Let L₄ be the language over = {0, 1} generated by the regular expression (01)*.

(a) Using the construction given in Theorem 1.54, draw the state diagram of L4.

(b) Using the subset construction given in Theorem 1.39, convert the NFA from part (a) into a DFA. (It suffices to draw the state diagram.) Your life will be much easier if you first get rid of all useless -transitions in your answer from part (a).