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From: joes <noreply@example.org>
Newsgroups: comp.theory
Subject: Re: DDD specifies recursive emulation to HHH and halting to HHH1
Date: Sun, 30 Mar 2025 08:32:45 -0000 (UTC)
Organization: i2pn2 (i2pn.org)
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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).

-- 
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.