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Given a NFA with N states, the maximum number of states in an equivalent minimized DFA is at least.

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Given a NFA with N states, the maximum number of states in an equivalent minimized DFA is at least.

(a) N^2

(b) 2^N

(c) 2N

(d) N!

This question was addressed to me during an online exam.

My question is taken from Finite Automata and Regular Expressions topic in division Compiler Introduction of Compiler

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Right choice is (b) 2^N

To explain: The initial state of the DFA constructed from this NFA is the set of all NFA states that are reachable from state 1 by ε-moves; that is, it is the set {1, 2, and 3}. A transition from states1, 2, and 3 by input symbol 0 must follow either the arrow from state 1 to 2, or from state 3 to 4. Also, neither state 2 nor 4 have outgoing ε-moves.

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