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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: Two dozen people were simply wrong --- Try to prove otherwise
Date: Mon, 3 Jun 2024 13:20:59 -0500
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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).

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