Re: Turing computable functions

On 3/25/2025 4:02 PM, dbush wrote:

On 3/25/2025 4:50 PM, olcott wrote:

On 3/25/2025 3:05 PM, dbush wrote:

On 3/25/2025 3:47 PM, olcott wrote:

On 3/25/2025 2:32 PM, dbush wrote:

On 3/25/2025 3:24 PM, olcott wrote:

Cannot possibly derive any outputs not computed from
their inputs.

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Correct, algorithms can only compute computable mathematical function.
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A Turing machine halt decider

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Does not exist because the required mapping is not computable:
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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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cannot possibly report
on the behavior of any directly executing process.
No Turing machine can every do this. This has always
been beyond what any Turing machine can ever do.

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Strawman: reporting on an executing process is not a requirement.

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YOU JUST SAID THAT IT WAS
YOU KEEP MINDLESSLY REPEATING THAT IT IS
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On 3/25/2025 2:32 PM, dbush wrote:
 > (<X>,Y) maps to 1 if and only if X(Y) halts when executed directly
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>

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I never said it had to actually watch an executing process, only report what would happen if it did run.
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*It has been conclusively proven as a verified*
*fact many hundreds of times over several years*
That the behavior that the finite string input specifies

 Is

NOT ALWAYS

the behavior of directly executing the described Turing machine.

WHEN THIS FINITE STRING DEFINES A PATHOLOGICAL
RELATIONSHIP WITH ITS SIMULATING TERMINATION ANALYZER.
I can't help but believe that ALL of my reviewers are
flat out dishonest on this one point.
--
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer