Homework 1

Homework Guidelines

0.  [Warmup, not be be handed in] Exercises 0.1‐0.9. Problems 0.10, 0.11, 0.12, 0.13.

1.  Do Exercise 1.3 on page 83.

2.  Do Exercise 1.4(c) on page 83 as follows.

1. Show a DFA that recognizes the language

          { w : w has an even number of a's }
          

2. Show a DFA that recognizes the language

          { w : w has one or two b's }.
          

3. Use product construction as done in class to combine the two DFA's above into a DFA that recognizes the language

          { w : w has an even number of a's and one or two b's }
          

   and show this combined DFA. Do not simplify the resulting DFA.

• draw a transition diagram of the DFA, or
• give a transition table, start state, and set of accept states for the DFA.

3.  Do Exercises 1.6(f) and 1.6(j) on page 84. Do not use product construction for 1.6(j).

4.  Do Exercises 1.7(b) and 1.7(c) on page 84.

5.  Do Exercise 1.13 on page 85 as follows. First draw the state diagram of a 4-state NFA for recognizing F̄. Then draw the state diagram of a 5-state DFA for recognizing F.

Extra credit.  Do any of the problems 1.32, 1.33, 1.34, 1.35, 1.36, 1.37, or 1.38 on pages 88–89.