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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 13:41:02 -0500
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On 3/28/2025 8:53 AM, Richard Damon wrote:
> On 3/27/25 10:10 PM, olcott wrote:
>> On 3/27/2025 8:24 PM, dbush wrote:
>>> On 3/27/2025 9:21 PM, olcott wrote:
>>>> On 3/27/2025 8:09 PM, dbush wrote:
>>>>> On 3/27/2025 9:07 PM, olcott wrote:
>>>>>> On 3/27/2025 7:38 PM, dbush wrote:
>>>>>>> On 3/27/2025 8:34 PM, olcott wrote:
>>>>>>>> On 3/27/2025 7:12 PM, dbush wrote:
>>>>>>>>> On 3/27/2025 8:11 PM, olcott wrote:
>>>>>>>>>> On 3/27/2025 7:02 PM, dbush wrote:
>>>>>>>>>>> On 3/27/2025 7:36 PM, olcott wrote:
>>>>>>>>>>>> On 3/27/2025 1:27 PM, dbush wrote:
>>>>>>>>>>>>> On 3/27/2025 1:50 PM, olcott wrote:
>>>>>>>>>>>>>> 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:
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> _DDD()
>>>>>>>>>>>>>>>> [00002172] 55         push ebp      ; housekeeping
>>>>>>>>>>>>>>>> [00002173] 8bec       mov  ebp,esp  ; housekeeping
>>>>>>>>>>>>>>>> [00002175] 6872210000 push 00002172 ; push DDD
>>>>>>>>>>>>>>>> [0000217a] e853f4ffff call 000015d2 ; call HHH(DDD)
>>>>>>>>>>>>>>>> [0000217f] 83c404     add  esp,+04
>>>>>>>>>>>>>>>> [00002182] 5d         pop  ebp
>>>>>>>>>>>>>>>> [00002183] c3         ret
>>>>>>>>>>>>>>>> Size in bytes:(0018) [00002183]
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> 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.
>>>>>>>>>>>>>> HHH correctly rejects DDD because DDD correctly
>>>>>>>>>>>>>> emulated by HHH cannot possibly reach its own
>>>>>>>>>>>>>> final halt state.
>>>>>>>>>>>>>
>>>>>>>>>>>>> In other words, HHH is not a halt decider because it is not 
>>>>>>>>>>>>> computing the required mapping:
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> Troll
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> On Monday, March 6, 2023 at 3:19:42 PM UTC-5, olcott wrote:
>>>>>>>>>>>  > In other words you could find any error in my post so you 
>>>>>>>>>>> resort to the
>>>>>>>>>>>  > lame tactic of ad hominem personal attack.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> Troll
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> On 7/22/2024 10:51 AM, olcott wrote:
>>>>>>>>>  > *Ad Hominem attacks are the first resort of clueless wonders*
>>>>>>>>>
>>>>>>>>
>>>>>>>> I corrected your error dozens of times and you
>>>>>>>> ignore these corrections and mindlessly repeat
>>>>>>>> your error like a bot 
>>>>>>>
>>>>>>> Which is what you've been doing for the last three years.
>>>>>>>
>>>>>>> Projection, as always.  I'll add the above to the list.
>>>>>>>
>>>>>>
>>>>>> TM's cannot possibly ever report on the behavior
>>>>>> of the direct execution of another TM. 
>>>>>
>>>>> False:
>>>>>
>>>>
>>>> I did not say that no TM can ever report on
>>>> behavior that matches the behavior of a directly
>>>> executing TM.
>>>
>>> Good, because that's all that's required for a solution to the 
>>> halting problem:
>>>
>>
>> There are sometimes when the behavior of TM Description
>> D correctly simulated by UTM1 does not match the behavior
>> correctly simulated by UTM2.
> 
> Show a case.
> 
> Remember the DEFINITION of a UTM, it is a machine that exactly 
> reproduces the behavior of the program that is decribed by its input.

Then that definition is incorrect.
When a finite number of steps of input D are simulated
according to the semantics of its language the directly
executed D halts and the D that calls its own UTM never halts.

I spent years carefully studying this as the Peter Linz
example. https://www.liarparadox.org/Linz_Proof.pdf

When Ĥ is applied to ⟨Ĥ⟩
and embedded_H is a UTM based halt decider
Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞
Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn

Pages 4-6
https://www.researchgate.net/publication/374806722_Does_the_halting_problem_place_an_actual_limit_on_computation

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