Prove that for each n 0, a language Bn exists where a B n is recognizable by an NFA that has n states, and b if B n A 1 A k , for regular languages A i , then at least one of the A i requires a DFA with exponentially many states

Question: Prove that for each n > 0, a language Bn exists where a. B n is recognizable by an NFA that has n states, and

Prove that for each n > 0, a language Bn exists where

a. B_n is recognizable by an NFA that has n states, and

b. if B_n = A₁ ∪ · · · ∪ A_k, for regular languages A_i, then at least one of the A_i requires a DFA with exponentially many states.

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