CS 172
Computability and Complexity Prof. Luca Trevisan Spring 2004


Note: all homeworks and solutions are offline
(clicking on a homework or solution takes you to an `access
denied' page)
Note: all exams and solutions are offline
(all homeworks and solutions are offline)
Topic  Readings  Problem sets  
1: January 20  Summary of the course  Chapter 0  . 
2: January 22  Finite Automata  Sections 1.1  Homework 1 out 
3: January 27  Closure properties  Section 1.2  . 
4: January 29  Regular expressions  Section 1.3  Homework 2 out 
5: February 3  Pumping lemma  Section 1.4 Handout 1 

6: February 5  MyhillNerode theorem  Handout 2  Homework 3 out 
7: February 10  State minimization  Handout 2  
8: February 12  Turing machines, ChurchTuring thesis  Chapter 3 Turing's paper 
Homework 4 out 
9: February 17  Variants of Turing machines  Chapter 3  . 
10: February 19  Halting problem  Chapter 4  Practice Midterm 
11: February 24  Reducibility and more undecidability  Sections 5.2, 5.3  
February 26  MIDTERM I  Homework 5 out  
12: March 2  Rice's theorem and more undecidability  Handout 3  
13: March 4  Godel's incompleteness theorem  Handout 4  Homework 6 out 
14: March 9  A decidable logical theory  Section 6.2  . 
15: March 11  Kolmogorov complexity  Section 6.4  Homework 7 out 
16: March 16  The classes P and NP  Sections 7.1, 7.2, 7.3  . 
17: March 18  NPcompleteness  Section 7.4 Section 9.3 
Homework 8 out 
March 2226  Spring break  
18: March 30  More NPcompleteness  Section 7.5 Handout 5 

19: April 1  PSPACE, Savitch's theorem  Section 8.1, 8.2  Practice Midterm 2 
20: April 6  PSPACEcompleteness  Section 8.3 (only TQBF) 

April 8  MIDTERM II  Homework 9 out  
21: April 13  NL, NLcompleteness  Section 8.4,8.5 Handout 6 

22: April 15  NL=coNL  Section 8.6 Handout 6 
Homework 10 out 
23: April 20  Hierarchy theorems  Section 9.1 Handout 7 

April 22  No Class  Homework 11 out  
24: April 27  Randomized Algorithms  Section 10.2 (no primality test) 
. 
25: April 29  Randomized Algorithms and circuits  Section 10.2, Handout 8 
Homework 12 out 
26: May 4  Randomized Algorithms  Section 10.2  
27: May 6  Interactive proofs and Zero Knowledge  Section 10.4 Handout 9 

28: May 11  PCP theorem and applications  Section 10.1, Notes 
(for fun, not for credit)
Alan Turing, Alonzo Church, Kurt Gödel, Michael Rabin, Dana Scott, Steve Cook, Leonid Levin, Dick Karp, Manuel Blum