1. Give state diagrams of DFAs with as few states as you can recognizing the following languages.

L3 = {w | w is a string of the form x1y1x2y2 . . . xnyn for some natural number n such that if x is the integer with binary representation x1x2 . . . xn and y is the integer with binary representation y1y2 . . . yn then x > y}. Both x and y are presented starting from the most significant bit and can have leading 0s