From Newsgroup: comp.theory

On 8/26/25 11:31 AM, olcott wrote:

On 8/26/2025 2:28 AM, Richard Heathfield wrote:

On 26/08/2025 05:25, olcott wrote:

On 8/25/2025 10:42 PM, Richard Heathfield wrote:

<snip>

DD simulated by HHH is of no interest to the Halting Problem.

The Halting Problem only wants to know whether DD halts.

It does not. It needs HHH to compute the mapping from its input to
the actual behavior actually specified by this input.

The actual behaviour specified by DD is to halt.

It is not the behavior specified by DD that matters.
It is the behavior of the input to HHH(DD) that matters.

And if that differes, you are just working on POOP, and not the Halting Problem.

One way to derive that actual behavior actually specified
by the input to HHH(DD) is DD emulated by HHH according
to the semantics of the x86 language. That DD cannot possibly
halt.

Right, and if HHH tries to do that, it fails to answer. But then that
*IS* what HHH is,

If you start with an HHH that aborts to return 0, then that program HHH doesn't do a correct simulation so you can't use that criteria, but if
you DO a correct simulation of that input by another simulator, we find
it halts.
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