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CS 172: Computability and Complexity

CS 172
Computability and Complexity

Prof. Luca Trevisan

Spring 2007
Mondays and Wednesdays 2:30-4:00pm
320 Soda

News

You can use two pages (one two-sides sheet) of notes for the final
Solutions to practice final
Madhur will hold a review section in 511 Soda on Wednesday 5/9 at 6pm
5/8 Practice Final
5/7 Solutions to Homework 9 and Homework 10
5/3 Handout 6, notes on zero knowledge, Discussion handout 14
4/26 Homework 10, Discussion handout 13
4/23 Handout 5, Solutions to Homework 8
4/19 Homework 9, Midterm 2 Solutions
4/13 Homework 8
4/10 Practice Midterm 2 Solutions
4/7 Solutions to Homework 6, Solutions to Homework 7, Practice Midterm 2
4/4 Handout 4
3/22 Homework 7
3/14 Homework 6
3/7 The long-awaited Handout 3
3/6 Homework 5
3/6 Solutions to Midterm 1
Madhur will hold a review section on Monday Feb 26, 5:30-7:00pm, 511 Soda
2/24 Solutions to Homework 3 and Homework 4
2/21 Practice Midterm
2/21 Handout for Discussion Section 5
2/21 Handout 2, notes on Rice's theorem
2/12 Homework 4
2/8 Solutions to Homework 2
2/7 Homework 3
2/5 Solutions to Homework 1
1/29 Handout 1, notes on state minimization, is out
1/29 Homework 2 is out
1/22 Homework 1 is out
12/28 The web site is up. See you on Wednesday, January 17

Textbook

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

Information

Course overview: prerequisites, grading, etc
Schedule of discussion sections:
Tuesdays 3-4pm, 3107 Etcheverry
Getting help: schedule of instructor and TA office hours:
Luca Trevisan: Tuesdays, 2-3pm, 679 Soda Hall
Madhur Tulsiani: Fridays, 10-11am, 511 Soda Hall
Access the ucb.class.cs172 newsgroup.
From off-campus you can read the newsgroup using google

Work

Homeworks are due in the CS172 drop box in 283 Soda
Solutions are only accessible from within the berkeley.edu domain
Discussion Sections
Lecture Notes
- Handout 1, notes on state minimization
- Handout 2, notes on Rice's theorem
- Handout 3, notes on Goedel's theorem
- Handout 4, notes on NP-completeness
- Handout 5, notes on space-bounded complexity
- Handout 6, notes on zero knowledge

Exams

Lectures

So far:

	Topic	Readings	Problem sets
1: January 17	Summary of the course, Finite Automata	Chapter 0, Section 1.1	.
2: January 22	Non-deterministic 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	Myhill-Nerode 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 (non-determinism, 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	First-order 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	NP-completeness of Circuit-SAT and 3SAT	Section 7.4 Section 9.3	Homework 7
18: April 2	More NP-completeness	Section 7.5 Handout 4
19: April 4	NL, Savitch's theorem	Sections 8.2, 8.4	Practice Midterm 2
20: April 9	NL-completeness and PSPACE-completeness	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	Non-deterministic 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	Myhill-Nerode theorem	Handout 1	Homework 3 out
7: February 7	State minimization	Handout 1
8: February 12	Turing machines, Church-Turing 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	NP-completeness of Circuit-SAT and 3SAT	Section 7.4 Section 9.3
Spring Break	No Class
18: April 2	More NP-completeness	Section 7.5 Handout 4	Practice Midterm 2
19: April 4	NL, Savitch's theorem	Sections 8.2, 8.4
20: April 9	NL-completeness	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

Weekly Theory Mettings

Wednesdays, 5:00-6:30pm, 615 Soda undergraduate reading group

Wednesdays, noon-1pm, Wozniak Lounge (Soda, 4th floor) theory lunch