CS 172
Computability and Complexity Prof. Luca Trevisan Fall 2009


So far:
Topic  Readings  Problem sets  
1: August 27  Summary of the course  Chapter 0  . 
2: September 1  Deterministic and nondeterministic automata, Regular expression  Sections 1.1,1.2  Homework 1 out 
3: September 3  Equivalence of regular expression and finite automata  Section 1.3  . 
4: September 8  Equivalence of deterministic and nondeterministic automata  Section 1.3  Homework 2 out 
5: September 10  Pumping lemma  Section 1.4 Handout 1 

6: September 15  MyhillNerode theorem  Handout 1  Homework 3 out 
7: September 17  State minimization  Handout 1  
8: September 22  Turing machines, ChurchTuring thesis  Chapter 3 Turing's paper 
Homework 4 out 
9: September 29  Examples of Turing machines  Chapter 3  
10: October 1  Variants of Turing machines, nondeterminism, enumerators  Chapter 3  
11: October 2  Decidability, Halting problem  Chapter 4  Practice Midterm 
12: October 6  Undecidability  Section 5.1  Homework 5 out 
October 8  MIDTERM I  
13: October 13  Reducibility, Rice's theorem  Section 5.3, Handout 2  
14: October 15  Godel's incompleteness theorem  Handout 3  .Homework 6 out 
15: October 20  Kolmogorov complexity  Section 6.4, Handout 4  
16: October 22  The classes P and NP  Sections 7.1, 7.2, 7.3  Homework 7 out 
17: October 27  Boolean circuits and the NPcompleteness of CircuitSAT  Section 7.4 Section 9.3 

18: October 29  NPCompleteness of 3SAT, Independent Set  Section 7.5 Handout 5 
Homework 8 out 
19: November 3  NPcompleteness of Clique, Vertex Cover, Subset Sum etc.  Handout 5  
20: November 5  NPcompleteness of Steiner Tree and TSP  Handout 5  Practice midterm 
November 10  MIDTERM II  
21: November 12  NL, NLcompleteness  Sections 8.2, 8.5 Handout 6 
Homework 9 out 
22: November 17  Savitch's theorem, NL=coNL (beginning)  Sections 8.4, Section 8.6 Handout 6 

23: November 19  NL=coNL, Hierarchy Theorems  Section 8.6, 9.1 Handout 6, Handout 7 
Homework 10 out 
The plan:
Topic  Readings  Problem sets  
1: August 27  Summary of the course, Finite Automata  Chapter 0, Section 1.1  . 
2: September 1  Nondeterministic automata, Regular expression  Section 1.2  Homework 1 out 
3: September 3  Equivalence of regular expression and finite automata  Section 1.3  . 
4: September 8  Equivalence of regular expression and finite automata  Section 1.3  Homework 2 out 
5: September 10  Pumping lemma  Section 1.4 Handout 1 

6: September 15  MyhillNerode theorem  Handout 1  Homework 3 out 
7: September 17  State minimization  Handout 1  
8: September 22  Turing machines  Chapter 3 Turing's paper 
Homework 4 out 
9: September 29  Examples of Turing machines  Chapter 3  
10: October 1  Variants of Turing machines, nondeterminism, enumerators  Chapter 3  
11: October 2  Decidability, Halting problem  Chapter 4  Practice Midterm 
12: October 6  Reducibility and more undecidability  Sections 5.1, 5.3  Homework 5 out 
October 8  MIDTERM I  
13: October 13  Rice's theorem and more undecidability  Handout 2  
14: October 15  Godel's incompleteness theorem  Handout 3  .Homework 6 out 
15: October 20  Kolmogorov complexity  Section 6.4, Handout 4  
16: October 22  The classes P and NP  Sections 7.1, 7.2, 7.3  Homework 7 out 
17: October 27  NPcompleteness of CircuitSAT and 3SAT  Section 7.4 Section 9.3 

18: October 29  More NPcompleteness  Section 7.5 Handout 5 
Practice Midterm 2 
19: November 3  NL, Savitch's theorem  Sections 8.2, 8.4  
20: November 5  NLcompleteness  Section 8.5 Handout 6 
Homework 8 out 
November 10  MIDTERM II  
21: November 12  NL=coNL  Section 8.6 Handout 6 
Homework 9 out 
22: November 17  Hierarchy theorems  Section 9.1 Handout 6 

23: November 19  Hierarchy theorems  Section 9.1 Handout 7 
Homework 10 out 
24: November 24  Zero knowledge and cryptography  Handout 8  . 
25:December 1  Zero knowledge and cryptography  Handout 8  
26:December 3  Zero knowledge and cryptography  Handout 8  
27: December 8  Review  
28: December 10s  Review 