Lecture 05

Today:

• 1. Closures.

  2. Reading questions from Lecture 04.

  3. Homework time.

For next time:

• 1. Do Homework 3.

  2. Read from Sipser and answer the questions below.

  3. Prepare for a quiz.

Reading questions

Sipser, pages 31 - 47

1) Can you think of a simple, familiar system that can be modeled with a finite state machine? Draw a state transition diagram for the system.

2) What is the meaning of δ: Q × Σ → Q?

3) In what state does M1 end with input string 00110?

4) In what state does M2 end with input string 00110?

5) What is the definition of a regular language?

6) What steps and techniques does Sipser recommend for designing a finite automaton?

7) Why can't you "rewind the input tape" to simulate two FSMs?

8) What does it mean to say that the set of regular languages is closed under union?

9) What kind of proof is used to prove that regular languages are closed under union?

You can stop reading on page 47 before Section 1.2.

9) Do exercise 1.4 on page 83, parts (a) and (b), and read

the rest to convince yourself that you could do them if

they showed up on a quiz or something.