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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory,sci.logic
Subject: Re: Two dozen people were simply wrong --- Try to prove otherwise
Date: Tue, 4 Jun 2024 12:46:51 -0500
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On 6/4/2024 3:40 AM, Mikko wrote:
> On 2024-06-03 18:20:59 +0000, olcott said:
> 
>> On 6/3/2024 9:49 AM, Mikko wrote:
>>> On 2024-06-03 13:16:12 +0000, olcott said:
>>>
>>>> On 6/3/2024 5:03 AM, Mikko wrote:
>>>>> On 2024-05-31 15:13:02 +0000, olcott said:
>>>>>
>>>>>> On 5/31/2024 3:30 AM, Mikko wrote:
>>>>>>> On 2024-05-31 01:54:52 +0000, olcott said:
>>>>>>>
>>>>>>>> On 5/30/2024 8:37 PM, Richard Damon wrote:
>>>>>>>>> On 5/30/24 9:31 AM, olcott wrote:
>>>>>>>>>> On 5/30/2024 2:40 AM, Mikko wrote:
>>>>>>>>>>> On 2024-05-30 01:15:21 +0000, olcott said:
>>>>>>>>
>>>>>>>>>>>> x <is> a finite string Turing machine description that 
>>>>>>>>>>>> SPECIFIES behavior. The term: "representing" is inaccurate.
>>>>>>>>>>>
>>>>>>>>>>> No, x is a description of the Turing machine that specifies 
>>>>>>>>>>> the behaviour
>>>>>>>>>>> that H is required to report.
>>>>>>>>>>
>>>>>>>>>> That is what I said.
>>>>>>>>>
>>>>>>>>> Note, the string doesn't DIRECTLY specify behavior, but only 
>>>>>>>>> indirectly as a description/representation of the Turing Mach
>>>>>>>>>
>>>>>>>>
>>>>>>>> The string directly SPECIFIES behavior to a UTM or to
>>>>>>>> any TM based on a UTM.
>>>>>>>
>>>>>>> An UTM interpretes the string as a specification of behaviour
>>>>>>
>>>>>> YES, exactly !!!
>>>>>>
>>>>>>> and another Turing machine may interprete likewise. But in a
>>>>>>> different context the interpretation is different.
>>>>>>>
>>>>>>
>>>>>> When Ĥ is applied to ⟨Ĥ⟩
>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞
>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
>>>>>>
>>>>>> When embedded_H <is> a UTM or <is> a halting computation based on a
>>>>>> UTM then the ⟨Ĥ⟩ ⟨Ĥ⟩ input to embedded_H SPECIFIES that ⟨Ĥ⟩ ⟨Ĥ⟩ 
>>>>>> correctly
>>>>>> simulated by embedded_H cannot possibly reach its own simulated final
>>>>>> state at ⟨Ĥ.qn⟩.
>>>>>
>>>>> There is no requirement to follow the pecifications by embedded_H.
>>>>
>>>>
>>>> In other words embedded_H can simply play bingo and never halt and 
>>>> still correctly decide the halt status of its input?
>>>
>>> Not of the input text but of the machine and input that the text
>>> describes. The input to H contains enough information that the
>>> machine can be constructed and run with the input. If the prediction
>>> by H differs from the actual execution of the machine the prediction
>>> is wrong and H is not a halt decider.
>>>
>>
>>
>> int sum(int x, int y) { return x + y; }
>> sum(2,3) cannot return the sum of 5 + 6.
>>
>> DD correctly simulated by HH does have provably
>> different behavior than DD(DD) so HH is is not
>> allowed to report on the behavior of DD(DD).
> 
> Show the proof (or a pointer to the beginning of the proof).
> 

On 6/4/2024 11:28 AM, olcott wrote:
[Proof that executed HH(DD,DD) and simulated HH(DD,DD)
simulate DD correctly -- Mike Terry]

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