Re: How do computations actually work?

On 5/23/25 12:10 PM, olcott wrote:

On 5/23/2025 2:14 AM, Mikko wrote:

On 2025-05-23 03:31:15 +0000, olcott said:
>

On 5/22/2025 10:23 PM, wij wrote:

On Thu, 2025-05-22 at 21:47 -0500, olcott wrote:

[cut]

>
Q: How do computations actually work?
A: Computation is merely step-by-step algorithm.
Nothing says it has to be TM.
>
Do the exercises in textbooks first before any claim of it.
>

>
int main()
{
   DD(); // by what steps can the HHH that DD calls
}       // report on the behavior its caller?

>
If we don't insist that the report be correct:
1. guess
2. tell what was guessed
>

 This does not work because all computable functions
that implement termination analyzers must compute
the mapping from their input finite string according
to the behavior that it specifies. In my concrete
examples DDD must be simulated by HHH according to the
rules of the x86 language.
 _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]
 DDD specifies that it will continue to call HHH
until HHH sees the repeating pattern and aborts
its simulation.
 

Yes, they must compute the mapping, but the rules don't say HOW. If you are restricting how it can make its decision, that is limiting what questions it might be able to solve. Of course, the fact that correctly simulating the input, and deciding on it are contradictiory requirements, it seems you idea of Simulating Halt Deciders has an error in its definition as it is self-contradictory.
Since your input DDD can't be simulated as it references UNDEFINED (as part of the input) memory, it just isn't a valid input.
When you include that memory as part of the input, then DDD has fully valid behavior, and is a correct thing to ask about, and if HHH(DDD) returns any answer, the correct answer would be HALTING.
Thus, your HHH that returns non-halting is just wrong.