Re: DDD specifies recursive emulation to HHH and halting to HHH1

On 3/31/2025 10:02 PM, dbush wrote:

On 3/31/2025 10:57 PM, olcott wrote:

On 3/31/2025 9:48 PM, dbush wrote:

On 3/31/2025 10:38 PM, olcott wrote:

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HHH must report on the behavior that its input
actually specifies.

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And the input specifies an algorithm that halts when executed directly.
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Which is NOT how it is executed.

 But IS what it is required to report on.
 

It IS executed with recursive emulation.

 Finitely recursive emulation, which is part of the algorithm DDD that halts.
 

>

This seems way too difficult
for people that can only spout off words that
they learned by rote, with no actual understanding
of the underlying principles involved.
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Every actual computation can only transform input
finite strings into outputs. HHH does do this.

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But not as per the requirements:
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Given any algorithm (i.e. a fixed immutable sequence of instructions) X described as <X> with input Y:
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A solution to the halting problem is an algorithm H that computes the following mapping:
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(<X>,Y) maps to 1 if and only if X(Y) halts when executed directly
(<X>,Y) maps to 0 if and only if X(Y) does not halt when executed directly
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The "requirements" that you mindlessly spout off

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Which would make all true statements provable if they could be met.
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violate this foundational principle of functions
computed by Turing machines.

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Which just says that no Turing machine satisfies those requirements, as Linz and others proved.
>

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int sum(int x, int y)
{
   return 5;
}
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sum(2,3) does not compute the sum of 2 + 3.
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It absolutely does.  There are *NO* requirements on the implementation, only the result.

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Unless and algorithm transforms its inputs
into its outputs it is not a Turing computable
function.
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 The only requirements of an algorithm are to generate the results of a mapping.  How that is accomplished is irrelevant.

It may have been historically considered irrelevant.
When it comes down to determining that mere guesses
are not any sort of: "computing the mapping" then it
does become relevant.
--
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer