Show that both conditions in Problem 5.28 are necessary for proving that P is undecidable. Problem 5.28
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Show that both conditions in Problem 5.28 are necessary for proving that P is undecidable.
Problem 5.28
Let P be any nontrivial property of the language of a Turing machine. Prove that the problem of determining whether a given Turingmachine’s language has property P is undecidable.
In more formal terms, let P be a language consisting of Turing machine descriptions where P fulfills two conditions. First, P is nontrivial—it contains some, but not all, TM descriptions. Second, P is a property of the TM’s language—whenever L(M1) = L(M2), we have 〈M1〉 ∈ P iff 〈M2〉 ∈ P. Here, M1 and M2 are any TMs. Prove that P is an undecidable language.
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The problem of determining whether a given Turing machines language has property P is known as the P...View the full answer
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