CS 172
Computability and Complexity

Prof. Luca Trevisan

Fall 2009
Tuesdays and Thursdays 12:30-2:00pm
320 Soda

News

12/14 Practice final solutions
12/14 Practice final
12/14 Solutions to problem set 10
12/14 Handout 8 on zero knowledge proofs
12/14 Handout 7 on hierarchy theorems
12/8 Solutions to Homework 9
There will be a review on December 8, at the time and place of the class, and there will be no class on December 10
There will be no class on Thursday, December 3 and no office hours on Wednesday Dec. 2
11/20 Homework 10 is due December 2, take your time
11/19 Notes on space-bounded complexity
11/12 Homework 9
The second midterm will be Tuesday, November 10, in the Wozniak Lounge
11/8 Notes on NP-completeness
11/7 Solutions to Homework 7 and Homework 8
There will be a review session in the Wozniak Lounge, Friday November 6, 2-4pm
11/5 Practice Midterm 2
11/4 Some typos corrected in Homework 8 (numbers in example of definition of 'independence' did not add up)
10/29 Homework 8 is online and due Friday, November 6. (Homework 9 will be out in two weeks, next week we'll post practice problems for Midterm 2)
10/27 Additional Notes on Kolmogorov Complexity
10/27 Solutions to Homework 6
10/22 Solutions to Homework 5
10/21 Homework 7 is online
10/21 Handout 3, notes on Godel's theorem, is out
10/16 Two typos corrected in Homework 6. Thanks to Mark Landry for pointing them out
10/14 Homework 6 is out and due October 21
10/14 Handout 2 is online
10/8 Homework 5 is online and due October 14
10/7 Notes from Monday's review session
10/7 Solutions to Homework 4 are online
10/7 Solutions to Homework 3 have been revised. (The diagram in the solution of problem 3 was missing a transition.)
10/2 Practice Problems for Midterm 1
9/30 Solutions to Homework 3 are online
Solutions to Homework 1 and to Homework 2 are online (accessible only within berkeley.edu)
The midterm will be on Thursday, Oct 8. Sample problems will be out on Friday, Oct 2. No homework next week. There will be a review session on Monday, Oct 5, 4-6pm 511 Soda
NO CLASS on September 24 there will be a make-up lecture on October 2, 2-3pm Wozniak Lounge
Bill's September 24 section is NOT canceled
9/22 Homework 4 is out. It will be due on Monday October 5, 10am
9/15 Homework 3 is out
9/13 In problem 3 of homework 2, a string is in the language provided that the pattern abaa appears at least twice
9/10 Handout 1 is out
9/8 Homework 2 is out, due September 16
9/8 The drop box in 283 Soda now has a slot labeled 172 into which your homework 1 may safely be dropped
Bill will have office hours this Friday Sept 4, 3-4pm, 411 Soda
9/1 Homework 1 is out, due September 9
8/26 The web site is up. See you tomorrow

Textbook

Michael Sipser
Introduction to the Theory of Computation (2nd Edition)
Thompson, 2005

Information

Course overview: prerequisites, grading, etc
Schedule of discussion sections:
Thursdays 5-6pm, 6 Evans
Getting help: schedule of instructor and TA office hours:
Luca Trevisan: Wednesdays, 2-3pm, 679 Soda Hall
Bill McCloskey Mondays 11am-noon, 411 Soda Hall

Work

Homeworks are out (online only) on Tuesdays after class and are due in the CS172 drop box by 5pm on Wednesday the following week
Solutions are only accessible from within the berkeley.edu domain
1. Homework 1 is due September 9
  - Solutions
2. Homework 2 is due September 16
  - Solutions
3. Homework 3 is due September 23
  - Solutions
4. Homework 4 is due October 5
  - Solutions
5. Homework 5 is due October 15 14
  - Solutions
6. Homework 6 is due October 21
  - Solutions
7. Homework 7 is due October 28
  - Solutions
8. Homework 8 is due November 6
  - Solutions
9. Homework 9 is due November 18
10. Homework 10 is due December 2
Discussion Sections
- Week 1, Sept 3
Lecture Notes

Exams
- Practice Problems for Midterm 1

Lectures

So far:

	Topic	Readings	Problem sets
1: August 27	Summary of the course	Chapter 0	.
2: September 1	Deterministic and non-deterministic 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 non-deterministic automata	Section 1.3	Homework 2 out
5: September 10	Pumping lemma	Section 1.4 Handout 1
6: September 15	Myhill-Nerode theorem	Handout 1	Homework 3 out
7: September 17	State minimization	Handout 1
8: September 22	Turing machines, Church-Turing 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, non-determinism, 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 NP-completeness of Circuit-SAT	Section 7.4 Section 9.3
18: October 29	NP-Completeness of 3SAT, Independent Set	Section 7.5 Handout 5	Homework 8 out
19: November 3	NP-completeness of Clique, Vertex Cover, Subset Sum etc.	Handout 5
20: November 5	NP-completeness of Steiner Tree and TSP	Handout 5	Practice midterm
November 10	MIDTERM II
21: November 12	NL, NL-completeness	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

Novsember 23: Hierarchy theorems; December 1: Zero Knowledge; December 3: no class; December 8: Review, all questions answered; December 10 No class

The plan:

	Topic	Readings	Problem sets
1: August 27	Summary of the course, Finite Automata	Chapter 0, Section 1.1	.
2: September 1	Non-deterministic 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	Myhill-Nerode 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, non-determinism, 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	NP-completeness of Circuit-SAT and 3SAT	Section 7.4 Section 9.3
18: October 29	More NP-completeness	Section 7.5 Handout 5	Practice Midterm 2
19: November 3	NL, Savitch's theorem	Sections 8.2, 8.4
20: November 5	NL-completeness	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