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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: How Partial Simulations correctly determine non-halting ---Ben's
 10/2022 analysis
Date: Mon, 10 Jun 2024 10:22:05 -0500
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On 6/10/2024 2:54 AM, Mikko wrote:
> On 2024-06-09 16:15:08 +0000, olcott said:
> 
>> On 6/9/2024 10:13 AM, Mikko wrote:
>>> On 2024-06-09 14:03:08 +0000, olcott said:
>>>
>>>> On 6/9/2024 3:52 AM, Mikko wrote:
>>>>> On 2024-06-08 13:46:07 +0000, joes said:
>>>>>
>>>>>> Am Sat, 08 Jun 2024 08:04:14 -0500 schrieb olcott:
>>>>>>> On 6/8/2024 1:42 AM, Mikko wrote:
>>>>>>>> On 2024-06-07 22:26:05 +0000, olcott said:
>>>>>>>>> On 6/7/2024 4:00 PM, joes wrote:
>>>>>>>>>> Am Fri, 07 Jun 2024 09:47:35 -0500 schrieb olcott:
>>>>>>>>>>> On 6/7/2024 1:30 AM, Mikko wrote:
>>>>>>>>>>>> On 2024-06-06 15:31:36 +0000, olcott said:
>>>>>>>>>>>>> On 6/6/2024 10:14 AM, Mikko wrote:
>>>>>>>>>>>>>> On 2024-06-06 13:53:58 +0000, olcott said:
>>>>>>>>>>>>>>> On 6/6/2024 5:15 AM, Mikko wrote:
>>>>>>>>>>>>>>>> On 2024-06-05 13:29:28 +0000, olcott said:
>>>>>>>>>>>>>>>>> On 6/5/2024 2:37 AM, Mikko wrote:
>>>>>>>>>>>>>>>>>> On 2024-06-04 18:02:03 +0000, olcott said:
>>>>>>
>>>>>>>> Any finite string can be an input to some Turing machine.
>>>>>>>> Can you prove that a Turing machine is not a finite string?
>>>>>>> By definition Turing Machines are not finite strings in the 
>>>>>>> conventional
>>>>>>> model. In my x86utm model of computation x86 machine language 
>>>>>>> <is> the
>>>>>>> input to another function written in the x86 language.
>>>>>> In your model, the machine code is also finite.
>>>>>>
>>>>>>>> Your own attempts of a conter-proof are not about Turing 
>>>>>>>> machines but C
>>>>>>>> programs. C programs are finite strings, so a C program is a valid
>>>>>>>> input to a C program (and a Turing machine, too).
>>>>>>> They are about Turing Machines yet cannot be sufficiently understood
>>>>>>> with less than the 100% compete precision of the x86 language. They
>>>>>>> x86utm model is required to prove that false assumptions about the
>>>>>>> nature of correct simulation are false assumptions.
>>>>>> You can't hide behind an x86 implementation. The same arguments hold.
>>>>>> Which assumptions are false?
>>>>>>
>>>>>>> I have all of the details of the machine code and C code for HH 
>>>>>>> and DDD.
>>>>>>> I can't to the same thing for embedded_H and ⟨Ĥ⟩ ⟨Ĥ⟩ so we have 
>>>>>>> to learn
>>>>>>> by analogy.
>>>>>> Why can't you do that? The simulator can simulate itself.
>>>>>>
>>>>>>>>>>> This means that H is not allowed to report on the behavior of 
>>>>>>>>>>> the
>>>>>>>>>>> directly executed P(P).
>>>>>>>>>> So on which program does it report then?
>>>>>>> DD(DD) is just like infinite recursion that gets terminated at its
>>>>>>> second recursive call. DD(DD) halts only because HH(DD,DD)
>>>>>>> correctly determines that its input DOES NOT HALT.
>>>>>>> If HH(DD,DD) did not correctly determine that its input DOES NOT 
>>>>>>> HALT
>>>>>>> then DD(DD) would never halt.
>>>>>> That doesn't make sense. The function halts because a simulator 
>>>>>> says it
>>>>>> doesn't?
>>>>>
>>>>> You missed an important point: The function halts because a simulator
>>>>> CORRECTLY says it doesn't.
>>>>>
>>>>
>>>> The first recursive call halts because the second recursive
>>>> call has been aborted. That the second recursive call had to
>>>> be aborted proves that the entire computation is non-halting.
>>>>
>>>> DD(DD) is just like infinite recursion that gets terminated at
>>>> its second recursive call. DD(DD) halts only because HH(DD,DD)
>>>> correctly determines that its input DOES NOT HALT.
>>>>
>>>> If HH(DD,DD) did not correctly determine that its input
>>>> DOES NOT HALT then DD(DD) would never halt.
>>>
>>> Nice to see that you don't disagree with my silly remark.
>>>
>>
>> Directly executed DD(DD) and DD correctly simulated by HH are
>> two different sequences of configurations and HH is only held
>> accountable for the latter.
>>
>> The everyone disagrees with this verified fact that
>> HH correctly simulated by DD DOES NOT HALT is less
>> than no rebuttal at all.
> 
> Still nice to see that you don't disagree with my silly remark.
> Though might get boring at some point. Perhaps I should post
> another silly remark before that.
> 

When I conclusively prove that DD correctly simulated by HH has
non-halting behavior then we know that HH(DD,DD) is correct to
reject DD as non-halting.

Simulating Halt Decider HH computes the mapping FROM ITS INPUT DD
to its own accept or reject on the basis of the behavior that DD
correctly simulated by HH specifies.

People that say HH must report on the provably different
behavior the non input of directly executed DD(DD) simply
don't have a clue that deciders are not allowed to do this.

Prior to Pythagoras there was a universal consensus that
the Earth was flat. A consensus of ignoring how deciders
actually work is this same sort of error.


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