Homework 1

Due Date: Feb 21, 2014

Be sure to follow the homework guidelines.

1. Let Σ = {a, b} be an alphabet. Find a language A over the alphabet Σ satisfying all of the following 4 properties:

  1. A ≠ {ε}
  2. A ≠ Σ*
  3. A* = A+ = A
  4. ab ∉ A.
Note that you have to give me one language that satisfies all 4 properties, not 4 languages.

2. Do Exercise 1.3 on page 83.

3. Do Exercise 1.4(e) on page 83 as follows.

  1. Draw a transition diagram of a DFA that recognizes the language 
           { w : w starts with an a }
  2. Draw a transition diagram of a DFA that recognizes the language 
           { w : w has at most one b }.
  3. Use product construction to combine the two machines above into one that recognizes the language 
           { w : w starts with an a and has at most one b }.

4. Exercise 1.5(c) on page 84.

5. Do Exercises 1.6 (e) on page 84.

6. Do Exercises 1.6 (j) on page 84.

Extra credit: Do Problem 1.37 on page 89.