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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory
Subject: Re: Incorrect requirements --- Computing the mapping from the input
 to HHH(DD)
Date: Sat, 10 May 2025 19:04:26 -0400
Organization: i2pn2 (i2pn.org)
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On 5/10/25 4:26 PM, olcott wrote:
> On 5/10/2025 3:07 PM, Alan Mackenzie wrote:
>> Mr Flibble <flibble@red-dwarf.jmc.corp> wrote:
>>> On Sat, 10 May 2025 18:48:12 +0000, Alan Mackenzie wrote:
>>
>>>> olcott <polcott333@gmail.com> wrote:
>>>>> On 5/10/2025 7:37 AM, Bonita Montero wrote:
>>
>>>> [ .... ]
>>
>>>>>> I guess that not even a professor of theoretical computer science
>>>>>> would spend years working on so few lines of code.
>>
>>
>>>>> I created a whole x86utm operating system.
>>>>> It correctly determines that the halting problem's otherwise
>>>>> "impossible" input is actually non halting.
>>
>>>> You've spent over 20 years on this matter.  Compare this with Alan
>>>> Turing's solution of the Entscheidungsproblem.  He published this in
>>>> 1936 when he was just 24 years old.
>>
>>> Turing didn't solve anything: what he published contained a mistake: the
>>> category (type) error that I have described previously in this forum.
>>
>> What arrogant self-important ignorance!  Turing indeed solved the
>> Entscheidungsproblem.  His procedure has been verified by hundreds of
>> thousands of mathematicians over the last century, and none of them have
>> found flaws in it.
>>
>> It is overwhelmingly likely that your lack of mathematical training has
>> led you to delude yourself about finding an error.  The same applies to
>> Peter Olcott.
>>
>>> /Flibble
>>
> 
> Once we understand that functions computed
> by models of computation must apply the sequence
> of steps of an algorithm to derive their output
> from their input then we have one key element.

Yes, but non-computable functions do not.

> 
> Then we also need to understand that termination
> analyzers are required to compute the mapping from
> this input to the behavior ACTUALLY SPECIFIED by
> this input.

And that behavior is SPECIFIED as the behavior of the program their 
input represents when it is actually run, (with any and all input for a 
termination analyser)

> 
> The last step is understanding is that computing
> the mapping to the behavior specified by this
> input finite string must be according to the
> model's computation language.

Only what the computation the generates, not the mapping for the CORRECT 
answer.

> 
> This means that HHH is correct to reject its
> input DD because DD emulated by HHH according
> to the rules of the x86 language specifies
> recursive emulation (non halting behavior).

Nope. As the input represents a program that will HALT since the decider 
it uses says it will not halt.

Of course, this requires that you actually built a program as the input, 
and as the decider, and thus they both have fixed behavior.

That means that when we correctly emulate that D, it *WILL* use the 
algorithm form the H that returned non-halting, and thus get that answer 
and thus halt.

THe fact that H's incorrect emulation didn't get there is irrelevent.

> 
> *Likewise for the Linz Proof*
> 
> When Ĥ is applied to ⟨Ĥ⟩
> Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞
> Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
> 
> (a) Ĥ copies its input ⟨Ĥ⟩
> (b) Ĥ invokes embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩
> (c) embedded_H simulates ⟨Ĥ⟩ ⟨Ĥ⟩  ...
> 
> ⟨Ĥ⟩ correctly simulated by embedded_H cannot possibly
> ever reach its own simulated final state ⟨Ĥ.qn⟩
> 

But ⟨Ĥ⟩ isn't correctly simulated by embedded_H, as the H that it is a 
copy of has been said to abort and go to qn, is it will also.

You are just showing that you believe it is ok to lie in your logic.