Re: DDD specifies recursive emulation to HHH and halting to HHH1

Am Sat, 29 Mar 2025 16:33:13 -0500 schrieb olcott:

On 3/29/2025 2:51 PM, joes wrote:

Am Sat, 29 Mar 2025 13:54:22 -0500 schrieb olcott:

On 3/29/2025 4:19 AM, joes wrote:

 

Even a constant function is a "computation", even if it doesn't
actually do any work.

That is not transforming an input finite string into its corresponding
output finite string.

Yes it is: transforming every input into the same output.

Deciders must transform inputs into accept or reject states on the basis
of a syntactic or semantic property specified by the input.

If every input has length 5, you don't need to transform anything.

The actual requirement is to compute the mapping from a finite
string to its length using a sequence of algorithmic steps.
Likewise for halting. Compute the mapping from a finite string of
machine code to the behavior that this finite string specifies.

Do you reckon the direct execution of a TM contradicts the
specification?

Direct execution itself cannot possibly contradict anything.
Read what I said above as many times as needed to get it.

I don't, that's why I ask. The direct execution of D contradicts
the return value of H(D).

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Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.