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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory,sci.logic
Subject: Re: How Partial Simulations correctly determine non-halting ---Ben's
 10/2022 analysis
Date: Fri, 7 Jun 2024 20:48:42 -0400
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On 6/7/24 8:35 PM, olcott wrote:
> On 6/7/2024 7:25 PM, Python wrote:
>> Le 08/06/2024 à 00:26, olcott a écrit :
>> ...
>>> No actual Turing machine can be the input to any other actual
>>> Turing machine. Turing machines only take finite string inputs.
>>
>> Any Turing Machine can be represented by a finite strint inpput.
>>
> 
> When Ĥ is applied to ⟨Ĥ⟩
> Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞
> Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
> 
> It turns out that the behavior of Ĥ ⟨Ĥ⟩ is verifiably different
> that the behavior of ⟨Ĥ⟩ ⟨Ĥ⟩ correctly simulated by embedded_H
> even if an expert in comp theory named Jesus told you otherwise.


If can't be, amd be a correct simulation.

You just don't understand the DEFINITION of being correct.

> 
> To overcome the religious belief that they are the same one must
> examine this at the x86 machine code level with complete understanding
> of the x86 machine code.
> 

SO do it, and tell us which is the first instruction where the direct 
exectuion of DD(DD) and the "correct simulation" of that input differ in 
results.

My guess is that it will be a non-simulated call to HH, where your 
"correct simulation" presumes incorrect behavior for the function.