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

On 2025-03-24 17:42, olcott wrote:

On 3/24/2025 6:05 PM, André G. Isaak wrote:

On 2025-03-24 17:04, olcott wrote:

_III()
[00002172] 55         push ebp      ; housekeeping
[00002173] 8bec       mov  ebp,esp  ; housekeeping
[00002175] 6872210000 push 00002172 ; push III
[0000217a] e853f4ffff call 000015d2 ; call EEE(III)
[0000217f] 83c404     add  esp,+04
[00002182] 5d         pop  ebp
[00002183] c3         ret
Size in bytes:(0018) [00002183]
>
When III is emulated by pure emulator EEE for any finite
number of steps of emulation according to the semantics
of the x86 language it never reaches its own "ret"
instruction final halt state THUS DOES NOT HALT.
>
When III is directly executed calls an EEE instance
that only emulates finite number of steps then this
directly executed III always reaches its own "ret"
instruction final halt state THUS HALTS.

>
And that has what, exactly, to do with the post you are allegedly responding to?
>
André
>

  THE INPUT FINITE STRING DOES SPECIFY RECURSIVE EMULATION.
 The behavior specified by the finite string input to a
computable function implemented on a model of computation
 does differ from the direct execution of this same finite
string because the direct execution avoids the pathological
self-reference that causes the recursive emulation.
 THE INPUT FINITE STRING DOES SPECIFY RECURSIVE EMULATION.

In the post you were responding to I pointed out that computable functions are mathematical objects. The above copypasta doesn't address this.
I pointed out that the domain of a computable function needn't be a string. The above copypasta doesn't address this.
I pointed out that there is no bijection natural numbers and strings, but rather a one-to-many relation. The above copypasta doesn't address this.
I pointed out that the exact same sort of one-to-many relation exists between computations and strings. The above copypasta doesn't address this.
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