1. Find an NFA-
for the regular expression 
. 2. Let
denote the set of states that can be reached from p by k
-transitions (i.e. through k -transitions) in an NFA- .
Answer the following questions. (a) Inductively (i.e. recursively) define
for natural numbers k. (b) Prove by induction that for any natural number k
. Note that
is defined inductively for a set S of states as follows: Basis:
Induction: For any state q, if
, then 
. Extremal Clause
3. Find an NFA equivalent to the NFA-
of Fig. 1 on the next page. 4. Find an FA equivalent to the NFA of Fig. 2 on the next page.
5. Find the (Kleene) star (i.e. *) of the NFA-
of Fig. 3 on the next page.