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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: DDD specifies recursive emulation to HHH and halting to HHH1
Date: Fri, 28 Mar 2025 13:56:31 -0500
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On 3/27/2025 5:01 PM, joes wrote:
> Am Thu, 27 Mar 2025 12:50:12 -0500 schrieb olcott:
>> On 3/27/2025 2:18 AM, Fred. Zwarts wrote:
>>> Op 27.mrt.2025 om 04:09 schreef olcott:
>>>> On 3/26/2025 8:22 PM, Richard Damon wrote:
> 
>>>>> Non-Halting is that the machine won't reach its final staste even if
>>>>> an unbounded number of steps are emulated. Since HHH doesn't do that,
>>>>> it isn't showing non-halting.
>>>> DDD emulated by any HHH will never reach its final state in an
>>>> unbounded number of steps.
>>>> DDD emulated by HHH1 reaches its final state in a finite number of
>>>> steps.
>>> It is not very interesting to know whether a simulator reports that it
>>> is unable to reach the end of the simulation of a program that halts in
>>> direct execution.
>> That IS NOT what HHH is reporting.

> That is exactly what it does, and you have said so before(tm).
> 

You are saying that HHH is reporting that HHH is screwing
up THAT IS FALSE. HHH IS REPORTING THAT DDD IS SCREWING UP.

>> HHH correctly rejects DDD because DDD correctly emulated by HHH cannot
>> possibly reach its own final halt state.

> DDD doesn't *do* anything, it is being simulated. HHH can't reach
> DDD's existing halt state.
> 

DDD specifies a recursive emulation relationship with HHH

>>> It is interesting to know:
>>> 'Is there an algorithm that can determine for all possible inputs
>>> whether the input specifies a program that [...]
>>> halts when directly executed?'
>>> This question seems undecidable for Olcott.
>> It is the halts while directly executed that is impossible for all
>> inputs. No TM can ever report on the behavior of the direct execution of
>> any other TM.
> The direct execution of a TM is obviously computable from its description.
> 
>> A TM can only report on the behavior that the machine code of another TM
>> specifies. When it specifies a pathological relationship then the
>> behavior caused by the pathological relationship MUST BE REPORTED.

> No, the machine code doesn't "specify a pathological relationship", that
> is purely a feature of trying to simulate it with the included simulator.
> 
The classic HP counter-example input HAS ALWAYS SPECIFIED
A PATHOLOGICAL RELATIONSHIP TO ITS DECIDER.

The question has always been what Boolean value can H
correctly return when D is able to do the opposite of
whatever value that H returns?

When we prove that it is impossible for D to do the
opposite of whatever value that H returns the original
question becomes moot.

-- 
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer