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Consider an NFA on n states. Is it possible to determine whether it is empty accepts all strings in poly(n) time?

Suppose the NFA above has an equivalent DFA on d states. Is it possible to construct this DFA in poly(n,d) time?

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Emptiness and determinization of NFAs

Consider an NFA on n states. Is it possible to determine whether it is empty in poly(n) time?

Suppose the NFA above has an equivalent DFA on d states. Is it possible to construct this DFA in poly(n,d) time?