# CMPSCI 250: Introduction to Computation

### David Mix Barrington

### Spring, 2005

# Homework Assignment #7

#### Posted Sunday 24 April 2005

#### Due on paper in class, Monday 2 May 2005

There are ten questions for 100 total points.
All are from the textbook, *A
Mathematical Foundation for Computer Science*, from the brown volume.
"Problem 1.1.2", for
example, refers to Problem #2 in Section 1.1, and similarly. The number after each
problem is its point value. Make sure
you don't do an Exercise when a Problem is assigned!

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

- Page 8-14: Problem 8.2.4 (10)
- Page 8-23: Problem 8.3.2 (10)
- Page 9-7: Problems 9.1.1 (10), 9.1.6 (10), and the following
*variant*
of Problem 9.1.7 (10). The solution to Exercise 9.1.3 tells you that there are 64
different two-state DFA's. Rather than find the languages of all of them, you are to
figure out *exactly how many* have language ∅ and *exactly how many*
have language Σ^{*}.
- Page 9-13: Problems 9.2.1 (10) and 9.2.4 (10)
- Page 9-20: Problems 9.3.4 (10) and 9.3.5 (10). For 9.3.4,
you may find it
useful by beginning with the cases of k=0, k=1, and k=2 and then generalizing your
answer. Problem 9.3.5 has a typo, please see the
q&a page.
- Page 9-28: Problem 9.5.1 (10)

Last modified 1 May 2005