1. Regular operations Sipser 1.2 (pages 47-63)

2. First… a sample proof http://minerva.cs.mtholyoke.edu/courses/cs311F08/notes/notes5/DFAtoNFA.pdf

3. CS 311 Fall 2008 3 Kleene star Theorem: The class of regular languages is closed under the Kleene star operation.

4. CS 311 Fall 2008 4 And… closure under union!

5. CS 311 Fall 2008 5 NFA A nondeterministic finite automaton (NFA) is a 5-tuple (Q, Σ, δ, q 0, F), where – Q is a finite set called the states – Σ is a finite set called the alphabet – δ: Q × Σε → P(Q) is the transition function – q 0 ∈ Q is the start state – F ⊆ Q is a set of accept states In-class exercise:

6. CS 311 Fall 2008 6 NFA computation Let N=(Q, Σ, δ, q 0, F) be a NFA and let w be a string over the alphabet Σ Then N accepts w if – w can be written as w 1 w 2 w 3 …w m with each w i ∈ Σε and –There exists a sequence of states s 0,s 1,s 2,…,s m exists in Q with the following conditions: 1.s 0 =q 0 2.s i+1 ∈ δ(s i,w i+1 ) for i = 0,…,m-1 3.s n ∈ F