Let

? ₃ contains all size 3 columns of 0s and 1s. A string of symbols in ? gives three rows of 0s and 1s. Consider each row to be a binary number and let

B = {w ? ? | the Bottom row of w is the sum of the top two rows }

Show that B is regular.

Hint: It is easier to work with B ^R and construct a finite automaton that checks the sum from right to left.

I 0 0 = 3 {]-[88][B]}- I 0