Re: Turing Machine computable functions apply finite string transformations to inputs

On 4/28/2025 11:54 AM, dbush wrote:

On 4/28/2025 12:38 PM, olcott wrote:

On 4/28/2025 10:41 AM, dbush wrote:

On 4/28/2025 11:35 AM, olcott wrote:

On 4/28/2025 10:18 AM, dbush wrote:

On 4/28/2025 11:01 AM, olcott wrote:

On 4/28/2025 2:33 AM, Richard Heathfield wrote:

On 28/04/2025 07:46, Fred. Zwarts wrote:
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So we agree that no algorithm exists 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.
Correct?

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Correct. We can, however, construct such an algorithm just as long as we can ignore any input we don't like the look of.
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The behavior of the direct execution of DD cannot be derived
by applying the finite string transformation rules specified
by the x86 language to the input to HHH(DD). This proves that

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The assumption that an H exists that meets the below requirements is false, as shown by Linz and others:
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I have just proved that those requirements are stupidly wrong

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Category error.  The mapping exists

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Computable functions are the formalized analogue
of the intuitive notion of algorithms, in the
sense that a function is computable if there
exists an algorithm that can do the job of the
function, i.e.

 i.e. a computable function is a mathematical mapping for which an algorithm exists to compute in.
 And the halting function below is not a computable function:
 

It is NEVER a computable function because no halt
decider can ever directly see the behavior of
the directly executed DD because this DD IS NOT AN INPUT.
The one that IS AN INPUT SPECIFIES DIFFERENT BEHAVIOR.
I don't understand how you can stupidly disagree with
the x86 language without being a troll having no interest
in  truth.
--
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer