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

On 4/30/2025 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.
 This would have been fully acknowledged years ago if
people understood that HHH/DD is analogous (thus isomorphic)
to Linz and Functions

Meaning that the following mapping is assumed to be computable and HHH computes it:
Given any algorithm (i.e. a fixed immutable sequence of instructions) X described as <X> with input Y:
A solution to the halting problem is an algorithm H that computes the following mapping:
(<X>,Y) maps to 1 if and only if X(Y) halts when executed directly
(<X>,Y) maps to 0 if and only if X(Y) does not halt when executed directly

computed by Turing Machines are ONLY
allowed to derive outputs by applying finite string transformations
to inputs.
 This requirement forbids HHH to report on DD(DD)
because the mapping from the input to HHH(DD)
specifies something else.

i.e. a contradiction is reached, therefore the assumption that an H exists that can compute the above mapping is proven false, as show by Linz and you have *explicitly* agreed is correct.

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

All mappings exist.  Whether or not a mapping is computable is another matter.