GATE CS 2018 Set 1 — Question 16
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Theory of Computation → Finite Automata & Regular Languages → NFA to DFA (Subset Construction)
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Question
Let be an NFA with states. Let be the number of states of a minimal DFA which is equivalent to . Which one of the following is necessarily true?
Correct answer
(D) k ≤ 2ⁿ
Solution
According to the subset construction algorithm (also known as the powerset construction), any Nondeterministic Finite Automaton (NFA) with states can be converted into an equivalent Deterministic Finite Automaton (DFA) with at most states. Since is the number of states in the minimal DFA equivalent to , it must be less than or equal to the number of states in any DFA equivalent to . Thus, is necessarily true.
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