Lecture 5 (REs to NFAs), 2/06/06
Concepts, definitions, theorems:
- Table-based and set-based representations of NFAs
- NFAs with e-transitions
- Creating an NFA whose language is the union/concatenation/star
of languages for two other NFAs.
- Every RE has an equivalent NFA (p. 64)
- Proof by structural induction -- for a set that is defined
recursively
Reading:
- Section 1.3, from middle of p. 66 ("EQUIVALENCE
")
to end of p. 69 (figure 1.59)
Skills:
- Know new definitions, understand new concepts
- Understand the proof that for any RE, there exists an NFA accepting the same language
- Understand why the construction for STAR needed a new initial state
Notes:
- NFA ex: k'th letter from end of w is c
- NFA ex: the number of characters is divisible by 2 or by 3
- In the next class, we'll do an example of converting an RE to an NFA.