Does there exist a universal finite automaton? More precisely, is there a DFA U such that L(U) is equal to the language L = {(D, w) | D is a DFA and w is a string that D accepts.}? In the above. (D, w) represents the encoding of the DFA D and the string w using some sensible encoding scheme, perhaps similar to the one used in the discussion of the universal Turing machine. The actual details of the encoding shouldn't matter in your solution. Note that an equivalent question is to determine if the language L is regular