CS 390 Test II

April 3, 1997

1(a). Find an NFA that recognizes the same language as the following :

The initial state is 1 and the accepting state is 3.
(b) Find .
(c) Find .

2. Find an FA that recognizes the same language as the following NFA:

The initial state is 1 and the accepting state is 2.

3. Construct an that accepts the language corresponding to
from the simplest NFA's. DO NOT SIMPLIFY.

4. for natural numbers k is inductively (i.e. recursively) defined as follows:
Basis: .
Induction: for any natural number k, .

Prove by induction that for any natural number k, , .
You must prove if you need it.

Note that is defined inductively for a set S of states as follows:
Basis:
Induction: For any state q, if , then .
Extremal Clause

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