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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: comp.theory
Subject: Re: Two dozen people were simply wrong --- Try to prove otherwise
Date: Mon, 3 Jun 2024 17:49:58 +0300
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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.

-- 
Mikko