# CMPSCI 401: Theory of Computation

### David Mix Barrington

### Spring, 2011

# Homework Assignment #2

#### Posted Sunday 6 February 2011

#### Due on paper in class, Monday 14 February 2010

There are ten questions for 80 total points.
All but two are
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 B-1 (10) Show the steps of the state minimization
algorithm on the eight-state DFA for Exercise 1.6 part (l). Is this
DFA minimal? If you are using the solutions for
HW#1,
note that the diagram there is missing a 1-loop on state q1d.
- Problem B-2 (10) Create a DFA from the NFA of Exercise 1.10
part (a). Find a minimal DFA for this language, and describe the
classes of the Myhill-Nerode equivalence relation.
If you are using the solutions for HW#1, note
that
you must add a 1-loop on state q5 to make the NFA correct.
- Problem 1.35 (10)
- Problem 1.49 part (b) only (10)
- Problem 1.51 (5)
- Problem 1.62 (5)
- Exercise 2.1 part (c) only (5)
- Exercise 2.9 (10)
- Exercise 2.13 (10)
- Exercise 2.16 (5)

Last modified 12 February 2011