Let M = (Q, 2, 8, s, F) be a DFA. (a) Show that for any qe Q and P C Q, the following language is regular: {we * |S* (q, w) e P} Clearly describe a procedure to construct a DFA for this language, in terms of M. (b) If A is a language over alphabet , define undouble(A) def {w EE* | ww A }. Show that if A is regularthen so is undouble(A). Example: if A = {E, 0, 11,0010, 0101} then undouble(A) = {E, 1,01}. Hint: First consider a simpler version where I fix the middle state q, so: {we * | ww A and S* (s, w) = q} In the real version of the problem, the middle state is not fixed