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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory,sci.logic
Subject: Re: Unconventional termination analyzer H correctly reports halt
 status of HP input
Date: Sat, 11 May 2024 19:24:59 -0400
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On 5/11/24 2:46 PM, olcott wrote:
> Unconventional termination analyzer H correctly reports
> the halt status of the halting problem's counter-example
> input D. (The same applies to the Peter Linz proof)

"Unconventional" for sure, you definiotn of (d) below says your system 
doesn't obey the basic rules of programs as used in fields like 
computaiton theory, as those give answers only in final states.

How can H return its answer to its caller, and still continue?

You just added the need to fully define what you mean by a program.

So, it seems you finally broke down and admitted that none of your work 
has ANYTHING to do with the fields you claim to be in, because all of 
those are based on the conventional definition of a program, which you 
just admitted you are not using.

> 
> 00 int H(ptr x, ptr x)  // ptr is pointer to int function
> 01 int D(ptr x)
> 02 {
> 03   int Halt_Status = H(x, x);
> 04   if (Halt_Status)
> 05     HERE: goto HERE;
> 06   return Halt_Status;
> 07 }
> 08
> 09 int main()
> 10 {
> 11   H(D,D);
> 12 }
> 
> *A simulator is the conventional meaning of an x86 emulator or a UTM*
> Unconventional termination analyzer is exactly the conventional
> term-of-the-art {termination analyzer} except that it need not halt.
> 
> *D simulated by H where H can*
> (a) Watch all of the state changes of its input.
> (b) Analyze these state changes.
> (c) Correctly determine that its input (and itself) would never halt.
> (d) Continue to report that its input would never halt by
> transitioning to a special non-final state indicating this.
> 
> *All the while remaining a pure simulator with extra features*
> 
> This H is neither a halt decider nor a conventional {termination
> analyzer}. It is an unconventional {termination analyzer} that
> correctly reports the halt status of its pathological input.
> 
> This exact same reasoning applies to the Peter Linz halting problem
> proof where embedded_H is an unconventional {termination analyzer}.

NBo such thing. You are just proving how utterly ignorant you are of how 
Turing Machines actually work.

> 
> When Peter Linz Ĥ is applied to ⟨Ĥ⟩
> Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞
> Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
> 
> *Termination Analyzer H is Not Fooled by Pathological Input D*
> https://www.researchgate.net/publication/369971402_Termination_Analyzer_H_is_Not_Fooled_by_Pathological_Input_D