Recursive simulation must be reported and not ignored.

On 5/10/2025 8:07 PM, Richard Damon wrote:

On 5/10/25 9:00 PM, olcott wrote:

On 5/10/2025 6:56 PM, Mr Flibble wrote:

On Sat, 10 May 2025 18:40:53 -0400, Richard Damon wrote:
>

On 5/10/25 4:38 PM, Mr Flibble wrote:

How my refutation differs to Peter's:
>
* Peter refutes the halting problem based on pathological input
manifesting in a simulating halt decider as infinite recursion, this
being treated as non-halting.
* Flibble refutes the halting problem based on patholgical input
manifesting as decider/input self-referencial conflation, resulting in
the contradiction at the heart of the halting problem being a category
(type) error, i.e. ill-formed.
>
These two refutations are related but not exactly the same.
>
/Flibble

>
And the problem is that you use incorrect categories.
>
The decider needs to be of the category "Program".
>
The input also needs to be of the category "Program", but provided via a
representation. The act of representation lets us convert items of
category Program to the category of Finite String which can be an input.

>
Those two categories you have identified are different hence the category
error.
>

>
That is correct. A running program and an input finite
string ARE NOT THE SAME.

 But there is a direct relationship between the two.
 

void DDD()
{
   HHH(DDD);
   return;
}
_DDD()
[00002172] 55         push ebp      ; housekeeping
[00002173] 8bec       mov  ebp,esp  ; housekeeping
[00002175] 6872210000 push 00002172 ; push DDD
[0000217a] e853f4ffff call 000015d2 ; call HHH(DDD)
[0000217f] 83c404     add  esp,+04
[00002182] 5d         pop  ebp
[00002183] c3         ret
Size in bytes:(0018) [00002183]
The key thing is that they don't always have the same
behavior.
When they do have different behavior the termination
analyzer is only allowed to report on the recursive
simulation behavior that its input specifies.
It is not allowed to ignore this on the basis that the
direct execution or UTM simulation has no recursive
simulation.
--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer