Write a DFA to be a mod-4 machine (a machine that accepts strings in which the number of a's mod 4 is equal to the number of b's mod 4) that accepts strings over the alphabet {a, b}.

It accepts strings, where both the number of a's and the number of b's are multiples of 4, or the number of a's and the number of b's, are each one more than a multiple of 4, or the number of a's and the number of b's are each two more than a multiple of 4, and finally when the number of a's and the number of b's are each three more than a multiple of 4.

So aaaa, bbabaa, bbabbabaaaaaaa would be accepted, but aaaabbb would not.

Also any character that is not an 'a' or a 'b' causes the string to reject.