GATE | GATE CS 2018 | Question 26

Let N be an NFA with n states. Let k be the number of states of a minimal DFA which is equivalent to N. Which one of the following is necessarily true?

(A) k ≥ 2n
(B) k ≥ n
(C) k ≤ n2
(D) k ≤ 2n

Answer: (D)

Explanation: The minimum number of state in DFA will be 1 when we have only starting state and all other states will not be reachable from stating state.
The maximum number of state in DFA will be 2n as the number of subsets of a set with n elements in the worst case.

Therefore, k ≤ 2n
Option (D) is correct.

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