# CMPSCI 250: Introduction to Computation

### David Mix Barrington

### Spring, 2006

# Homework Assignment #7

#### Posted Friday 28 April 2006

#### Due on paper in class, Wednesday 10 May 2006

There are twelve questions for 100 total points.
All are from
the textbook, *A
Mathematical Foundation for Computer Science*. "Problem 1.1.2", for
example, is at the end of Section 1.1 and is labeled "P1.1.2".
The number after each problem is its individual point value. Make sure
you don't do an Exercise when a Problem is assigned! (Though the Exercises
should be good practice and the answers to them are in the back of the book.)
Also, be careful of problems with multiple parts that go from one page to the
next -- make sure you do the whole problem.

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

This homework is divided into two parts,
an **individual assignment**, where each student is responsible
for an independent writeup, and a **group assignment**. Homework
groups have been posted on the main web page. Each group
of 2-3 people is to hand in one writeup of the group problems -- you should
meet together at least once to do the work and each member of the group is
responsible for the answers.

#### Individual Problems (50):

- Page 9-7: Problems 9.1.1 (5) and 9.1.6 (10)
- Page 9-13: Problem 9.2.1 (5)
- Page 9-20: Problem 9.3.5 (10) There's a typo in this
problem -- instead of "∀u:∀v:∃w:uv≡
_{L}w",
I intended for you to prove
"∀u:∀w:∃v:uv≡_{L}w". The former statement
is true, and you'll get credit for proving it, but only the latter statement
is really relevant to the final question about the connectivity of the
**directed multigraph** of the minimal DFA.
- Pages 9-27 and 9-28: Problem 9.5.1 (10)
- Pages 9-34: Problem 9.6.1 (5)
- Pages 9-42: Problem 9.7.2 (5)

#### Group Problems (50):

- Page 9-7: Problem 9.1.5 (10)
- Page 9-13: Problem 9.2.4 (10)
- Page 9-20: Problem 9.3.1 (10)
- Pages 9-27 and 9-28: Problem 9.5.3 (10)
- Page 9-34: Problem 9.6.2 (10)

Last modified 10 May 2006