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From: joes <noreply@example.org>
Newsgroups: comp.theory
Subject: Re: HHH(DD) --- COMPUTE ACTUAL MAPPING FROM INPUT TO OUTPUT --- Using
 Finite String Transformations
Date: Wed, 23 Apr 2025 11:22:02 -0000 (UTC)
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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.