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

Op 22.apr.2025 om 21:50 schreef olcott:

On 4/22/2025 2:30 PM, Fred. Zwarts wrote:

Op 22.apr.2025 om 21:14 schreef olcott:

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.
>

Therefore HHH should report on the actual input, the finite string that describes a halting program. Not on the hypothetical input that does not halt, because it is based on a hypothetical HHH that does not abort.
>
Why do you maintain that HHH should process the hypothetical input instead of the actual input.
Do you really believe that 3+2 equals 5+3?

 I have proven that the directly executed DD and DD
emulated by HHH according to the semantics of the
x86 language have a different set of state changes
many hundreds of times for several years.

You never showed a proof. You only repeated a dream. You are dreaming many years without any logic. You failed to show the first state change where the direct execution is different from the simulation. You only showed an erroneous HHH that fails to reach the end of the simulation of a halting program.