# CMPSCI 250: Introduction to Computation

### David Mix Barrington

### Spring, 2006

# Homework Assignment #5

#### Posted Monday 3 April 2006

#### Due on paper in class, Wednesday 12 April 2006

There are fourteen questions for 100 total points plus ten extra credit.
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 5-5: Problem 5.1.3 (5)
- Pages 5-9 and 5-10: Problems 5.2.2 (10) and 5.2.5 (5)
- Page 5-15: Problem 5.4.2 (5) Note the restriction to a one-letter
alphabet -- the result is not true for strings over a larger alphabet.
Correction added 10 April: As pointed out in lecture today,
the thing you are asked to prove is
*false*. For full credit, you may
either (1) prove the weaker true statement "(ST)^{*} ⊆
S^{*}T^{*}", or (2) give an example of an S and T making the
original statement false. Sorry!
- Page 6-8: Problems 6.1.1 (5) and 6.1.2 (5)
- Pages 6-14 and 6-15: Problems 6.2.2 (10) and 6.2.4 (5)

#### Group Problems (50+10XC):

- Page 4-57: Problem 4.11.2 (10)
- Page 5-9: Problem 5.2.1 (10)
- Page 5-15: Problems 5.4.4 (10) and 5.4.5 (10XC)
- Page 5-22: Problems 5.5.1 (10) and 5.5.3 (10)

Last modified 10 April 2006