4.30 Let A be a Turing-recognizable language consisting of descriptions of Turing ma- chines, ((M1), (M2), ...), where every M, is a decider. Prove that some decidable language D is not decided by any decider M, whose description appears in A. (Hint: You may find it helpful to consider an enumerator for A.)

C++ Programming: From Problem Analysis to Program Design
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Chapter13: Overloading And Templates
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4.30 Let A be a Turing-recognizable language consisting of descriptions of Turing ma-
chines, ((M1), (M2), ...), where every M, is a decider. Prove that some decidable
language D is not decided by any decider M, whose description appears in A.
(Hint: You may find it helpful to consider an enumerator for A.)
Transcribed Image Text:4.30 Let A be a Turing-recognizable language consisting of descriptions of Turing ma- chines, ((M1), (M2), ...), where every M, is a decider. Prove that some decidable language D is not decided by any decider M, whose description appears in A. (Hint: You may find it helpful to consider an enumerator for A.)
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