Parallel Repetition 2 

22  2020.11.10  Interactive Oracle Proofs 1 

23  2020.11.12  Interactive Oracle Proofs 2 

24  2020.11.17  Interactive Oracle Proofs 3 

25  2020.11.19  Interactive Oracle Proofs 4 

X  2020.11.24  No class. 

X  2020.11.26  No class. 

26  2020.12.01  Class Project Presentations 1 

27  2020.12.03  Class Project Presentations 2 

X  2020.12.08  No class. 

X  2020.12.10  No class. 