(a) Given a Turing machine M with an input string w, describe a TM M 3 with the property that M accepts w if only if M 3 accepts 0 (To describe M 3 , consider an arbitrary input string x and say how M 3 operates on x Thus, description of M 3 should begin with M 3 on input x b) What does part (a) imply about the language L M 3 M 3 is a TM that accepts 0

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Question: (a) Given a Turing machine M with an input string w, describe a TM M 3 with the property that M accepts w if &

(a) Given a Turing machine M with an input string w, describe a TM M₃ with the property that M accepts w if & only if M₃ accepts 0. (To describe M₃, consider an arbitrary input string x and say how M₃ operates on x. Thus, description of M₃ should begin with: "M₃ on input x: .... ". b) What does part (a) imply about the language L = { < M₃> | M₃ is a TM that accepts 0}.

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