Prof. Luca Trevisan
Spring 2015
Tuesdays and Thursdays 2:00-3:30pm
306 Soda
So far:
Topic | Readings | Problem sets | |
1: January 20 | Summary of the course | Chapter 0 | . |
2: January 22 | Deterministic Finite Automata | Section 1.1 | Homework 1 out |
3: January 27 | Nondeterministic finite automata | Section 1.2 | . |
4: January 29 | Equivalence of regular expression and finite automata | Section 1.3 | Homework 2 out |
5: February 3 | Myhill-Nerode theorem | Handout 1 | |
6: February 5 | State minimization | Handout 1 | Homework 3 out |
7: February 10 | Streaming algorithms | Handout 2 | |
8: February 12 | Turing machines | Chapter 3 Turing's paper |
Homework 4 out |
9: February 17 | Variants of Turing machines, non-determinism, enumerators | Chapter 3 | |
10: February 19 | Halting problem | Chapter 4 | Practice Midterm |
11: February 24 | More decidability and undecidability results | Chapter 4 | |
February 26 | MIDTERM I | Homework 5 out | |
12: March 3 | Reducibility, Rice's theorem, and more undecidability results | Sections 5.1, 5.3, Handout 3 | |
13: March 5 | Godel's incompleteness theorem | Handout 4 | Homework 6 out |
14: March 10 | Kolmogorov complexity | Section 6.4, Handout 5 | |
15: March 12 | The classes P and NP | Sections 7.1, 7.2, 7.3 | Homework 7 out |
16: March 17 | Boolean circuits | Section 9.3 | |
17: March 19 | NP-completeness of SAT | Sections 7.4, 9.3 | Homework 8 out |
18: March 31 | More NP-complete problems | Handout 6 | |
19: April 2 | More NP-complete problems | Handout 6 | Practice midterm |
20: April 7 | NL-completeness | Sections 8.2, 8.5 | |
April 9 | MIDTERM II | Homework 9 out | |
21: April 14 | Savitch's theorem, NL=coNL | Sections 8.4, Handout 7 | |
22: April 16 | PSPACE-completeness, hierarchy theorem | Sections 8.3, 9.1, Handout 8 | Homework 10 out |
23: April 21 | Zero knowledge proofs | Handout 9, Handout 10 | |
24: April 23 | More on Zero knowledge proofs | Handout 9, Handout 10 | Homework 11 out |
25: April 28 | The PCP Theorem | Handout 11 | |
26: April 30 | Complexity of Approximation | Handout 11 | Practice Final |
The plan:
Topic | Readings | Problem sets | |
1: January 20 | Summary of the course, Finite Automata | Chapter 0, Section 1.1 | . |
2: January 22 | Non-deterministic automata, Regular expression | Section 1.2 | Homework 1 out |
3: January 27 | Equivalence of regular expression and finite automata | Section 1.3 | . |
4: January 29 | Equivalence of regular expression and finite automata | Section 1.3 | Homework 2 out |
5: February 3 | Myhill-Nerode theorem | Handout 1 | |
6: February 5 | State minimization | Handout 1 | Homework 3 out |
7: February 10 | Streaming algorithms | Handout 2 | |
8: February 12 | Turing machines | Chapter 3 Turing's paper |
Homework 4 out |
9: February 17 | Examples of Turing machines | Chapter 3 | |
10: February 19 | Variants of Turing machines, non-determinism, enumerators | Chapter 3 | Practice Midterm |
11: February 24 | Decidability, Halting problem | Chapter 4 | |
February 26 | MIDTERM I | Homework 5 out | |
12: March 3 | Reducibility and more undecidability | Sections 5.1, 5.3 | |
13: March 5 | Rice's theorem and more undecidability | Handout 3 | Homework 6 out |
14: March 10 | Godel's incompleteness theorem | Handout 4 | |
15: March 12 | Kolmogorov complexity | Section 6.4, Handout 5 | Homework 7 out |
16: March 17 | The classes P and NP | Sections 7.1, 7.2, 7.3 | |
17: March 19 | Boolean circuits | Section 9.3 | Homework 8 out |
18: March 31 | NP-completeness of SAT | Sections 7.4, 9.3 | |
19: April 2 | More NP-complete problems | Handout 6 | Practice midterm |
20: April 7 | More NP-complete problems | Handout 6 | |
April 9 | MIDTERM II | Homework 9 out | |
21: April 14 | NL, Savitch's theorem | Sections 8.2, 8.4 | |
22: April 16 | NL-completeness | Section 8.5 | Homework 10 out |
23: April 21 | NL=coNL | Handout 7 | |
24: April 23 | Hierarchy theorems | Section 9.1 Handout 8 |
Homework 11 out |
25: April 28 | Zero knowledge and cryptography | Handout 9 | . |
26:April 30 | Zero knowledge and cryptography | Handout 9 | Practice final |
27: May 5 | Zero knowledge and cryptography | Handout 9 | |
27: May 7 | Review |