Economics 14.odt - Prove that each of the following...

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Prove that each of the following languages is decidable.4a. {<D, R> : D is a DFA and R is a regex and there exists a string that’s accepted by one but not the other} Based on the basics learned in class you should know that EQ DFA={A,B|A and B are DFAs and L(A) =L(B)}is decidable.Lets use M as a Turing machine that decides this language. We construct a new TM M′ that uses M to decide EQ DFA..RE as follows:M′= “On inputD,R, where Dis a DFA andRis a regular expression:1.Convert R to an equivalent DFA A by using the procedure for the conversion given in Theorem 1.28.2.Run M onD,A.3.If M accepts, accept; if M rejects, reject.” 4.Since M accepts iff L(D) =L(A), and since L(A) =L(R) this procedure is correct.

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