In the sequence alignment problem, suppose you knew that the input strings were relatively similar, in the sense that there is an optimal alignment that uses at most k gaps, where k is much smaller than the lengths m and n of the strings. Show how to compute the NW score in O((m+n)k) time.

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A: Let ENFA = {N | N is an NFA and L(N) = Ø}. Prove that ENFA is in P.