Computable Functions --- OUTPUTS MUST CORRESPOND TO INPUTS

On 4/22/2025 1:07 PM, Fred. Zwarts wrote:

Op 22.apr.2025 om 18:28 schreef olcott:

On 4/22/2025 7:57 AM, joes wrote:

Am Tue, 15 Apr 2025 15:44:06 -0500 schrieb olcott:

On 4/15/2025 2:03 PM, dbush wrote:

On 4/15/2025 2:50 PM, olcott wrote:

On 4/15/2025 11:05 AM, dbush wrote:

On 4/15/2025 11:29 AM, olcott wrote:

>

*corresponding output to the input*
Not freaking allowed to look at any damn thing else besides the
freaking input. Must compute whatever mapping ACTUALLY EXISTS FROM
THIS INPUT.
>

So the algorithm HHH that you've implemented computes *some*
computable function, but it does not compute the halting function as
it is not computable.
>

*corresponding output to the input*
>

That doesn't refute anything I said.
>

You continue to stupidly insist that int sum(int x, int y) {return x +
y; }
returns 7 for sum(3,2) because you incorrectly understand how these
things fundamentally work.
>
It is stupidly wrong to expect HHH(DD) report on the direct execution of
DD when you are not telling it one damn thing about this direct
execution.

What else is it missing that the processor uses to execute it?
>

>
int DD()
{
   int Halt_Status = HHH(DD);
   if (Halt_Status)
     HERE: goto HERE;
   return Halt_Status;
}
>
_DD()
[00002133] 55         push ebp      ; housekeeping
[00002134] 8bec       mov ebp,esp   ; housekeeping
[00002136] 51         push ecx      ; make space for local
[00002137] 6833210000 push 00002133 ; push DD
[0000213c] e882f4ffff call 000015c3 ; call HHH(DD)
[00002141] 83c404     add esp,+04
[00002144] 8945fc     mov [ebp-04],eax
[00002147] 837dfc00   cmp dword [ebp-04],+00
[0000214b] 7402       jz 0000214f
[0000214d] ebfe       jmp 0000214d
[0000214f] 8b45fc     mov eax,[ebp-04]
[00002152] 8be5       mov esp,ebp
[00002154] 5d         pop ebp
[00002155] c3         ret
Size in bytes:(0035) [00002155]
>
libx86emu <is> a correct x86 processor and does emulate
its inputs correctly.

 The key thing here is that Olcott consistently does not understand that HHH is given a finite string input that according to the semantics of the x86 language specifies a halting program,

That is stupidly incorrect. The only question that HHH
must answer is the behavior that its input specifies.
All computation is defined to be represented as finite
string transformations to finite strings.
a function is computable if there exists an algorithm
that can do the job of the function, i.e. given an input
of the function domain it can return the corresponding output.
https://en.wikipedia.org/wiki/Computable_function
On Turing Machines inputs <are> finite strings, and
finite string transformation rules <are> applied to
these finite strings to derive corresponding outputs.
People here stupidly assume that the outputs are not
required to correspond to the inputs. That comes from
learn-by-rote with zero depth of understanding.
--
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer