Consider the compute decision problem: Does Turing machine M compute u on input

Question

Consider the compute decision problem: Does Turing machine M compute u on input w?

A notation for the “yes” answer is:

                                    q0 w |--*M q f u

Meaning: If M starts in state q0 with its read-write head positioned on the first character in w, then after some sequence of moves, M is arrive in a final state qf with some string u on the tape.

For a “no” answer, machine M can make no sequence of moves from q0w to qfu.

Show that there is no Turing machine MC that decides the compute problem. That is, there is no machine MC whose behavior is:

                            MC(M, w,u) = { yes q0w |--* M q f u

                                                    no         otherwise

(Hint: Assume MC exists and use it to construct a Turing machine that decides the halting problem. Use a machine M' that enumerates all of the strings u * .)

Explain plz. I want to learn

Explanation / Answer

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