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

On 5/4/25 8:41 PM, olcott wrote:

On 5/4/2025 5:27 PM, Mr Flibble wrote:

On Sun, 04 May 2025 17:15:04 -0500, olcott wrote:
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On 5/4/2025 2:21 PM, Richard Heathfield wrote:

On 04/05/2025 18:55, olcott wrote:

Changing my words then rebutting these changed words is dishonest.
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Functions computed by Turing Machines require INPUTS and produce
OUTPUTS DERIVED FROM THESE INPUTS.

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Counter-example: a Turing Machine can calculate pi without any input
whatsoever.
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As Mikko rightly said: a Turing machine does not need to require an
input.
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IT IS NOT COMPUTING FUNCTION THEN IT IS NOT COMPUTING FUNCTION THEN IT
IS NOT COMPUTING FUNCTION THEN IT IS NOT COMPUTING FUNCTION THEN
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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
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given an input of the function domain it can return the corresponding
output.
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given an input of the function domain it can return the corresponding
output.
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given an input of the function domain it can return the corresponding
output.
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*Computer science is ONLY concerned with computable functions*

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Computer science is also concerned with intractable problems.
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/Flibble

 I think the computability aspect of computer science
is only concerned with computable functions.

Which is where you are wrong.
It is the DETERMINATION of which Functions are Computable, and which are not.

 Computing the mapping from INPUTS to OUTPUTS on
the basis of finite string transformation rules
specified by an algorithm.
 The assembly language version of DD is the same
sort of state transition directed graph as the
Linz proof, thus zero vagueness or ambiguity.

But only when it includes the code for the decider, and thus that decider has been fixed, and thus can't be presumed to do something it doesn't do.

 DD correctly emulated by HHH CANNOT POSSIBLY
REACH ITS OWN FINAL STATE. Many dozens of
people have been STUPIDLY disagreeing with this
for several years.
 

But HHH doesn't correctly emulate DD, as has been proven by running your HHH defined in Halt7.c, and thus we see that it DOES abort its emulation, and thus is NOT a correct emulation.
You are just proving that you live in a fantasy world of make believe where truth and reality don't need to exist.