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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: Mon, 5 May 2025 07:28:29 -0400
Organization: i2pn2 (i2pn.org)
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On 5/5/25 12:32 AM, olcott wrote:
> On 5/4/2025 7:18 PM, Richard Damon wrote:
>> On 5/4/25 1:55 PM, olcott wrote:
>>> On 5/2/2025 4:16 AM, Mikko wrote:
>>>> On 2025-04-30 15:09:45 +0000, olcott said:
>>>>
>>>>> On 4/29/2025 5:01 AM, Mikko wrote:
>>>>>> On 2025-04-28 16:27:56 +0000, olcott said:
>>>>>>
>>>>>>> On 4/28/2025 4:14 AM, Mikko wrote:
>>>>>>>> On 2025-04-26 15:59:39 +0000, olcott said:
>>>>>>>>
>>>>>>>>> On 4/26/2025 3:19 AM, Mikko wrote:
>>>>>>>>>> On 2025-04-25 16:31:58 +0000, olcott said:
>>>>>>>>>>
>>>>>>>>>>> On 4/25/2025 3:46 AM, Mikko wrote:
>>>>>>>>>>>> On 2025-04-24 15:11:13 +0000, olcott said:
>>>>>>>>>>>>
>>>>>>>>>>>>> On 4/23/2025 3:52 AM, Mikko wrote:
>>>>>>>>>>>>>> On 2025-04-21 23:52:15 +0000, olcott said:
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Computer Science Professor Eric Hehner PhD
>>>>>>>>>>>>>>> and I all seem to agree that the same view
>>>>>>>>>>>>>>> that Flibble has is the correct view.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Others can see that their justification is defective and 
>>>>>>>>>>>>>> contradicted
>>>>>>>>>>>>>> by a good proof.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Some people claim that the unsolvability of the halting 
>>>>>>>>>>>>>> problem is
>>>>>>>>>>>>>> unproven but nobody has solved the problem.
>>>>>>>>>>>>>
>>>>>>>>>>>>> For the last 22 years I have only been refuting the
>>>>>>>>>>>>> conventional Halting Problem proof.
>>>>>>>>>>>>
>>>>>>>>>>>> Trying to refute. You have not shown any defect in that 
>>>>>>>>>>>> proof of the
>>>>>>>>>>>> theorem. There are other proofs that you don't even try to 
>>>>>>>>>>>> refute.
>>>>>>>>>>>
>>>>>>>>>>> Not at all. You have simply not been paying enough attention.
>>>>>>>>>>>
>>>>>>>>>>> Once we understand that Turing computable functions are only
>>>>>>>>>>> allowed
>>>>>>>>>>
>>>>>>>>>> Turing allowed Turing machines to do whatever they can do.
>>>>>>>>>
>>>>>>>>> Strawman deception error of changing the subject away
>>>>>>>>> from computable functions.
>>>>>>>>
>>>>>>>> Attempt to deceive by a false claim. The term "computable 
>>>>>>>> function" is
>>>>>>>> defined in terms of Turing machines so Turing machines are on 
>>>>>>>> topic.
>>>>>>>
>>>>>>> Since there is no universally agreed upon definition
>>>>>>> of the Turing Machine language it is impossible to
>>>>>>> provide the 100% concrete details in this Turing
>>>>>>> Machine language.
>>>>>>
>>>>>> Irrelevant. There is sufficient agreement what Turing machines are.
>>>>>
>>>>> Turing machine computable functions must apply
>>>>> finite string transformation rues to inputs
>>>>> to derive outputs.
>>>>
>>>> A Turing machine does not need to require an input.
>>>
>>> Changing my words then rebutting these changed
>>> words is dishonest.
>>>
>>> Functions computed by Turing Machines require INPUTS
>>> and produce OUTPUTS DERIVED FROM THESE INPUTS.
>>>
>>
>> Right, and for the Turing Machine to correctly compute a Function, its 
>> computed mapping must match the mapping defined by the function.
>>
> 
> That is correct. You and I agree more on these aspects
> than anyone else. You seems to be very intelligent
> in some very important things.
> 
>> THe Halting Function, which a Halting Decider is to compute, is the 
>> mapping of a Program (or its representation) to whether that Program 
>> will Halt when run.
>>
> 
> That is not the way that these mappings work.
> They ONLY works on finite string inputs. They
> never ever work directly on any executable program.
> 
> 

TURING Machines need finits strings.

FUNCTIONS do not, they can work on virtually any sort of object.

After all, the "add" function takes two numbers, numbers are NOT "finite 
strings" but can be represeted by finite strings.

In the same way, the Halting Function takes Programs with their Inputs 
as the Input to their Mapping. Just like the "add" program needed the 
"Number" to be converted to a string with a representation, the "halt 
decider" program needs the Program that was the input, to be converted 
to a finite string to be its input, via some representation.

You are just proving you don't understand what you are talking about, 
and don't actually know what a "Function" is, as it is too abstract of a 
concept for you.

The Halt Mappins *IS* a mapping of ACTUAL PROGRAM to its ACTUAL BEHAVIOR 
WHEN EXECUTED. PERIOD.

That you don't understand this just shows your ignorance.

We convert these concepts to finite strings to give it to the algorithm.