Theorem 1.54: A language is regular if and only if some regular expression describes it

[10 points] 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 e-transitions in your answer from part (a)