CMPSCI 250: Introduction to Computation

David Mix Barrington

Spring, 2011

Questions and Answers on Homework Assignment #8

HW#8 due on paper in (lecture) class, Friday 22 April 2011

Question text is in black, answers in blue.

• Question 8.1, posted 21 April: What does "L(M)^R" mean in the statement of Problem 14.7.2?

  This is the reversal of the language L(M), which is the set {w^R: w ∈ L(M)}. The reversal of a language is defined on page 5-19 of the book.

• Question 6.2, posted 21 April: In Problem 14.6.3, I'm not really clear what you are asking.

  According to some person on the internet, there are 12143 different words in the King James Bible -- maybe they average five or seven letters each? You can estimate the number of states in your NFA from these numbers. Then I want to know how the number of states in the DFA will compare with the number in the NFA. Bigger? Smaller? Way bigger, like 2^k when k is the number in the NFA? Answering this means figuring out how the Subset Construction is going to affect this particular NFA.

• Question 6.3, posted 21 April: In Problem 14.3.5, I have a very easy proof of the first statement that doesn't even use the assumption. Did I do something wrong?

  No, I did something wrong. I meant to have you prove ∀u:∀v:∃w: uw ≡_L v, instead of what is written there with uv ≡_L w. So there is an easy proof that doesn't use the assumption, and since it is too late to fix the mistake I will give you five points for that proof. I'll give an additional five for proving what I wanted. The second question is correctly posed (and worth five points to answer), but the bad first part doesn't help you much -- the good first part does.

  You may want to rewrite the assumption as ∀x:∃y: xy ≡_L λ, to avoid confusion with the variable names. All these variables represent strings.

  Last modified 21 April 2011