Problems 145 13. () For the examples derived earlier, which algorithmic method produces product ma chines with fewer states, the direct (Problem 5) or the NFA (Problem 8)7 what are the maximum number of states possible in each of the machines corre- (b) By building NFAs and then converting them into FAs. (ii) If some automaton, FA, has n states and some other automaton, FA2, has m states, sponding to FA, + FA, FA, FA, (FA)* that are produced. (a) By the subset method described in the proof of Kleene's theorem. 14. Convert each of the following NFAs into FAs using the constructive algorithm presented in Proof 2 of Theorem 7,. (iv) Stat