I have simple problem involving finite automaton.
Let 'A' be some (infinite) language which is a subset of natural
numbers.
Let B(A) the the language over the alphabet {0,1} such that B(A)
contains all (and only) the members of A in binary form.
Similarly let C(A) contain all (and only) the members of A in base 3.
For example, let A = { 3 , 5 } then
B(A) = { 11, 101 } and C(A) = { 10, 12 }. Here I used finite A but A is
actually infinite.
Now the problem is to find an A such that B(A) is regular language (an
NFA exists for this) but C(A) is not regular.
Thanks
