Re: Correcting the definition of the halting problem --- Computable functions

On 3/25/2025 3:54 AM, joes wrote:

Am Mon, 24 Mar 2025 17:43:14 -0500 schrieb olcott:

On 3/24/2025 4:49 PM, André G. Isaak wrote:

On 2025-03-24 14:11, olcott wrote:

On 3/24/2025 12:35 PM, dbush wrote:

On 3/24/2025 12:44 PM, olcott wrote:

On 3/24/2025 10:14 AM, dbush wrote:

On 3/24/2025 11:03 AM, olcott wrote:

On 3/24/2025 6:23 AM, Richard Damon wrote:

On 3/23/25 11:09 PM, olcott wrote:

 

It is impossible for HHH compute the function from the direct
execution of DDD because DDD is not the finite string input
basis from which all computations must begin.
https://en.wikipedia.org/wiki/Computable_function

WHy isn't DDD made into the correct finite string?i

DDD is a semantically and syntactically correct finite stirng of
the x86 machine language.

Which includes the machine code of DDD, the machine code of HHH,
and the machine code of everything it calls down to the OS level.
>
>

That seems to be your own fault.
The problem has always been that you want to use the wrong string
for DDD by excluding the code for HHH from it.

DDD emulated by HHH directly causes recursive emulation because it
calls HHH(DDD) to emulate itself again. HHH complies until HHH
determines that this cycle cannot possibly reach the final halt
state of DDD.

Which is another way of saying that HHH can't determine that DDD
halts when executed directly.

given an input of the function domain it can return the
corresponding output.
Computable functions are only allowed to compute the mapping from
their input finite strings to an output.

The HHH you implemented is computing *a* computable function, but
it's not computing the halting function:

The whole point of this post is to prove that no Turing machine ever
reports on the behavior of the direct execution of another Turing
machine.

UTMs do.
 

They never do, they only report on the behavior that
their input finite string specifies. When their input
finite string defines a pathological relationship
with its simulator then the specified behavior can
differ from the behavior of the direct execution.
Everyone here has been happily denying this verified
fact disagreeing with the behavior that the semantics
of the x86 language species. That is like disagreeing
with arithmetic just to make sure to be disagreeable.
--
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer