12. (12%) Consider the language {ucw | u, w {a,b}*, |ula = |Wlb}, which comprises the words made from a's and b's that are divided into two parts by c such that the number of a's in the left-hand part is the same as the number of b's in the right-hand part. 3 (a) Design a context-free grammar that generates this language. (b) Design a push-down automaton that accepts this language. (c) What is the language over {a,b} defined by the following context-free grammar with start variable S: S asa, S + Tb, T +T, T + b Is this language regular? Give an informal explanation of your