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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: Hypothetical possibilities -- I reread this again more carefully
Date: Sun, 21 Jul 2024 10:08:29 -0500
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On 7/21/2024 9:54 AM, joes wrote:
> Am Sun, 21 Jul 2024 09:34:57 -0500 schrieb olcott:
>> On 7/21/2024 9:24 AM, joes wrote:
>>> Am Sun, 21 Jul 2024 08:08:53 -0500 schrieb olcott:
>>>> On 7/21/2024 6:37 AM, Richard Damon wrote:
>>>>> On 7/21/24 12:15 AM, olcott wrote:
> 
>>>> (b) We know that a decider is not allowed to report on the behavior
>>>> computation that itself is contained within. Deciders only take finite
>>>> string inputs. They do not take executing processes as inputs. Thus
>>>> HHH is not allowed to report on the behavior of this int main() {
>>>> DDD(); }.
>>> That IS exactly the input.
>> The behavior of emulated DDD after it has been aborted changes the
>> behavior of the directly existed DDD.
> A deterministic program can't change. It was always going to be aborted.
> 

None-the-less we can examine the exhaustively complete set
of every HHH/DDD pair that can possibly exist and find that
all of the HHH instances that never abort their simulation
of DDD never stop running.

>> When the second call of what would otherwise be infinite recursion is
>> required to be aborted to prevent the infinite execution of the first
>> call this proves that HHH(DDD)==0 is correct even though the directly
>> executed DDD() halts.
> The second call stops simulating just like all others.
> 
>>>> Therefore we map the finite string input to HHH(DDD) to the behavior
>>>> that it species on the basis of DDD correctly emulated by any pure
>>>> function HHH that can possibly exist.
>>> The basis is the direct behaviour.
>> Unless you think the idea of UTMs is wrong-headed nonsense the behavior
>> of DDD correctly emulated by HHH determines the actual behavior
>> specified by the input to HHH(DDD).
> HHH is not an UTM.
> 

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