GATE | Gate IT 2008 | Question 6

Let N be an NFA with n states and let M be the minimized DFA with m states recognizing the same language. Which of the following in NECESSARILY true?
(A) m ≤ 2ⁿ
(B) n ≤ m
(C) M has one accept state
(D) m = 2ⁿ


Answer: (A)

Explanation: A state in a DFA is proper subset of states of NFA of corresponding DFA

=> set of states of NFA =n

=> no of subsets of a set with n elements = 2ⁿ

=> m<=2ⁿ

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