Homework 2

Be sure to follow the homework guidelines.

1. Do Exercises 1.7(b), (c), and (e) on page 84.

2. Do Exercises 1.12 on page 85.

3. Do Exercises 1.13 on page 85. Hint: Describe the language F positively, i.e., using a predicate without negation.

4. Do Exercises 1.16(b) on page 86 as follows.

1. Convert the NFA of Exercise 1.16 (b) to an equivalant NFA without ε-transitions. Use the algorithm given in class. Your answer should be a transition table or state diagram of the equivalent ε-less NFA.
2. Now convert the resulting ε-less NFA to an equivalent DFA as done in class (and also described in Theorem 1.39 page 55-56). You answer should be a transition table, noting the start state and the accept states. While you are at it, you should also eliminate states that are unreachable from the start state from the table. Do this by breath-first searching while creating the table, the way I demonstrated in class.

5. Do Exercise 1.18 on page 86.

Extra credit: Do Problem 1.41 or 1.42 on page 89.