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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: comp.theory
Subject: Re: Hypothetical possibilities
Date: Tue, 23 Jul 2024 10:32:06 +0300
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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.

-- 
Mikko