# Homework Assignment #5

#### 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)