# CMPSCI 501: Theory of Computation

### David Mix Barrington

### Spring, 2015

# Homework Assignment #1

#### Posted Monday 9 February 2015

#### Due on paper in class, Wednesday 18 February 2015

There are twelve
questions for 80 total points plus
10
extra credit.
All but one are from
the textbook, *Introduction to the Theory of Computation*
by Michael Sipser (second/third edition). though some are adapted as
indicated.
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 B-1 (10): Find minimal DFA's for the languages of
Exercises 1.6h and 1.28c. Describe all the Myhill-Nerode
equivalence
classes for each of the two languages.
- Exercise 1.29 part b only (5): Use either the Pumping Lemma
or Myhill-Nerode.
- Problem 1.40 part b only (10)
- Problem 1.67 (10XC). This problem is not in the second edition, it
reads: "Let the
**rotational closure** of language A be RC(A) =
{yx: xy ∈ A}. Part (a): Show that for any language A, we have that
RC(A) = RC(RC(A)). Part (b): Show that the class of regular languages is
closed under rotational closure (that is, show that if A is any regular
langauge, RC(A) is also regular)."
- Exercise 2.4 parts b, e, f only (5).
- Exercise 2.5 parts b, e, f only (5):
You need not use the construction on your results from 2.4.
- Exercise 2.6 part d only (5)
- Exercise 2.11 (5)
- Problem 2.23 (10)
- Problem 2.25 (10).
- Problem 2.26 (5)
- Problem 2.44 (10)

Last modified 11 February 2015