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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: Correcting the definition of the halting problem --- Computable
 functions
Date: Tue, 25 Mar 2025 08:14:43 -0500
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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 turning 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 only report on the behavior that
their input finite string specifies. When their input
finite string defines a pathological relationship
with its simulator then the specified behavior can
differ from the behavior of the direct execution.

Everyone here has been happily denying this verified
fact disagreeing with the behavior that the semantics
of the x86 language species. That is like disagreeing
with arithmetic just to make sure to be disagreeable.

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