Path: news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail
From: dbush <dbush.mobile@gmail.com>
Newsgroups: comp.theory
Subject: Re: Turing Machine computable functions MUST apply finite string
 transformations to inputs
Date: Thu, 1 May 2025 07:55:15 -0400
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In-Reply-To: <vuut58$1s83v$2@dont-email.me>

On 5/1/2025 12:26 AM, olcott wrote:
> 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.
>>
> 
> Algorithms must apply finite string
> transformations to inputs. sum does not do that.
> 

Sure it does, it does a correct translation based on the following mapping:


For all integers X and Y:

(X,Y) maps to 5

>> 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.
>>
>>
> 
>