If a language (L) is recognized by an n-state NFA, can it also be recognized by a DFA with no more than 2 ^ n states?

Question

I think so, because the upper bound would be 2 ^ n, and given that these are both finite machines, the intersection of both the n-state NFA and the DFA with 2 ^ n or less states would be valid.

Am I wrong here?

Answer 1

You're right. 2 ^ n is the upper limit, so the generated DFA cannot have more states than this limit. But this is the worst case scenario. In most common scenarios there are fewer states than in the resulting DFA. Sometimes it can be even less than in the original NFA.

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Answer 2

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