5. (35 pts.) Does a DFA accept everything? (a) (20 pts.) Describe an efficient algorithm to decide whether a DFA D accepts all strings, i.e. whether L(D) = ?*. You may use standard graph algorithms as subroutines. (b) (5 pts.) What is the asymptotic runtime of your algorithm, assuming D has n states and |?| = m? (c) (10 pts.) Would your algorithm also work for an NFA? If so, explain why. If not, give an example of an NFA where your algorithm returns the wrong answer.

          5. (35 pts.) Does a DFA accept everything?
(a) (20 pts.) Describe an efficient algorithm to decide whether a DFA D accepts all strings, i.e. whether L(D) = ?*. You may use standard graph algorithms as subroutines.
(b) (5 pts.) What is the asymptotic runtime of your algorithm, assuming D has n states and |?| = m?
(c) (10 pts.) Would your algorithm also work for an NFA? If so, explain why. If not, give an example of an NFA where your algorithm returns the wrong answer.

5. (35 pts.) Does a DFA accept everything?
(a) (20 pts.) Describe an efficient algorithm to decide whether a DFA D accepts all strings, i.e. whether L(D) = ?*. You may use standard graph algorithms as subroutines.
(b) (5 pts.) What is the asymptotic runtime of your algorithm, assuming D has n states and |?| = m?
(c) (10 pts.) Would your algorithm also work for an NFA? If so, explain why. If not, give an example of an NFA where your algorithm returns the wrong answer.

Added by Enrique A.

Computer Science and Information Technology

Trishna Knowledge Systems 2018 Edition

Instant Answer

Solved by Expert Akash M

10/18/2023

Step 1

To decide whether a DFA D accepts all strings, we can use the following algorithm: Show more…

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Does a DFA accept everything? a) Describe an efficient algorithm to decide whether a DFA D accepts all strings, i.e. whether L(D) = ̑*. You may use standard graph algorithms as subroutines. b) What is the asymptotic runtime of your algorithm, assuming D has n states and |̑| = m? c) Would your algorithm also work for an NFA? If so, explain why. If not, give an example of an NFA where your algorithm returns the wrong answer.