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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory
Subject: Re: Correcting the definition of the halting problem --- Computable
 functions
Date: Tue, 25 Mar 2025 21:16:45 -0400
Organization: i2pn2 (i2pn.org)
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On 3/25/25 11:11 AM, olcott wrote:
> On 3/25/2025 9:59 AM, dbush wrote:
>> On 3/25/2025 9:14 AM, olcott wrote:
>>> On 3/25/2025 3:32 AM, joes wrote:
>>>> Am Mon, 24 Mar 2025 22:29:06 -0500 schrieb olcott:
>>>>> On 3/24/2025 10:12 PM, dbush wrote:
>>>>>> On 3/24/2025 10:07 PM, olcott wrote:
>>>>>>> On 3/24/2025 8:46 PM, André G. Isaak wrote:
>>>>>>>> On 2025-03-24 19:33, olcott wrote:
>>>>>>>>> On 3/24/2025 7:00 PM, André G. Isaak wrote:
>>>>>>>>
>>>>>>>>>> In the post you were responding to I pointed out that computable
>>>>>>>>>> functions are mathematical objects.
>>>>>>>>> Computable functions implemented using models of computation would
>>>>>>>>> seem to be more concrete than pure math functions.
>>>>>>>> Those are called computations or algorithms, not computable
>>>>>>>> functions.
>>>>>>> https://en.wikipedia.org/wiki/Pure_function Is another way to 
>>>>>>> look at
>>>>>>> computable functions implemented by some concrete model of
>>>>>>> computation.
>>>>>> And not all mathematical functions are computable, such as the 
>>>>>> halting
>>>>>> function.
>>>>
>>>>>>>> The halting problems asks whether there *is* an algorithm which can
>>>>>>>> compute the halting function, but the halting function itself is a
>>>>>>>> purely mathematical object which exists prior to, and 
>>>>>>>> independent of,
>>>>>>>> any such algorithm (if one existed).
>>>>>>> None-the-less it only has specific elements of its domain as its
>>>>>>> entire basis. For Turing machines this always means a finite string
>>>>>>> that (for example) encodes a specific sequence of moves.
>>>>>> False.  *All* turing machine are the domain of the halting function,
>>>>>> and the existence of UTMs show that all turnBing machines can be
>>>>>> described by a finite string.
>>>>> You just aren't paying enough attention. Turing machines are never in
>>>>> the domain of any computable function. <snip>
>>>
>>>> Fine, their descriptions are, and their behaviour is computable -
>>>> by running them.
>>>>
>>>
>>> Halt deciders
>>
>> Don't exist, because no H satisfies this requirement:
>>
> 
> Because no TM can ever take another actual TM as an input.

Sure it can, via a representation.

If you disallow using representations, then no program can add numbers 
or understand words, or do ANY task that isn't just a pure symbolic 
manipulation.

Sorry, you are just showing your utter ignorance of what you talk about, 
and that you are soo stupid you can't see the contradictions in your words.

> 
>>
>> Given any algorithm (i.e. a fixed immutable sequence of instructions) 
>> X described as <X> with input Y:
>>
>> A solution to the halting problem is an algorithm H that computes the 
>> following mapping:
>>
>> (<X>,Y) maps to 1 if and only if X(Y) halts when executed directly
>> (<X>,Y) maps to 0 if and only if X(Y) does not halt when executed 
>> directly
>>
>>
> 
>