# Homework Assignment #7

#### 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)