b.) Language B can be proved as non regular language
by Myhill – Nerode Theorem ,
suppose set, S = { 01, 001, 0001 …. (0^k)1 ,...}
and, z = 0^k
Now, take two pairs of set S to prove that they are distinguishable i.e, → 0^k1 , 0^n1
.. As , (0^k)(z) = (0^k1)0^k { which is accpeted by L(B) }
and, (0^k)(z) = (0^n1)0^k { which is not accepted by L(B) }
As, by def. of Myhill- Nerode Theorem,
there are infinite distinguishable equivalence strings { corresponding to elements in S }