Re: HHH(DD) --- COMPUTE ACTUAL MAPPING FROM INPUT TO OUTPUT --- Using Finite String Transformations

On 4/22/2025 1:10 PM, Fred. Zwarts wrote:

Op 22.apr.2025 om 18:38 schreef olcott:

>
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.
>

And it has been proven that no finite string transformations are possible that report the halting behaviour for all inputs that specify a correct program. 

int sum(int x, int y) { return x + y; }
Only when people stupid assume the same thing as
sum(3,2) should return the sum of 5 + 3.
The directly executed DD and DD emulated by HHH according
to the semantics of the x86 language have had provably
different set of state changes for several years now.
HHH is only accountable for the behavior that its input
actually specifies and strictly NOT ALLOWED to report on
anything else. HHH IS NOT ALLOWED TO REPORT ON THE BEHAVIOR
OF THE DIRECTLY EXECUTED DD. This breaks the computable
function requirement that OUTPUTS MUST CORRESPOND TO INPUTS.
Outputs are forced to correspond to inputs when finite string
transformation rules are applied to inputs to derive outputs.

There is no algorithm that can determine for all possible inputs whether the input specifies a program that (according to the semantics of the machine language) halts when directly executed.
Agreed?

--
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer