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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: Hypothetical possibilities
Date: Tue, 23 Jul 2024 09:41:11 -0500
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On 7/23/2024 2:32 AM, Mikko wrote:
> On 2024-07-22 15:05:41 +0000, olcott said:
> 
>> On 7/22/2024 6:05 AM, Mikko wrote:
>>> On 2024-07-20 15:28:31 +0000, olcott said:
>>>
>>>> void DDD()
>>>> {
>>>>    HHH(DDD);
>>>> }
>>>>
>>>> int main()
>>>> {
>>>>    DDD();
>>>> }
>>>>
>>>> (a) Termination Analyzers / Partial Halt Deciders must halt
>>>> this is a design requirement.
>>>
>>> For a partial analyzer or deciders this is not always required.
>>>
>>
>> *You can't even get my words correctly*
>> A termination analyzer must report on the behavior of at least
>> one input for all of the inputs of this one input. This is
>> met when a termination analyzer analyzes an input having no inputs.
>>
>> A partial halt decider must correctly determine the halt status
>> of at least one input and its specific input (if any).
>>
>> HHH is both a partial halt decider and a termination analyzer
>> for DDD and a few other inputs having no input.
>>
>>>> (b) Every simulating termination analyzer HHH either
>>>> aborts the simulation of its input or not.
>>>
>>> This must be interpreted to mean that a simulating termination analyzer
>>> may abort its simulation for some simulated abort and simulate others
>>> to the termination.
>>>
>>
>> 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.
>>
>>>> (c) Within the hypothetical case where HHH does not abort
>>>> the simulation of its input {HHH, emulated DDD and executed DDD}
>>>> never stop running.
>>>
>>> The case is not very hypothetical. Given the HHH you already have,
>>> it is fairly easy to construct the "hypothetical" HHH and see what
>>> it actually does.
>>>
>>
>> (a) HHH(DDD) is encoded to abort its simulation.
>> (b) HHH(DDD) is encoded to never abort its simulation.
>>
>>>> This violates the design requirement of (a) therefore HHH must
>>>> abort the simulation of its input.
>>>
>>> The violation simply means that the "hypothetical" HHH is not a
>>> termination analyzer of partial halt decider in sense (a). What
>>> it "must" be or do depends on the requirements.
>>>
>> 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.
> 
> No, it is not. The "must" and "non-halting" belong to different worlds.
> The word "must" blongs to requirements. The word "non-halting" is a
> feature of a program. They are unrelated, so one cannot be inferred
> from the other.
> 

When-so-ever there are two hypothetical possible way to encode
a simulating halt decider for a specific input
(a) one aborts its simulation of DDD
(b) never aborts its simulation of DDD

and the (b) scenario causes DDD to never halt this
(a) is correct to abort and reject this input as non-halting

Trying to disagree with a tautology makes you look very foolish.

If I say that all black cats are cats and you try to get away
with saying some black cats are dogs you are wrong.

<MIT Professor Sipser agreed to ONLY these verbatim words 10/13/2022>
     If simulating halt decider H correctly simulates its input D
     until H correctly determines that its simulated D would never
     stop running unless aborted then

     H can abort its simulation of D and correctly report that D
     specifies a non-halting sequence of configurations.
</MIT Professor Sipser agreed to ONLY these verbatim words 10/13/2022>

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