# CMPSCI 250: Introduction to Computation

### David Mix Barrington

### Spring, 2006

# Homework #8 Questions and Answers

### Question 8.3, 14 May 2006

It's a typo? I just did Problem 9.10.2 using the regular expression in
the book, and I think I got it right but it was very nasty. Do I have to do
the correct problem now as well?

I worked out the problem for the bad regular expression -- there's a seven-state
λ-NFA, a seven-state NFA with 31 letter moves, and a seven-state DFA
that minimizes to six states. As you should be able to tell from Exercise
9.10.3, the minimal DFA for the correct expression has only three states and
the other machines are simpler as well. Both problems are rather similar to
Discussion #11, for which I'm about to post solutions.

Normally if you do the wrong problem and it's at least as hard as the
regular problem, you get most but not all of the points. In this case, since
the mistake was mine, I will give you full credit *if* your answer to the
problem you did is fully correct.

### Question 8.2, 14 May 2006

Speaking of Exercise 9.10.3, there seems to be a mistake in the
solutions -- shouldn't the final regular expression be
(b+ab^{*}ab^{*}a)^{*} instead of
(b+ba^{*}ba^{*}b)^{*}?

Yes, you are right, this is a typo. Your
expression is correct.

### Question 8.1, 10 May 2006

Problem 9.10.3 is incredibly hard and annoying, with 9 huge state
eliminations needed. It's extra credit, so I don't have to do it, but
Problem 9.10.2 requires that I know the regular expression generated in
9.10.3 -- does that mean that I have to do 9.10.3 anyway?

No, because Problem 9.10.2 refers to *Exercise 9.10.3*, not Problem
9.10.3 -- answers to the Exercises are in the back of the book.

Last modified 15 May 2006