Question

1 (40 points) Consider the following NFAs (a) and (b) below: a 1 1 b a,b 2 (a) ? a 2 a,b 3 b (b) Answer the following questions: (a) (5 points) Give a formal definition of the NFA (a) (b) (10 points) As discussed in class, every NFA has an equivalent DFA. Give the for- mal definition of the DFA A (equivalent to NFA (a)) according to the construction given in Theorem 1.39. (c) (5 points) Draw the state diagram of the DFA A. (d) (5 points) Give a formal definition of the NFA (b) (e) (10 points) As discussed in class, every NFA has an equivalent DFA. Give the for- mal definition of the DFA B (equivalent to NFA (b)) according to the construction given in Theorem 1.39. (f) (5 points) Draw the state diagram of the DFA B.

          1 (40 points) Consider the following NFAs (a) and (b) below:
a
1
1
b
a,b
2
(a)
?
a
2
a,b
3
b
(b)
Answer the following questions:
(a) (5 points) Give a formal definition of the NFA (a)
(b) (10 points) As discussed in class, every NFA has an equivalent DFA. Give the for-
mal definition of the DFA A (equivalent to NFA (a)) according to the construction
given in Theorem 1.39.
(c) (5 points) Draw the state diagram of the DFA A.
(d) (5 points) Give a formal definition of the NFA (b)
(e) (10 points) As discussed in class, every NFA has an equivalent DFA. Give the for-
mal definition of the DFA B (equivalent to NFA (b)) according to the construction
given in Theorem 1.39.
(f) (5 points) Draw the state diagram of the DFA B.

1 (40 points) Consider the following NFAs (a) and (b) below:
a
1
1
b
a,b
2
(a)
?
a
2
a,b
3
b
(b)
Answer the following questions:
(a) (5 points) Give a formal definition of the NFA (a)
(b) (10 points) As discussed in class, every NFA has an equivalent DFA. Give the for-
mal definition of the DFA A (equivalent to NFA (a)) according to the construction
given in Theorem 1.39.
(c) (5 points) Draw the state diagram of the DFA A.
(d) (5 points) Give a formal definition of the NFA (b)
(e) (10 points) As discussed in class, every NFA has an equivalent DFA. Give the for-
mal definition of the DFA B (equivalent to NFA (b)) according to the construction
given in Theorem 1.39.
(f) (5 points) Draw the state diagram of the DFA B.

Added by Francisca F.

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