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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: Turing Machine computable functions MUST apply finite string
 transformations to inputs
Date: Wed, 30 Apr 2025 23:26:16 -0500
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On 4/30/2025 6:50 PM, Richard Damon wrote:
> On 4/30/25 1:32 PM, olcott wrote:
>> On 4/30/2025 11:11 AM, Richard Heathfield wrote:
>>> On 30/04/2025 16:44, joes wrote:
>>>> Am Wed, 30 Apr 2025 10:09:45 -0500 schrieb olcott:
>>>>> On 4/29/2025 5:01 AM, Mikko wrote:
>>>>
>>>>>> Irrelevant. There is sufficient agreement what Turing machines are.
>>>>>
>>>>> Turing machine computable functions must apply finite string
>>>>> transformation rues to inputs to derive outputs.
>>>>>
>>>>> This is not a function that computes the sum(3,2):
>>>>> int sum(int x, int y) { return 5; }
>>>> Yes it is, for all inputs.
>>>
>>> Not much of a computation, though, is it?
>>>
>>
>> It IS NOT a Turing Computable function
>> because it does not ever apply any finite
>> string transformation  rules to its inputs.
>>
>> THE OUTPUTS MUST CORRESPOND TO THE INPUTS.
>> sum(4,3) returns 5 proving that sum is
>> not a Turing Computable function.
>>
> 
> Sure it is. You just don't know that that mean.
> 

Computable functions must apply finite string
transformations to inputs. sum does not do that.

> THe function given computes the Computable Function defined by the 
> mapping of all pair (x, y) -> the value 5.
> 
> That is a perfectly fine Function, and easily proved to be computable.
> 
> It isn't a correct function for computing the addition function that 
> maps the pair (x, y) -> x+y, but that wasn't what you said, because you 
> don't know what you are talking about.
> 
> You don't seem to understand that "Functions" are defined just by the 
> input -> output mapping that they specify.
> 
> They are Computable if some Turing Machine exists that can create that 
> whole mapping (via some representation method for the inputs/outputs)
> 
> But the "Computable Function" still isn't defined by the code fo that 
> Turing Machine, but by the mapping.
> 
> NO "Turing Machine" is a "Turing Computable Function" as they are 
> different categories of things.
> 
> Turing Machine as strictly defined by the rules that they are built on 
> that create the mappings they compute.
> 
> Functions (Computable or Not) are defined by the Mapping of Input to 
> Output that they are.
> 
> 
> Turing Machine COMPUTE some Computable Function, they are not the 
> Function itself.
> 
> 


-- 
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer