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From: joes <noreply@example.org>
Newsgroups: comp.theory
Subject: Re: The halting problem as defined is a category error
Date: Thu, 24 Jul 2025 10:07:51 -0000 (UTC)
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Am Wed, 23 Jul 2025 16:08:51 -0500 schrieb olcott:
> On 7/23/2025 3:56 PM, joes wrote:
>> Am Wed, 23 Jul 2025 15:14:35 -0500 schrieb olcott:
>>> On 7/23/2025 2:06 PM, joes wrote:
>>>> Am Wed, 23 Jul 2025 09:24:15 -0500 schrieb olcott:
>>>>> On 7/23/2025 8:31 AM, joes wrote:
>>>>>> Am Wed, 23 Jul 2025 07:22:55 -0500 schrieb olcott:

>>>>> The actual behavior that is actually specified must include that in
>>>>> both of these cases recursive simulation is specified. We can't just
>>>>> close our eyes and pretend otherwise.
>>>> That is what HHH does: close its eyes and pretend that DDD called a
>>>> pure simulator instead of recursing. See below.
>>>>
>>> That you don't understand my code is ot a rebuttal. HHH simulate DDD
>>> that calls HHH(DDD) that causes the directly executed HHH to simulate
>>> itself simulating DDD until this simulated simulated DDD calls a
>>> simulated simulated HHH(DDD).
>> 
>> Of course, and then it incorrectly assumes that an unaborted simulation
>> *of this HHH*, which does in fact abort, wouldn't abort.
>> 
> If HHH(DDD) never aborts its simulation then this HHH never stops
> running.
If HHH (which aborts) was given to a UTM/pure simulator, it would
stop running. 

>>>>>> No, the best way to determine what the input "specifies" is to just
>>>>>> run it or use a UTM - unless you actually mean the behaviour of HHH
>>>>>> simulating DDD, in which case it is always tautologically correct.
>>>>
>>> HHH itself *is itself* a UTM that is smart enough to not get stuck in
>>> non-halting behavior. That is why I named my operating system x86UTM.
>> 
>> I.e. not a UTM. Those wouldn't need to halt on inputs that don't halt
>> *by themselves*, which DDD isn't.
>
> I red car *is* a car.
> A UTM that is also a halt decider is a UTM.

A car that is also a bicycle is not a car.
The simulation of a non-halting input doesn't halt.

-- 
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.