3. Find pushdown automata which accept (by empty stack and final state) the following lan guages over A = {a, b): (a) L = { I num(b, z) = 2 * num(a,z)), where num(a, x) denotes the number of symbols a in the string r; Hint: Push each symbol a on the stack as a pair of symbols, or match it with two symbols b on the stack. Make sure that the string bab is accepted (b) L {z A. I num(a,z) = num(b,z) ^ all sequences of a's have even length) = where num(a, x) denotes the number of occurrences of a in the string r