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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 09:34:57 -0500
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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:
>>>> When the simulation stops running the whole program exits to the
>>>> operating system.
> Yes. That doesn't mean that DDD itself would terminate.
> 
Correct.

>> Because (a) We know that it is a logical impossibility for any decider
>> HHH to report on the halt status of any input that does the opposite of
>> whatever it reports.
>> (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.

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.

>> 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).

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