# CMPSCI 401: Theory of Computation

### David Mix Barrington

### Spring, 2009

# Homework Assignment #1

#### Posted Tuesday 27 January 2009

#### Due on paper in class, Friday 13 February 2009

There are fourteen questions for 100 total points plus 10 extra
credit. All but one are from
the textbook, *Introduction to the Theory of Computation*
by Michael Sipser (second edition).
The number in parentheses following each problem
is its individual point value.

Students are responsible for understanding and following
the academic honesty
policies indicated on this page.

- Problem A1 (5): Following Theorem 0.22 on page 21, prove that if k is
any odd number, there is
*no* 3-regular graph with exactly k vertices.
- Problem 0.12 (5)
- Exercise 1.4 parts a and c only (5)
- Exercise 1.7 parts d and e only (5)
- Exercise 1.10 part a only (5)
- Exercise 1.12 (10)
- Exercise 1.21 part b only (5)
- Exercise 1.28 (10) You need not use the book's method -- any method is
ok as long as your writeup makes it clear that your answer is correct.
- Problem 1.33 (10)
- Problem 1.42 (10)
- Problem 1.45 (10 extra credit)
- Problem 1.48 (10)
- Problem 1.64 parts a, b, and c only (10)
- Problem 1.65 part a only (10)

Last modified 27 January 2009