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