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From: dbush <dbush.mobile@gmail.com>
Newsgroups: comp.theory
Subject: Re: Turing Machine computable functions MUST apply finite string
 transformations to inputs
Date: Wed, 30 Apr 2025 15:55:40 -0400
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On 4/30/2025 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

Lying by misuse of terms.

A turing computable function is a mapping for which an algorithm exists 
to compute it, not the algorithm itself.

Further use of "turing computable function" when what is meant is 
"algorithm" will result in the former being replaced with the later in 
future responses to your posts to make it clear what you are actually 
talking about.


> because it does not ever apply any finite
> string transformation  rules to its inputs.

Sure it does.  It computes the mapping of all pairs of integers to the 
number 5.

> 
> THE OUTPUTS MUST CORRESPOND TO THE INPUTS.

And it does, according to the following mapping which is a turning 
computable function:


For all integers X and Y:

(X,Y) maps to 5


> sum(4,3) returns 5 proving that sum is
> not an algorithm.
> 

Of course it's an algorithm.  It performs a fixed immutable sequence of 
instructions to compute a result from the input.