Halt Deciders must be computable functions --- dbush was always wrong

On 3/23/2025 4:49 AM, Mikko wrote:

On 2025-03-22 15:47:03 +0000, olcott said:
 

On 3/22/2025 9:57 AM, Mikko wrote:

On 2025-03-21 15:25:09 +0000, olcott said:
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On 3/21/2025 10:00 AM, olcott wrote:

On 3/21/2025 9:44 AM, dbush wrote:

On 3/17/2025 11:29 PM, olcott wrote:

On 3/17/2025 8:25 PM, dbush wrote:

On 3/17/2025 9:18 PM, olcott wrote:

On 3/17/2025 7:48 PM, dbush wrote:

On 3/17/2025 8:44 PM, olcott wrote:

On 3/17/2025 7:22 PM, dbush wrote:

On 3/17/2025 8:18 PM, olcott wrote:

On 3/17/2025 7:00 PM, dbush wrote:

On 3/17/2025 7:51 PM, olcott wrote:

On 3/17/2025 5:15 PM, dbush wrote:

On 3/17/2025 6:10 PM, olcott wrote:

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The halt decider does not and cannot possibly
compute the mapping from the actual behavior
of an executing process.
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No one claimed it should.  What it must do is determine what would happen in the hypothetical case that a direct execution is done.
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It can only do that when it assumes that the behavior
specified by the semantics of its input machine language
exactly matches this behavior. Its only basis is this
input finite string.

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i.e. the semantics of the x86 language when those actual instructions are actually executed on an actual x86 processor.
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A termination analyzer has no access to that.

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The input is required to be a complete description of the program that can be used to determine its full behavior.  In the case of DD, that description is the code of the function DD, the code of the function HHH, and everything that HHH calls down to the OS level.

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It does do that and this behavior does specify

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Halting behavior when executed directly, which is what is to be reported on as per the requirements:
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It has always been incorrectly assumed that the input
finite string is a perfect proxy for the behavior
of the direct execution.

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False.  The input finite string is REQUIRED to be a perfect proxy for direct execution, as per the requirements:
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It looks like you simply don't understand that a
counter-factual requirement is necessarily incorrect.

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Category error.  Requirements can't be false.  They can however be impossible to satisfy.
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When the definition of a [HALT decider] contradicts the definition of a [decider] in the same field of inquiry at least one of them is incorrect.

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No, there is nothing incorrect there. It simply means a halpt decider
is not a decider,

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It has always been stipulated that a [halt decider] is a type
of [decider]. This means that every halt decider only has the
behavior that its finite string input specifies as its only basis.

 No, it has not. "Halting decider" can be defined without mentioning
"decider" and some authors do so.
 

I forgot that the notion of computable function already proves my point
Computable functions are the basic objects of study in
computability theory. 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.
given an input of the function domain it can return the
corresponding output.
https://en.wikipedia.org/wiki/Computable_function
The behavior of a directly executing Turing Machine
cannot be computed because a directly executing Turing
machine cannot be the input to any computable function.
--
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer