Re: Turing Machine computable functions apply finite string transformations to inputs VERIFIED FACT

On 4/30/25 8:55 PM, olcott wrote:

On 4/30/2025 7:07 PM, Mike Terry wrote:

On 30/04/2025 23:04, Keith Thompson wrote:

olcott <polcott333@gmail.com> writes:

On 4/30/2025 2:46 PM, Keith Thompson wrote:

olcott <polcott333@gmail.com> writes:
[...]

Because you don't pay any attention at all
you did not bother to notice that I have never been
attacking the Halting Problem only the conventional
Halting Problem proof.

[...]
That's some interesting news, at least to me.
I was under the impression that you had explicitly claimed to have
solved the Halting Problem.  I don't read most of what you write,
and I don't remember all of what I've read, so my impression may
have been mistaken.
Now you're saying that you're only attacking the conventional proof.

>
That is ALL that I have been saying for several years.
Anyone can figure that out simply on the basis of
actually paying attention to my proof.
>
HHH(DD) does correctly report that the halting problem
proof's impossible input DOES NOT HALT SO THE PROOF
IS WRONG.

>
So your only claim is that the commonly known Halting Problem proof
is flawed.  (Others who have paid more attention might choose to
comment on that.)

>
My recollection is that PO does not claim to have a solution to the halting problem.
>
I made a recent post here (Wed, 30 Apr 2025 19:30:46 +0100) with some background, since another poster also seemed to think PO was claiming to have "solved the HP".
>
Several people [starting years ago with Ben] have explained to PO that there are multiple alternative proofs, including one in the Linz book which PO might be expected to have read, but PO blanks such discussions.  He wouldn't understand those proofs, of course.
 and

 A single minded focus of 22 years has correctly
refuted the conventional halting problem proof.

No, it shows that you have been ignorant of what you have been talking about for those 22 years.

 This would have been fully acknowledged years ago if
people understood that HHH/DD is analogous (thus isomorphic)
to Linz and Functions computed by Turing Machines are ONLY
allowed to derive outputs by applying finite string transformations
to inputs.

The problem is that first, they are NOT since HHH/DD are intertwined, and you use that intertwining to do things that can't be done in a Turing Machine, like recognize that

 This requirement forbids HHH to report on DD(DD)
because the mapping from the input to HHH(DD)
specifies something else.'

No it doesn't. The only mapping that HHH is supposed to be reporting on is the Halting Function mapping, which being a mathematical Function, isn't limited by your "finite string transformation" rule.
Beig a program, it only CAN report based

 You can't simply guess the mapping that you want
and then assume that it exists.

Right, which is why the mapping has a definition, and that definition is the objective criteria of the mapping of programs that halt when executed to 1, and that will never halt, even when run an unbounded number of steps to 0.
Since DD will reach a final state when actually run, HHH(DD) to follow that mapping must return 1, but it returns 0, and thus it is incorrect.
It makes the error you are pointing out, of simply "guessing" based on your faulty logic that this is an input that the call to HHH will not return from.

 

>
Do you have anything to say about whether the Halting Problem
is solvable?  (You snipped this question in your previous response.)
>

>
I'm actually not sure what PO would say!  I imagine he would sidestep the question by denying the validity of the "conventional" HP statement in some way.
>
>
Mike.
>