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

On 5/5/2025 8:19 PM, Richard Damon wrote:

On 5/4/25 8:35 PM, olcott wrote:

On 5/4/2025 5:34 PM, Mr Flibble wrote:

On Sun, 04 May 2025 23:30:54 +0100, Richard Heathfield wrote:
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On 04/05/2025 23:15, olcott wrote:

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

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Quoth Alan Turing:
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(viii) The limit of a computably convergent sequence is computable.
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  From (viii) and TT— 4(1—i-|--i—...) we deduce that TT is computable.
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No input required.
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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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That's a very second-rate summary of computability. Turing was far more
interested in whether a computation was possible than whether it needed
inputs. Do most computations need inputs? Most useful ones that we care
about, sure. But all? By no means.
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*Computer science is ONLY concerned with computable functions*

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Computer science is concerned with the Halting Problem.
The Halting Problem is concerned with an incomputable function.
Therefore computer science is concerned with at least one incomputable
function.

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The function is neither computable nor incomputable because there is no
function at all, just a category error.
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/Flibble

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You can look at it that way or you can look
at it as simulating termination analyzer HHH(DD)
does correctly determine that DD cannot possibly
reach its own final state, thus is correctly
rejected as non-halting.
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 Except that isn't the question that is being asked.
 In fact, that question has a trivial answer, as we can make an H0 that just aborts its emulation and returns 0 and it is correct by your definition,

No that is stupidly wrong as I have said at least 100 times recently.
The termination analyzer must compute the mapping from the input
on the basis of the behavior that this input actually specifies.
--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer