Myhill graph of the automaton, Theory of Computation

Exercise:  Give a construction that converts a strictly 2-local automaton for a language L into one that recognizes the language Lr. Justify the correctness of your construction. (That is, verify that the language that is recognized by the automaton your construction produces is actually the reversal of the language the given automaton recognizes.) What is the effect of your construction on the Myhill graph of the automaton?

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To see this, note that if there are any cycles in the Myhill graph of A then L(A) will be infinite, since any such cycle can be repeated arbitrarily many times. Conversely, if the