CS 172
Computability and Complexity Prof. Luca Trevisan Spring 2007


So far:
Topic  Readings  Problem sets  
1: January 17  Summary of the course, Finite Automata  Chapter 0, Section 1.1  . 
2: January 22  Nondeterministic automata, Regular expression  Section 1.2  Homework 1 
3: January 24  Equivalence of DFA, NFA and reg. exp.; pumping lemma  Sections 1.3, 1.4  . 
4: January 29  MyhillNerode theorem  Handout 1  Homework 2 
5: January 31  State minimization  Handout 1  
6: February 5  Definition of Turing machines  Chapter 3 Turing's paper 
Homework 3 
7: February 7  Variants of Turing machines (nondeterminism, multiple tapes...)  Chapter 3  
8: February 12  Examples of decidable problems, undecidability of Halting Problem  Chapter 4  Homework 4 
9: February 14  Reducibility and more undecidability  Sections 5.1, 5.3  
February 19  No Class  
10: February 21  Rice's theorem and more undecidability  Handout 2  Practice Midterm 1 
11: February 26  Godel's incompleteness theorem  Handout 3  
February 28  MIDTERM I  
12: March 5  Firstorder logic  Section 6.2  Homework 5 
13: March 7  A decidable logical theory  Section 6.2  
14: March 12  Kolmogorov complexity  Section 6.4  Homework 6 
15: March 14  The classes P and NP  Sections 7.1, 7.2, 7.3  
16: March 19  Boolean circuits  Section 9.3  
17: March 21  NPcompleteness of CircuitSAT and 3SAT  Section 7.4 Section 9.3 
Homework 7 
18: April 2  More NPcompleteness  Section 7.5 Handout 4 

19: April 4  NL, Savitch's theorem  Sections 8.2, 8.4  Practice Midterm 2 
20: April 9  NLcompleteness and PSPACEcompleteness  Section 8.5 

April 11  MIDTERM II  Homework 8  
21: April 16  NL=coNL  Section 8.6 Handout 5 

22: April 18  Randomized logspace, hierarchy theorems  Handout 5, Section 9.1  Homework 9 
23: April 23  Hierarchy theorems  Section 9.1  
24: April 25  Interactive Protocols  Handout 6  .Homework 10 
25:April 30  Zero knowledge and cryptography  Handout 6  
26:May 2  Zero knowledge and cryptography  Handout 6  
27: May 7  Bonus lecture on quantum computing 
Original plan:
Topic  Readings  Problem sets  
1: January 17  Summary of the course, Finite Automata  Chapter 0, Section 1.1  . 
2: January 22  Nondeterministic automata, Regular expression  Section 1.2  Homework 1 out 
3: January 24  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: January 31  Pumping lemma  Section 1.4 Handout 1 

6: February 5  MyhillNerode theorem  Handout 1  Homework 3 out 
7: February 7  State minimization  Handout 1  
8: February 12  Turing machines, ChurchTuring thesis  Chapter 3 Turing's paper 
Homework 4 out 
9: February 14  Variants of Turing machines  Chapter 3  
February 19  No Class  
10: February 21  Halting problem  Chapter 4  Practice Midterm 
11: February 26  Reducibility and more undecidability  Sections 5.1, 5.3  Homework 5 out 
February 28  MIDTERM I  
12: March 5  Rice's theorem and more undecidability  Handout 2  Homework 6 out 
13: March 7  Godel's incompleteness theorem  Handout 3  
14: March 12  A decidable logical theory  Section 6.2  .Homework 7 out 
15: March 14  Kolmogorov complexity  Section 6.4  
16: March 19  The classes P and NP  Sections 7.1, 7.2, 7.3  Homework 8 out 
17: March 21  NPcompleteness of CircuitSAT and 3SAT  Section 7.4 Section 9.3 

Spring Break  No Class  
18: April 2  More NPcompleteness  Section 7.5 Handout 4 
Practice Midterm 2 
19: April 4  NL, Savitch's theorem  Sections 8.2, 8.4  
20: April 9  NLcompleteness  Section 8.5 Handout 5 
Homework 9 out 
April 11  MIDTERM II  
21: April 16  NL=coNL  Section 8.6 Handout 5 
Homework 10 out 
22: April 18  Hierarchy theorems  Section 9.1 Handout 6 

23: April 23  Hierarchy theorems  Section 9.1 Handout 6 
Homework 11 out 
24: April 25  Zero knowledge and cryptography  Handout 7  . 
25:April 30  Zero knowledge and cryptography  Handout 7  
26:May 2  Zero knowledge and cryptography  Handout 7  
27: May 7  Review 
Wednesdays, 5:006:30pm, 615 Soda undergraduate reading group
Wednesdays, noon1pm, Wozniak Lounge (Soda, 4th floor) theory lunch
Mondays, 4:005:00pm, Wozniak Lounge theory seminar
(for fun, not for credit)