Consider the language {ucw | u, w {a, b} , |u|a = |w|b}, which comprises the words made from as and bs that are divided into two parts by c such that the number of as in the left-hand part is the same as the number of bs in the right-hand part.

(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 bT b, T bT, T b

Is this language regular?