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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

Answer»

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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