Fix strings x and y, |x| < |y| = n. For any 2 strings of different lengths, there is a DFA with O(logn) states that accept x and rejects y. Prove that this DFA exists.
My approach: I tried to find such a DFA and one obv one is with 2n states that accept x and rejects y. and now I know we use Myhill Nerode relations to minimize DFA but I have no idea how to find the equivalence classes so that I can minimize this DFA.