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

Am Tue, 22 Apr 2025 14:14:41 -0500 schrieb olcott:

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

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

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.

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.

Where do they diverge? The directly executed DD also calls a HHH that
tries to simulate itself.

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.

On the contrary, it is required to report on the behaviour of the
input when directly executed, otherwise a halt decider is of no interest.
I cannot produce a faulty simulator and claim that its result is
what counts.

Outputs are forced to correspond to inputs when finite string
transformation rules are applied to inputs to derive outputs.

There are many behaviours you could compute from the description of
DD, such as when run backwards or in a loop, and even other things
like the number of instructions.

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?

Agreed. Agreed?

--
Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.