# Homework Assignment #8

#### Due on paper to a box in the CMPSCI main office by 4:00 p.m. Monday 13 December 2004. (Recall that there is no lecture on that day.)

There are thirteen questions for 100 total points plus 10 extra credit. All are from the textbook, A Mathematical Foundation for Computer Science, from the red volume. "Problem 1.1.2", for example, refers to Problem #2 in Section 1.1, and similarly. Make sure you don't do an Exercise when a Problem is assigned or vice versa!

• Page 9-28: Problem 9.5.3 (10)

• Page 9-34: Problems 9.6.1 (5) and 9.6.4 (10)

• Page 9-42: Exercise 9.7.5 (10), Problems 9.7.1 (5) and 9.7.2 (5)

• Page 9-50: Problems 9.8.1 (10) and 9.8.4 (10)

• Pages 9-59 and 9-60: Problems 9.10.2 (10) and 9.10.3 (10 XC) (Hint for 9.10.3: State elimination on the natural nine-state DFA will work but gets rather nasty. Better is to first build an r.e.-NFA with three states as follows, taking advantage of the fact that all strings in this language have a length divisible by 3. Define the regular expressions A = aaa+bbb, B = aab+aba+baa, and C = abb+bab+bba. Let the states of the r.e.-NFA be 0, 1, and 2, put an A-loop on each state, and add B-edges and C-edges as appropriate. Now the state elimination proceeds much like that in Problem 9.10.2.)

• Pages 10-10 and 10-11: Problems 10.1.3 (10) and 10.1.5 (5)

• Page 10-43: Problem 10.6.1 (10)