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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: Turing computable functions
Date: Tue, 25 Mar 2025 15:50:33 -0500
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On 3/25/2025 3:05 PM, dbush wrote:
> On 3/25/2025 3:47 PM, olcott wrote:
>> On 3/25/2025 2:32 PM, dbush wrote:
>>> On 3/25/2025 3:24 PM, olcott wrote:
>>>> Cannot possibly derive any outputs not computed from
>>>> their inputs.
>>>
>>> Correct, algorithms can only compute computable mathematical function.
>>>
>>>>
>>>> A Turing machine halt decider 
>>>
>>> Does not exist because the required mapping is not computable:
>>>
>>>
>>> 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
>>>
>>>
>>>
>>>> cannot possibly report
>>>> on the behavior of any directly executing process.
>>>> No Turing machine can every do this. This has always
>>>> been beyond what any Turing machine can ever do.
>>>
>>>
>>> Strawman: reporting on an executing process is not a requirement. 
>>
>> YOU JUST SAID THAT IT WAS
>> YOU KEEP MINDLESSLY REPEATING THAT IT IS
>>
>> On 3/25/2025 2:32 PM, dbush wrote:
>>  > (<X>,Y) maps to 1 if and only if X(Y) halts when executed directly
>>
>>
> 
> I never said it had to actually watch an executing process, only report 
> what would happen if it did run.
> 

*It has been conclusively proven as a verified*
*fact many hundreds of times over several years*
That the behavior that the finite string input specifies
is not perfect proxy for the behavior of the underlying
directly executed machine.

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