On 7/31/25 8:47 AM, wij wrote:

HP can be defined as: H(D)=1 iff D() halts (in C function notation)

The result of HP is that such a H does not exist. The proof goes like
if the H exists, then a BadCase will exist, so that H(BadCase) never retunrs correctly: (the formal proof is much longer for preciseness and triky details,
but the principle is the same)

void BadCase() {
if(H(BadCase)==1) while(1) {};
}

This HP proof indicates that the implement of H is irrelevant.
Whether or not the implement is a 'correct' simulation is irrelevant.
Whether or not the implement is a multi-processes simulation or mult-return value, are irrelevant.
You can assume god lives inside the H to answer the question, but in vain, the (undecidable) result remains the same.

This is a simple fact, no 'theory' can defy.

Actually, there can't be just ANYTHING in H, but if it is a
deterministic algorithm that uses only its defined input, the proof
works, and that *IS* the restriction on programs in Computation Theory,
so it applies to anything that could be a Halt Decider.

The issue is that H could somehow look to see if it is being called with something like BadCase as its input, it checks if it is being called by BadCase, and if so, just loop forever, and if not, return 0.

That of course isn't a valid program, even though it sort of matches
what Peter is doing, only he tries to define the behavior by the
"correct simuation" of the input by H, and that H's correct simulaiton
of H(Badcase) is non-halting, and thus it can answer non-halting, even
though BadCase does halt when run.

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On 2025-07-31 12:47:19 +0000, wij said:

HP can be defined as: H(D)=1 iff D() halts (in C function notation)

The result of HP is that such a H does not exist. The proof goes like
if the H exists, then a BadCase will exist, so that H(BadCase) never retunrscorrectly: (the formal proof is much longer for preciseness and
triky details,
but the principle is the same)

There are two ways to present proofs: direct and indirect. Some people
find direct proors more understandable and convincing, others inderect
proofs.

In this case the discussion has been mainly about the indirect form,
so it might be more helpful to present proof in the direct form.

void BadCase() {
if(H(BadCase)==1) while(1) {};
}

One should also note that although there is no halting decider there
are partial deciders that can answer some cases but fail on some other
cases. A partial decider that never gives the wrong answer and gives
the right answer in at least some cases may be good enough for some
purposes.

This HP proof indicates that the implement of H is irrelevant.Whether
or not the implement is a 'correct' simulation is irrelevant.

That's right. A partial solution without simulation is possible, and so
is a partial solution with 'incorrect' simulation.

Whether or not the implement is a multi-processes simulation or mult-returnvalue, are irrelevant.

You can assume god lives inside the H to answer the question, but in vain, the (undecidable) result remains the same.

No, that is not the same. Although it is commonly believed that a function
is not computable if it is not Turing-computable, that is not proven.
Perhaps there is a solution method to the halting problem of Turing machines
or C probrams that cannot be expressed as a Turing machine or a C program.
Then the construction of BadCase is not possible.

--
Mikko

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On 2025-08-01 07:52:59 +0000, wij said:

On Fri, 2025-08-01 at 09:47 +0300, Mikko wrote:

On 2025-07-31 12:47:19 +0000, wij said:

HP can be defined as: H(D)=1 iff D() halts  (in C function notation)

The result of HP is that such a H does not exist. The proof goes like
if the H exists, then a BadCase will exist, so that H(BadCase) never> >
retunrscorrectly: (the formal proof is much longer for preciseness and>

triky details,

but the principle is the same)

There are two ways to present proofs: direct and indirect. Some people
find direct proors more understandable and convincing, others inderect
proofs.

In this case the discussion has been mainly about the indirect form,
so it might be more helpful to present proof in the direct form.

void BadCase() {
 if(H(BadCase)==1) while(1) {};
}

One should also note that although there is no halting decider there
are partial deciders that can answer some cases but fail on some other
cases. A partial decider that never gives the wrong answer and gives
the right answer in at least some cases may be good enough for some
purposes.

I cannot read useful information.

Have you tried to learn? It would be a more useful skill than writing
useless babble.

This HP proof indicates that the implement of H is irrelevant.Whether>

or not the implement is a 'correct' simulation is irrelevant.

That's right. A partial solution without simulation is possible, and so
is a partial solution with 'incorrect' simulation.

Whether or not the implement is a multi-processes simulation or> >
mult-returnvalue, are irrelevant.

You can assume god lives inside the H to answer the question, but in vain, >>> the (undecidable) result remains the same.

No, that is not the same. Although it is commonly believed that a function >> is not computable if it is not Turing-computable, that is not proven.
Perhaps there is a solution method to the halting problem of Turing machines >> or C probrams that cannot be expressed as a Turing machine or a C program. >> Then the construction of BadCase is not possible.

Not sure what the point is. Church-Turing thesis (as I understand) means no computation on earth that Turing Machine cannot compute. I don't find evidence
to refute.

But you don't find a proof, either.

--
Mikko

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On 2025-08-02 10:02:59 +0000, wij said:

On Sat, 2025-08-02 at 10:47 +0300, Mikko wrote:

On 2025-08-01 07:52:59 +0000, wij said:

On Fri, 2025-08-01 at 09:47 +0300, Mikko wrote:

On 2025-07-31 12:47:19 +0000, wij said:

HP can be defined as: H(D)=1 iff D() halts  (in C function notation) >>>>>
The result of HP is that such a H does not exist. The proof goes like >>>>> if the H exists, then a BadCase will exist, so that H(BadCase) never> >>>>> >> > > > retunrscorrectly: (the formal proof is much longer for
preciseness and>> > > > > triky details,
but the principle is the same)

There are two ways to present proofs: direct and indirect. Some people >>>> find direct proors more understandable and convincing, others inderect >>>> proofs.

In this case the discussion has been mainly about the indirect form,
so it might be more helpful to present proof in the direct form.

void BadCase() {
 if(H(BadCase)==1) while(1) {};
}

One should also note that although there is no halting decider there
are partial deciders that can answer some cases but fail on some other >>>> cases. A partial decider that never gives the wrong answer and gives
the right answer in at least some cases may be good enough for some
purposes.

I cannot read useful information.

Have you tried to learn? It would be a more useful skill than writing
useless babble.

This HP proof indicates that the implement of H is irrelevant.Whether>> >>>>> > > > > or not the implement is a 'correct' simulation is irrelevant. >>>>

That's right. A partial solution without simulation is possible, and so >>>> is a partial solution with 'incorrect' simulation.

Whether or not the implement is a multi-processes simulation or> >> > > >>>>> > mult-returnvalue, are irrelevant.

You can assume god lives inside the H to answer the question, but in vain,
the (undecidable) result remains the same.

No, that is not the same. Although it is commonly believed that a function >>>> is not computable if it is not Turing-computable, that is not proven.
Perhaps there is a solution method to the halting problem of Turing machines
or C probrams that cannot be expressed as a Turing machine or a C program. >>>> Then the construction of BadCase is not possible.

Not sure what the point is. Church-Turing thesis (as I understand) means no >>> computation on earth that Turing Machine cannot compute. I don't find evidence
to refute.

But you don't find a proof, either.

See other post, title "Proof of Church-Turing Thesis"

Even if I don't find proof, your idea is baseless or based on "no proof".

The lack of proof is a sufficient basis for the idea that there is no
known proof.

--
Mikko

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