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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: Turing computable functions
Date: Tue, 25 Mar 2025 16:46:16 -0500
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On 3/25/2025 4:12 PM, joes wrote:
> Am Tue, 25 Mar 2025 15:50:33 -0500 schrieb olcott:
>> 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
>>> 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.

> A TM can be completely specified in a finite string.
> 

That has different behavior when it is simulated by a UTM
that defines a pathological relationship to this UTM than
a UTM where no such pathological relationship exists.

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