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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: Infinite set of HHH/DDD pairs --- truisms
Date: Mon, 22 Jul 2024 10:08:03 -0500
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On 7/22/2024 9:32 AM, joes wrote:
> Am Mon, 22 Jul 2024 09:13:33 -0500 schrieb olcott:
>> On 7/22/2024 3:01 AM, Mikko wrote:
>>> On 2024-07-21 13:50:17 +0000, olcott said:
>>>> On 7/21/2024 4:38 AM, Mikko wrote:
>>>>> On 2024-07-20 13:28:36 +0000, olcott said:
>>>>>> On 7/20/2024 3:54 AM, Mikko wrote:
>>>>>>> On 2024-07-19 14:39:25 +0000, olcott said:
>>>>>>>> On 7/19/2024 3:51 AM, Mikko wrote:
> 
>>>>>>> Anyway you did not say that some HHHᵢ can simulate the
>>>>>>> corresponding DDDᵢ to its termination. And each DDDᵢ does
>>>>>>> terminate, whether simulated or not.
> 
> 
>>>> Then DDD correctly simulated by any pure function HHH cannot possibly
>>>> reach its own return instruction and halt, therefore every HHH is
>>>> correct to reject its DDD as non-halting.
>>> That does not follow. It is never correct to reject a halting
>>> comoputation as non-halting.
>> In each of the above instances DDD never reaches its return instruction
>> and halts. This proves that HHH is correct to report that its DDD never
>> halts.
> It can't return if the simulation of it is aborted.
> 
>> Within the hypothetical scenario where DDD is correctly emulated by its
>> HHH and this HHH never aborts its simulation neither DDD nor HHH ever
>> stops running.
> In actuality HHH DOES abort simulating.
> 
>> This conclusively proves that HHH is required to abort the simulation of
>> its corresponding DDD as required by the design spec that every partial
>> halt decider must halt and is otherwise not any kind of decider at all.
> Like Fred recognised a while ago, you are arguing as if HHH didn't abort.
> 
>> That HHH is required to abort its simulation of DDD conclusively proves
>> that this DDD never halts.
> You've got it the wrong way around.
> 

I am talking about hypothetical possible ways that HHH could be encoded.
(a) HHH(DDD) is encoded to abort its simulation.
(b) HHH(DDD) is encoded to never abort its simulation.

Therefore (a) is correct and (b) is incorrect according to the
design requirements for HHH that it must halt.

It is also a truism that any input that must be aborted
is a non-halting input.

-- 
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer