# Homework Assignment #7

#### 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.

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≡Lw", I intended for you to prove "∀u:∀w:∃v:uv≡Lw". 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)