Question

String digit sums. Consider strings over the alphabet 2= {0,1,2,3,4,5,6,7,8,9). We will recursively define the digsum function as follows: • digsum(€)=0 • digsum(ax)=a + digsum(x), where a e is interpreted as the numeric value of the digit.

Answer 1

For a $\epsilon$ L_odd, it should be odd. So for a single character, it is alway odd.

Now for ax $\epsilon$ L_odd, a should be even. Sum of an even and odd number is odd, so this case always yields an odd number.

Now for axb $\epsilon$ L_odd, a and b should be odd. Sum of two odd numbers is odd, and sum of an even and odd number is odd, so this case always yields an odd number too.

So, it will always result in odd.