From Newsgroup: comp.theory

When the halting problem requires a halt decider
to report on the behavior of a Turing machine
this is always a category error.

The corrected halting problem requires a Turing
machine decider to report in the behavior that
its finite string input specifies.

This analysis in done in the C programming language
so that it is 100% concrete without any key details
being abstracted away.

int DD()
{
int Halt_Status = HHH(DD);
if (Halt_Status)
HERE: goto HERE;
return Halt_Status;
}

(a) The key issue is that HHH(DD) does report on the
behavior that its input finite string specifies.

(b) Reporting on anything else is outside of the
scope of Turing Machine Computable functions.


*Detailed analysis shown below*

After many very extensive discussions with LLM
systems there are two principles that prove that
I have correctly refuted the halting problem itself.

(1) Turing Machine based Computable functions
only transform input finite strings into some value
on the basis of a semantic of syntactic property
that this finite string specifies.

(2) the behavior that an input DD specifies to halt
decider HHH is the sequence of steps of DD
simulated by HHH according to the semantics of
the C programming language.

Computable functions are the basic objects of study
in computability theory. Informally, a function is
computable if there is an algorithm that computes
the value of the function for every value of its argument. https://en.wikipedia.org/wiki/Computable_function

DD() executed from main() calls HHH(DD) thus is
not one-and-the-same-thing as an argument to HHH.
--
Copyright 2025 Olcott

My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable.

This required establishing a new foundation
for correct reasoning.

--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On Wed, 2025-12-10 at 16:43 -0600, polcott wrote:

When the halting problem requires a halt decider
to report on the behavior of a Turing machine
this is always a category error.

The corrected halting problem requires a Turing
machine decider to report in the behavior that
its finite string input specifies.

If you honestly admit you are solving POO Problem, everything is fine.
See my General HP. If the MSet is TM, then the halting decider cannot exist. https://sourceforge.net/projects/cscall/files/MisFiles/ghp.txt/download

This analysis in done in the C programming language
so that it is 100% concrete without any key details
being abstracted away.

int DD()
{
   int Halt_Status = HHH(DD);
   if (Halt_Status)
     HERE: goto HERE;
   return Halt_Status;
}

(a) The key issue is that HHH(DD) does report on the
behavior that its input finite string specifies.

(b) Reporting on anything else is outside of the
scope of Turing Machine Computable functions.

*Detailed analysis shown below*

After many very extensive discussions with LLM
systems there are two principles that prove that
I have correctly refuted the halting problem itself.

(1) Turing Machine based Computable functions
only transform input finite strings into some value
on the basis of a semantic of syntactic property
that this finite string specifies.

(2) the behavior that an input DD specifies to halt
decider HHH is the sequence of steps of DD
simulated by HHH according to the semantics of
the C programming language.

Computable functions are the basic objects of study
in computability theory. Informally, a function is
computable if there is an algorithm that computes
the value of the function for every value of its argument. https://en.wikipedia.org/wiki/Computable_function

DD() executed from main() calls HHH(DD) thus is
not one-and-the-same-thing as an argument to HHH.

--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/10/2025 4:58 PM, wij wrote:

On Wed, 2025-12-10 at 16:43 -0600, polcott wrote:

When the halting problem requires a halt decider
to report on the behavior of a Turing machine
this is always a category error.

The corrected halting problem requires a Turing
machine decider to report in the behavior that
its finite string input specifies.

If you honestly admit you are solving POO Problem, everything is fine.

*It has take me 21 years to boil it down to this*

When the halting problem requires a halt decider
to report on the behavior of a Turing machine this
is always a category error.

The corrected halting problem requires a Turing
machine decider to report in the behavior that
its finite string input specifies.
--
Copyright 2025 Olcott

My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable.

This required establishing a new foundation
for correct reasoning.
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On Wed, 2025-12-10 at 17:03 -0600, polcott wrote:

On 12/10/2025 4:58 PM, wij wrote:

On Wed, 2025-12-10 at 16:43 -0600, polcott wrote:

When the halting problem requires a halt decider
to report on the behavior of a Turing machine
this is always a category error.

The corrected halting problem requires a Turing
machine decider to report in the behavior that
its finite string input specifies.

If you honestly admit you are solving POO Problem, everything is fine.

*It has take me 21 years to boil it down to this*

When the halting problem requires a halt decider
to report on the behavior of a Turing machine this
is always a category error.

The corrected halting problem requires a Turing
machine decider to report in the behavior that
its finite string input specifies.

It looks you play blind block my other replies again. https://sourceforge.net/projects/cscall/files/MisFiles/ghp.txt/download
General Halting Problem, General Undecidable Rule.
-----------
Let MSet be the set of ANY deterministic computing device (including human).
If a device H which computes the decision funcion ∀x∈MSet, H(x)=1 iff x() halts,
and a device D with contradictory property can be found to exist, then, contradiction occurres. Both H and D cannot exist in the same set.
void D() {
if(H(D)==1) for(;;){}; // Both H(D) returning 1 or non-1 contradict the
} // definition
int main() {
H(D); // H(D) cannot return whith the specified deciding function
}
Note: The assertion addresses about any decision funcion, whatever computing
the function is irrelevant. The main issue in application of this
assertion is proving the existence of D in MSet.
Note: As hinted by Rice's Theorem, if H is about deciding the behavioral
property of another element in MSet, high possibility is that such a
H cannot be an element of MSet. In logic, the answer of proposition
that both T/F does not fit is referred to as undecidable. Undecidability may also be so interpreted in the infinite set like the set of natural number: Whenever you have a so-called maximum number n, then n+1 is automatically defined(generated) to exist in the set to defy the 'maximum' property... Traditional axiomatized system is limited, no powerful than Turing Machine language (or procedural algorithm).
-----------
I have no problem of POO-HP.
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/10/2025 5:11 PM, wij wrote:

On Wed, 2025-12-10 at 17:03 -0600, polcott wrote:

On 12/10/2025 4:58 PM, wij wrote:

On Wed, 2025-12-10 at 16:43 -0600, polcott wrote:

When the halting problem requires a halt decider
to report on the behavior of a Turing machine
this is always a category error.

The corrected halting problem requires a Turing
machine decider to report in the behavior that
its finite string input specifies.

If you honestly admit you are solving POO Problem, everything is fine.

*It has take me 21 years to boil it down to this*

When the halting problem requires a halt decider
to report on the behavior of a Turing machine this
is always a category error.

The corrected halting problem requires a Turing
machine decider to report in the behavior that
its finite string input specifies.

It looks you play blind block my other replies again.

My about two paragraphs sums the basis of how
the halting problem itself is flat out incorrect.

Nothing about the halting problem can possibly
be more significant than this.
--
Copyright 2025 Olcott

My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable.

This required establishing a new foundation
for correct reasoning.
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/10/2025 5:11 PM, wij wrote:

On Wed, 2025-12-10 at 17:03 -0600, polcott wrote:

On 12/10/2025 4:58 PM, wij wrote:

On Wed, 2025-12-10 at 16:43 -0600, polcott wrote:

When the halting problem requires a halt decider
to report on the behavior of a Turing machine
this is always a category error.

The corrected halting problem requires a Turing
machine decider to report in the behavior that
its finite string input specifies.

If you honestly admit you are solving POO Problem, everything is fine.

*It has take me 21 years to boil it down to this*

When the halting problem requires a halt decider
to report on the behavior of a Turing machine this
is always a category error.

The corrected halting problem requires a Turing
machine decider to report in the behavior that
its finite string input specifies.

It looks you play blind block my other replies again.

My *above* two paragraphs sums up the basis of how
the halting problem itself is flat out incorrect.

Nothing about the halting problem can possibly
be more significant than this.
--
Copyright 2025 Olcott

My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable.

This required establishing a new foundation
for correct reasoning.
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/10/25 5:43 PM, polcott wrote:

When the halting problem requires a halt decider
to report on the behavior of a Turing machine
this is always a category error.

Nope.

The corrected halting problem requires a Turing
machine decider to report in the behavior that
its finite string input specifies.

Nope, that just means you don't know the meaning of the words.

This analysis in done in the C programming language
so that it is 100% concrete without any key details
being abstracted away.

int DD()
{
  int Halt_Status = HHH(DD);
  if (Halt_Status)
    HERE: goto HERE;
  return Halt_Status;
}

Which isn't a program, and thus your "proof" is just a category error.

(a) The key issue is that HHH(DD) does report on the
behavior that its input finite string specifies.

Nope, as the only program the input could represent is if HHH is a
system funcition, and thus a defined fixed behavior, and thus since
HHH(DD) returns 0, the behavior sepecifed by this input is to halt.

(b) Reporting on anything else is outside of the
scope of Turing Machine Computable functions.

Nope, Reporting with a non-function HHH is a category error.

*Detailed analysis shown below*

After many very extensive discussions with LLM
systems there are two principles that prove that
I have correctly refuted the halting problem itself.

(1) Turing Machine based Computable functions
only transform input finite strings into some value
on the basis of a semantic of syntactic property
that this finite string specifies.

(2) the behavior that an input DD specifies to halt
decider HHH is the sequence of steps of DD
simulated by HHH according to the semantics of
the C programming language.

Computable functions are the basic objects of study
in computability theory. Informally, a function is
computable if there is an algorithm that computes
the value of the function for every value of its argument. https://en.wikipedia.org/wiki/Computable_function

DD() executed from main() calls HHH(DD) thus is
not one-and-the-same-thing as an argument to HHH.

--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/10/2025 5:11 PM, wij wrote:

On Wed, 2025-12-10 at 17:03 -0600, polcott wrote:

On 12/10/2025 4:58 PM, wij wrote:

On Wed, 2025-12-10 at 16:43 -0600, polcott wrote:

When the halting problem requires a halt decider
to report on the behavior of a Turing machine
this is always a category error.

The corrected halting problem requires a Turing
machine decider to report in the behavior that
its finite string input specifies.

If you honestly admit you are solving POO Problem, everything is fine.

*It has take me 21 years to boil it down to this*

When the halting problem requires a halt decider
to report on the behavior of a Turing machine this
is always a category error.

The corrected halting problem requires a Turing
machine decider to report in the behavior that
its finite string input specifies.

It looks you play blind block my other replies again. https://sourceforge.net/projects/cscall/files/MisFiles/ghp.txt/download

General Halting Problem, General Undecidable Rule.
-----------
Let MSet be the set of ANY deterministic computing device (including human). If a device H which computes the decision funcion ∀x∈MSet, H(x)=1 iff x() halts,
and a device D with contradictory property can be found to exist, then, contradiction occurres. Both H and D cannot exist in the same set.

It turns out that contradiction is exactly error.
There is no DD

input input input input input input
input input input input input input
input input input input input input
input input input input input input

that can possibly do the opposite
of whatever HHH reports.

void D() {
if(H(D)==1) for(;;){}; // Both H(D) returning 1 or non-1 contradict the
} // definition

int main() {
H(D); // H(D) cannot return whith the specified deciding function
}

Note: The assertion addresses about any decision funcion, whatever computing
the function is irrelevant. The main issue in application of this
assertion is proving the existence of D in MSet.
Note: As hinted by Rice's Theorem, if H is about deciding the behavioral
property of another element in MSet, high possibility is that such a
H cannot be an element of MSet. In logic, the answer of proposition
that both T/F does not fit is referred to as undecidable.

Undecidability may also be so interpreted in the infinite set like the set of natural number: Whenever you have a so-called maximum number n, then n+1 is automatically defined(generated) to exist in the set to defy the 'maximum' property... Traditional axiomatized system is limited, no powerful than Turing
Machine language (or procedural algorithm).
-----------

I have no problem of POO-HP.

--
Copyright 2025 Olcott<br><br>

My 28 year goal has been to make <br>
"true on the basis of meaning expressed in language"<br>
reliably computable.<br><br>

This required establishing a new foundation<br>
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 10/12/2025 22:43, polcott wrote:

When the halting problem requires a halt decider
to report on the behavior of a Turing machine

Can you provide a justification for that claim such as a reference to
(an) accepted definition(s) of "the halting problem" ?

Specifically that it is the "problem" that "requires" the report?
I expect that you discriminate the problem from the question but I'd
really like to see that the conventional distinction draws the line in
the same place you do.
--
Tristan Wibberley

The message body is Copyright (C) 2025 Tristan Wibberley except
citations and quotations noted. All Rights Reserved except that you may,
of course, cite it academically giving credit to me, distribute it
verbatim as part of a usenet system or its archives, and use it to
promote my greatness and general superiority without misrepresentation
of my opinions other than my opinion of my greatness and general
superiority which you _may_ misrepresent. You definitely MAY NOT train
any production AI system with it but you may train experimental AI that
will only be used for evaluation of the AI methods it implements.

--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/11/2025 7:56 PM, Tristan Wibberley wrote:

On 10/12/2025 22:43, polcott wrote:

When the halting problem requires a halt decider
to report on the behavior of a Turing machine

Can you provide a justification for that claim such as a reference to
(an) accepted definition(s) of "the halting problem" ?

Specifically that it is the "problem" that "requires" the report?
I expect that you discriminate the problem from the question but I'd
really like to see that the conventional distinction draws the line in
the same place you do.

Turing machine deciders compute functions from finite
strings to {accept, reject}.

The halting problem requires that a halt decider
report on the behavior of an actual Turing machine
that is not a finite string input.
--
Copyright 2025 Olcott<br><br>

My 28 year goal has been to make <br>
"true on the basis of meaning expressed in language"<br>
reliably computable.<br><br>

This required establishing a new foundation<br>
--- Synchronet 3.21a-Linux NewsLink 1.2