# CMPSCI 401: Theory of Computation

### David Mix Barrington

### Spring, 2008

# Homework Assignment #2

#### Posted Monday 18 February 2008

#### Due on paper in class, Monday 3 March 2008

There are fifteen questions for 100 total points plus 20 extra
credit. All are from
the textbook, *Introduction to the Theory of Computation*
by Michael Sipser (second edition).
Numbers in parentheses following each problem
are its individual point value.

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

- Exercise 1.29 part b only (10) -- five points for using the MN theorem,
five points for using the Pumping Lemma
- Problem 1.39 (5)
- Problem 1.42 (10)
- Problem 1.46 part c only (c)
- Problem 1.61 (5)
- Problem 1.63 (10XC) Hint: First solve the problem for
*unary*
languages, where Σ = {a}.
- Exercise 2.4 parts b, c, e, and f (10)
- Exercise 2.5 parts b, c, e, and f (10)
- Exercise 2.11 (10)
- Exercise 2.16 (10)
- Problem 2.22 (10)
- Problem 2.30 parts a and d (10)
- Problem 2.31 (5) Hint: Use the result of Problem 2.18
- Problem 2.32 (5) Hint: Use the result of Problem 2.18
- Problem 2.38 (10XC)

Last modified 18 February 2008