Math 166:Computability Theory

Home page for Math 166, Winter 1999

Theory of Computation


Date/Time: Winter Quarter, Monday-Wednesday-Friday. 10:10-11:00
Place: Peterson Hall 102. University of California, San Diego.

Instructor: Sam Buss
Office: APM 6210
Phone: 534-6455
Office hours: Monday 9:00-9:50 and Wednesday 9:00-9:50 and 1:30-2:30. (valid thru March 10).

Teaching Assistant: Tom Langley,
Office: APM 2202
Office hours: Wednesday 12:15-1:15, and Thursday 2:00-4:00. (thru March 11)


Review session: Tuesday, March 16, 3:00-4:30pm. APM 2301.

Exam week office hours for Sam Buss, APM 6210:
Monday and Thursday: 11:00-12:00 and 1:30-2:30.
Tuesday: 1:30-2:45.

Exam week office hours for Tom Langley, APM 2202:
Wednesday: 10:00-12:00 and 2:00-4:00.
Thursday: 3:00-6:00.

Soft reserves: By Wednesday, March 10, will have all midterm, homework and quiz answers (except for last quiz and homework).
Some past years' final exams and other sample final exam problems were handed out in class March 10. If you missed class, please pick them up from Tom or Sam.

Course announcement & Grading Policy

The textbook is Introduction to the Theory of Computation by M. Sipser.

This course will cover Automata and Regular and Context-free languages (Part I of the textbook), plus selected topics from Abstract Computability (Part II, Turing machines, etc.) and from Feasible Computability (Part III). These are basic topics in the foundations of the theory of computation, plus form the mathematical foundations for compiler design theory and for analysis of algorithmic efficiency.

The course will have a midterm exam on February 12 and a final exam. There will be quizes in the Thursday section meeting on most weeks. Popquizes have been given in class, but not many more (if any) are planned. Homework assignments will typically be due in class on Friday. Course grading will be 50% final, 30% midterm, 10% homework, 10% quizes, 0% popquizes. You may drop your lowest two quiz scores. The percentages may change slightly, if so I will announce the change.

Homework Assignments

Homework #1, due Friday, January 15.
Read chapter 0 and chapter 1 through page 43.
Pages 23-25: Problems 0.1, 0.2, 0.3, 0.4, 0.5,
Pages 83-90: Problems 1.1, 1.2, 1.3, and 1.4a,b,c.

Homework #2, due Friday, January 22.
Pages 83-90: Problems 1.4e,f,g,i,k,l,m,n, 1.5a-d.
And: Prove that the language over the alphabet {0,1,...,9} containing the integers (in base 10 representation) which are multiples of 7 is a regular language.

Homework #3, due Friday, January 29.
Pages 83-88: Exercises: 1.5f,g, 1.6a, 1.7a, 1.8a, 1.9, 1.12
Pages 88-90: Problems: 1.24, 1.44* (* = challenge problem).
Hint for 1.24: given an finite automaton M, construct an NFA recognizing the reversal of L(M).

Homework #4, due Friday, February 5.
Pages 83-88: Exercises: 1.10b, 1.14a, 1.15, 1.16, 1.17.
Pages 88-90: Problems: 1.23, 1.32a.
Revised due date: 1.17 and 1.23 are due on Monday, February 8.

Homework #5, due Friday, February 19.
Pages 119-121: Exercises: 2.1, 2.3, 2.4, 2.6a,b, 2.9.
Pages 121-122: Problems: *2.21.

Homework #6, due Friday, February 26.
Pages 119-121: Exercises: 2.5, 2.10, 2.11.
Pages 121-122: Problems: 2.15, 2.17a.
Hint: For 2.17a, use the equivalence of CFG's and PDA's (so you may work with PDA's). This will make problem 2.17a conceptually quite simple. Problem 2.15 may be done with either CFG's or with PDA's.

Homework #7, due Friday, March 5.
Pages 121-122: Problems: 2.17b, 2.18, *2.26, *2.27.

Homework #8, due Friday, March 12.
Page 149: Problems: 3.14, 3.15.
Also: Construct a Turing machine which decides the language containing all odd length length strings which have a "0" as their center character. (Alphabet = {0,1}).


As a courtesy for Prof. Bender's class, I've added pdf versions and gif versions of the files. (Now that I know that "distill" and "pstogif" are available.)

Pop Quiz #1. Set notation, if .. then .., set formation.
Also in pdf format and gif format.

Pop Quiz #2. Set notation, if .. then .., set formation. Again!
Also in pdf format and gif format.

Quiz #1, January 14.
Set notation, if .. then .., set formation. Again!!!!!!!
Also in pdf format and gif format.

Quiz #2, January 21.
DFA's. State diagrams. The 5-tuple definition of DFA's.
Also in pdf format and gif format.

Quiz #3, January 28.
NFA's. Construct NFA's recognizing given language. Convert an NFA into an equivalent DFA.
Also in pdf format and gif format.

Quiz #4, February 4.
Regular expressions and the languages they represent. Convert a 2-state DFA into a regular expression.
Also in pdf format and gif format.

Quiz #5, February 10 - Note different time: Wednesday in class
Proving languages are non-regular. The Pumping Lemma.
Answer key available immediately after class.
Also in pdf format and gif format.

Quiz #6, February 25.
Construct a context-free grammar. And construct a pushdown automaton.
Also in pdf format and gif format.

Quiz #7, March 4.
Prove that a language is not context-free with the aid of the pumping lemma.
Also in pdf format and gif format.

Quiz #8, March 11.
Construct a Turing machine to recognize a specified language. (By drawing its state diagram).
Also in pdf format and gif format.

Course Handouts

Course announcement and homework #1.

Soft reserves has homework, midterm and quiz answers.

Practice problems and old midterm handed out in class, February 8.
Old final exams and more practice problems handed out in class, March 10.

UCSD Mathematics Department home page

Author: Sam Buss,