CS 390 Test II

June 16, 1998

1. Let S and T be sets of states of an NFA- .
(a) Prove that by structural induction.
(b) Show that is in general not equal to .

2. Prove that { } is not regular.

3. Find an NFA that accept the same language as the following NFA-

The initial state is and the accepting state is .

4. For the NFA given below answer the following questions:
(a) Find R(3,3,3) using the recursive formula given by Kleene's Theorem.
(b) Verify that R(3,3,3) obtained in (a) is equal to .

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