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From: joes <noreply@example.org>
Newsgroups: comp.theory
Subject: Re: My reviewers think that halt deciders must report on the behavior
 of their caller
Date: Thu, 10 Jul 2025 10:12:44 -0000 (UTC)
Organization: i2pn2 (i2pn.org)
Message-ID: <c74920a0e6e73da1eb8a57b10e7ebf930af8fd88@i2pn2.org>
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Am Wed, 09 Jul 2025 11:06:03 -0500 schrieb olcott:
> On 7/9/2025 10:42 AM, joes wrote:
>> Am Wed, 09 Jul 2025 09:06:42 -0500 schrieb olcott:
>>> On 7/9/2025 8:37 AM, joes wrote:
>>>> Am Wed, 09 Jul 2025 08:02:16 -0500 schrieb olcott:
>>>>> On 7/9/2025 3:58 AM, Fred. Zwarts wrote:

>>>>> All Turing machine deciders only compute the mapping from their
>>>>> actual inputs. This entails that they never compute any mapping from
>>>>> non-inputs.
>>>> It matters more what they map it to, i.e. which mapping they compute.
>>>> HHH does not compute the halting function.
>>> It is a matter of verified fact that HHH does correctly determine that
>>> DDD correctly emulated by HHH cannot possibly reach its own emulated
>>> final halt state.
>> Yes. That is not the halting function.
> Yes it is the halting function.
> The actual question posed to HHH is:
> Does your input specify behavior that cannot reach its own final halt
> state?
Yes, that is not the mathematical function that pairs encodings of
programs with their halting state.

>> I have another program here that (tautologically) determines that it
>> cannot simulate ANY code (according to x86 semantics) to a halting
>> state - by simulating zero steps :-) That tells me nothing about
>> whether the input halts when executed.
> That changes the words of the question thus becomes the strawman error.
No, it answers the same question as HHH: does the simulation halt?

>> How can your beloved Aprove even say anything about its inputs?
Since programs are not in its domain...

>>>> How could HHH abort and not halt?
>>> None of the code in HHH can possibly help DDD correctly emulated by
>>> HHH to reach its own emulated final halt state.
>> The abort could, if you hadn't botched it with static variables.
> DDD emulated by HHH according to the semantics of the x86 language
> continues to emulate the first four instructions of DDD in recursive
> emulation until HHH aborts its emulation immediately killing every DDD
> before any of them reach their own "ret" instruction.
Or before they reach the abort.

> I keep asking for your credentials because you seem to not have enough
> technical knowledge about ordinary programming.
Doesn't sound like a degree would convince you.

>>> The behavior that the input to HHH(DDD) actually specifies is the only
>>> behavior that any decider can possibly report on.
>>> That anyone believes that HHH is required to report on the behavior of
>>> a non-input merely proves a lack of sufficient understanding of how
>>> Turing machine deciders work.
>> Yes, what a processor does - turning code into behaviour - is clearly
>> uncomputable.
I'll take that as agreement.

-- 
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.