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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory,sci.logic
Subject: Re: D correctly simulated by H cannot possibly halt --- templates and
 infinite sets --- deciders
Date: Thu, 30 May 2024 14:01:26 -0500
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On 5/30/2024 1:50 PM, Fred. Zwarts wrote:
> Op 30.mei.2024 om 19:00 schreef olcott:
>> On 5/30/2024 10:20 AM, Fred. Zwarts wrote:
>>> Op 30.mei.2024 om 16:43 schreef olcott:
>>>> On 5/28/2024 11:16 AM, olcott wrote:
>>>>>
>>>>> When Ĥ is applied to ⟨Ĥ⟩
>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞
>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
>>>>>
>>>>> *Formalizing the Linz Proof structure*
>>>>> ∃H  ∈ Turing_Machines
>>>>> ∀x  ∈ Turing_Machines_Descriptions
>>>>> ∀y  ∈ Finite_Strings
>>>>> such that H(x,y) = Halts(x,y)
>>>>>
>>>>
>>>> A decider computes the mapping from finite string inputs to
>>>> its own accept or reject state.
>>>>
>>>> A decider does not and cannot compute the mapping from
>>>> Turing_Machine inputs to its own accept or reject state.
>>>>
>>>> Halts(x,y) would report on the direct execution of x(y) thus ignores
>>>> the pathological behavior of x correctly simulated by pure function H.
>>>> This makes Halts(x,y) an incorrect measure of the correctness of 
>>>> H(x,y).
>>>
>>> Why are you referring to the 'pathological behavior of x' if your 
>>> claim is that the simulator does not even reach the part of DD 
>>> (below) that contradicts the result of HH? This 'pathological 
>>> behavior of x' is completely irrelevant. 
>>
>> It is totally relevant because it is the reason why D correctly
>> simulated by H cannot possibly halt.
> 
> Incorrect. Your own words are that lines 04, 05 and 06 are nor reachable 
> for the simulator.

Because D correctly simulated by H remains stuck in recursive simulation
because D calls H(D,D) in recursive simulation D cannot possibly reach
past its own line 03.

You must must 100% complete attention to the exact words that I exactly 
say.

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