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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: Correcting the definition of the halting problem --- Computable
 functions
Date: Mon, 24 Mar 2025 15:11:12 -0500
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On 3/24/2025 12:35 PM, dbush wrote:
> On 3/24/2025 12:44 PM, olcott wrote:
>> On 3/24/2025 10:14 AM, dbush wrote:
>>> On 3/24/2025 11:03 AM, olcott wrote:
>>>> On 3/24/2025 6:23 AM, Richard Damon wrote:
>>>>> On 3/23/25 11:09 PM, olcott wrote:
>>>>>> It is impossible for HHH compute the function from the direct
>>>>>> execution of DDD because DDD is not the finite string input
>>>>>> basis from which all computations must begin.
>>>>>> https://en.wikipedia.org/wiki/Computable_function
>>>>>
>>>>> WHy isn't DDD made into the correct finite string?i
>>>>>
>>>>
>>>> DDD is a semantically and syntactically correct finite
>>>> stirng of the x86 machine language.
>>>
>>> Which includes the machine code of DDD, the machine code of HHH, and 
>>> the machine code of everything it calls down to the OS level.
>>>
>>>>
>>>>> That seems to be your own fault.
>>>>>
>>>>> The problem has always been that you want to use the wrong string 
>>>>> for DDD by excluding the code for HHH from it.
>>>>>
>>>>
>>>> DDD emulated by HHH directly causes recursive emulation
>>>> because it calls HHH(DDD) to emulate itself again. HHH
>>>> complies until HHH determines that this cycle cannot
>>>> possibly reach the final halt state of DDD.
>>>>
>>>
>>> Which is another way of saying that HHH can't determine that DDD 
>>> halts when executed directly.
>>>
>>
>> given an input of the function domain it can
>> return the corresponding output.
>> https://en.wikipedia.org/wiki/Computable_function
>>
>> Computable functions are only allowed to compute the
>> mapping from their input finite strings to an output.
>>
> 
> 
> The HHH you implemented is computing *a* computable function, but it's 
> not computing the halting function:
> 

The whole point of this post is to prove that
no Turing machine ever reports on the behavior
of the direct execution of another Turing machine.

> 
> 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

Cannot possibly be a computable function because computable
functions cannot possibly have directly executing Turing
machines as their inputs.


> (<X>,Y) maps to 0 if and only if X(Y) does not halt when executed directly
> 
> 

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