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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: Fri, 31 May 2024 10:13:02 -0500
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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⟩.

> Note that there are specifications of behaviour that do not
> describe. A specification can be an algorithm that takes
> the input and output of a Turing machine and from then computes
> whether the output is correct. That kind of specification cannot
> be used as an input to an UTM or other Turing machine that expects
> a description.
> 

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