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

On 5/4/25 6:15 PM, 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
IT IS NOT COMPUTING FUNCTION THEN
IT IS NOT COMPUTING FUNCTION THEN
IT IS NOT COMPUTING FUNCTION THEN

Right, not all Turing Machine compute Functions, they all do perform Computations.

 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
 given an input of the function domain it can return the corresponding output.

Right, and the input to a Halt Decider is the representation of a Program, and the correct output is based on the behavior of that progrma when run.
Note, There was no requirement of a Halt Decider to BE trying to compute a "Computable Function", just a Function, to see if it is, in fact, Computable.

 given an input of the function domain it can return the corresponding output.
 given an input of the function domain it can return the corresponding output.
 *Computer science is ONLY concerned with computable functions*