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I am trying to understand whether it is possible to construct a Turing Machine (TM) that accepts an input if and only if it halts on that input. My question is closely related to the halting problem.

I want to reduce the halting problem on empty input (H_0) to the acceptance problem for TM's on empty input (A_0). My idea for the reduction is:

  1. Clean the tape
  2. Simulate M_w
  3. If M_w halts M_w' is going to accept

Any insights into whether such a construction is theoretically feasible or why it isn't would be greatly appreciated.

Best regards

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Yes.

  1. Transition to an accepting state.
  2. Halt.

This Turing machine accepts all inputs and halts on all inputs.

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