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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory
Subject: Re: Turing computable functions
Date: Tue, 25 Mar 2025 18:34:31 -0400
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On 3/25/25 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

Right, we don't neefd to see the executing process, and it never needs 
to be executed to have the behavior, the mapping just is what it is.

Something you seem to stupid to understand.

> 
> On 3/25/2025 2:32 PM, dbush wrote:
>  > (<X>,Y) maps to 1 if and only if X(Y) halts when executed directly
> 
>