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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory
Subject: Re: Turing Machine computable functions apply finite string
 transformations to inputs
Date: Sun, 4 May 2025 20:21:07 -0400
Organization: i2pn2 (i2pn.org)
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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.
>>>
>>> Functions computed by Turing Machines require INPUTS
>>> and produce OUTPUTS DERIVED FROM THESE INPUTS.
>>
>> Counter-example: a Turing Machine can calculate pi without any input 
>> whatsoever.
>>
>> As Mikko rightly said: a Turing machine does not need to require an 
>> input.
>>
> 
> 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*
>