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From: dbush <dbush.mobile@gmail.com>
Newsgroups: comp.theory
Subject: Re: Turing Machine computable functions apply finite string
 transformations to inputs +++
Date: Mon, 28 Apr 2025 18:11:52 -0400
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On 4/28/2025 5:47 PM, olcott wrote:
> On 4/28/2025 3:21 PM, Richard Heathfield wrote:
>> On 28/04/2025 21:03, olcott wrote:
>>> On 4/28/2025 2:58 PM, dbush wrote:
>>
>> <snip>
>>
>>>> Category error.  The halting function below is fully defined, and 
>>>> this mapping is not computable *as you have explicitly admitted*.
>>>>
>>>
>>> Neither is the square root of an actual onion computable.
>>>
>>> Turing Computable Functions are required to apply finite
>>> string transformations to their inputs. The function defined
>>> below ignores that requirement PROVING THAT IT IS INCORRECT.
>>
>> No, it proves that you agree that it's not a computable function. QED.
>>
> 
> Computing the actual behavior the direct execution
> of any input is ALWAYS IMPOSSIBLE.

So you again agree that Linz is correct.

> 
> No halt decider 

So you assume that an algorithm exists that can perform the following 
mapping:


Given any algorithm (i.e. a fixed immutable sequence of instructions) X 
described as <X> with input Y:

(<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



> can ever directly see the actual
> behavior of any directly executed input.
> 

And you reach a contradiction, proving the assumption false, as Linz 
proved and you *explicitly* agreed is correct.

>>>> Given any algorithm (i.e. a fixed immutable sequence of 
>>>> instructions) X described as <X> with input Y:
>>>>
>>>> (<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
>>
>>
> 
>