# CMPSCI 401: Theory of Computation

### David Mix Barrington

### Spring, 2009

# Homework Assignment #2

#### Posted Tuesday 17 February 2009

#### Due on paper in class, Friday 27 February 2009

There are fifteen questions for 100 total points plus 10 extra
credit. All but two 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.

Correction 22 February: 2.43 instead of 2.42!

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

- Problem B1 (5): Let Q be the language {u$v: u and v are binary strings
and the integer denoted by v is exactly three times the integer denoted by u}.
Prove that q is not regular.
- Problem 1.46 part d only (5)
- Problem 1.53 (5) (This is much easier with Myhill-Nerode.)
- Problem 1.54 (10)
- Problem B-2 (10) For each of the languages of Problem 1.55, give a DFA
that uses the minimum possible number of states for that language. For five of
those languages (of your choice) show that your DFA has the minimum number of
states for that language.
- Exercise 2.1 (5)
- Exercise 2.9 (10)
- Exercise 2.10 (5)
- Exercise 2.12 (10)
- Exercise 2.13 (5)
- Problem 2.21 (10 extra credit)
- Problem 2.32 (5)
- Problem 2.39 (10)
- Problem 2.43 part a (10) (corrected 22 February, recorrrected 26 February)
- Problem 2.43 part b (5) (corrected 22 February, recorrected 26 February)

Last modified 26 February 2009