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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: Hypothetical possibilities
Date: Mon, 22 Jul 2024 10:05:41 -0500
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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.

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