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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: DDD correctly emulated by HHH is correctly rejected as
 non-halting.
Date: Sun, 14 Jul 2024 09:13:41 -0500
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On 7/14/2024 3:40 AM, Mikko wrote:
> On 2024-07-13 12:22:24 +0000, olcott said:
> 
>> On 7/13/2024 3:00 AM, Mikko wrote:
>>> On 2024-07-12 13:20:53 +0000, olcott said:
>>>
>>>> On 7/12/2024 3:03 AM, Mikko wrote:
>>>>> On 2024-07-11 14:10:24 +0000, olcott said:
>>>>>
>>>>>> On 7/11/2024 1:25 AM, Mikko wrote:
>>>>>>> On 2024-07-10 17:53:38 +0000, olcott said:
>>>>>>>
>>>>>>>> On 7/10/2024 12:45 PM, Fred. Zwarts wrote:
>>>>>>>>> Op 10.jul.2024 om 17:03 schreef olcott:
>>>>>>>>>> typedef void (*ptr)();
>>>>>>>>>> int HHH(ptr P);
>>>>>>>>>>
>>>>>>>>>> void DDD()
>>>>>>>>>> {
>>>>>>>>>>    HHH(DDD);
>>>>>>>>>> }
>>>>>>>>>>
>>>>>>>>>> int main()
>>>>>>>>>> {
>>>>>>>>>>    HHH(DDD);
>>>>>>>>>> }
>>>>>>>>>
>>>>>>>>> Unneeded complexity. It is equivalent to:
>>>>>>>>>
>>>>>>>>>        int main()
>>>>>>>>>        {
>>>>>>>>>          return HHH(main);
>>>>>>>>>        }
>>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>> Every time any HHH correctly emulates DDD it calls the
>>>>>>>> x86utm operating system to create a separate process
>>>>>>>> context with its own memory virtual registers and stack,
>>>>>>>> thus each recursively emulated DDD is a different instance.
>>>>>>>
>>>>>>> However, each of those instances has the same sequence of 
>>>>>>> instructions
>>>>>>> that the x86 language specifies the same operational meaning.
>>>>>>>
>>>>>>
>>>>>> *That is counter-factual*
>>>>>> When DDD is correctly emulated by HHH according to the
>>>>>> semantics of the x86 programming language HHH must abort
>>>>>> its emulation of DDD or both HHH and DDD never halt.
>>>>>
>>>>> There is not "must" anywhere in the semantics of the programming 
>>>>> language.
>>>>>
>>>>
>>>> The semantics of the language specifies the behavior of
>>>> the machine code thus deriving the must.
>>>
>>> How can one derive "must" from the semantics of the machine code?
>>>
>>
>> Deciders are required to (thus must) halt.
> 
> The semantics of the x86 language does not require that, nor that any of
> the programs is a decider.
> 

The subject our our conversion is a simulating termination
analyzer AKA partial halt decider that accepts a finite string
of x86 code as specifying halting behavior or rejects this
finite string. Deciders are required to halt thus must abort
the emulation of any input that would prevent this.

*You can comprehend this is a truism or fail to*
*comprehend it disagreement is necessarily incorrect*
Any input that must be aborted to prevent the non
termination of HHH necessarily specifies non-halting
behavior or it would never need to be aborted.

Technically any program that halts is a decider.
In the early days simply halting was acceptance of the input.
The input was rejected by getting stuck in an infinite loop.

In computability theory, a decider is a Turing machine that
halts for every input.
https://en.wikipedia.org/wiki/Decider_(Turing_machine)

*Here the the definition that I go by*
Intuitively, a decider should be a Turing machine that given
an input, halts and either accepts or rejects, relaying its
answer in one of many equivalent ways, such as halting at
an ACCEPT or REJECT state, or leaving its answer on the output
tape. https://cs.stackexchange.com/questions/84433/what-is-decider

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