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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: Turing Computations <are> finite string transformations of inputs
Date: Sat, 26 Apr 2025 17:33:39 -0500
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On 4/26/2025 5:18 PM, André G. Isaak wrote:
> On 2025-04-26 15:28, olcott wrote:
>> On 4/26/2025 4:03 PM, André G. Isaak wrote:
>>> On 2025-04-25 21:28, olcott wrote:
>>>> On 4/25/2025 5:28 PM, André G. Isaak wrote:
>>>>> On 2025-04-25 10:31, olcott wrote:
>>>>>
>>>>>> Once we understand that Turing computable functions are only
>>>>>> allowed to derived their outputs by applying finite string
>>>>>> operations to their inputs then my claim about the behavior
>>>>>> of DD that HHH must report on is completely proven.
>>>>>
>>>>> You're very confused here.
>>>>>
>>>>> Computable functions are *functions*. That is, they are mappings 
>>>>> from a domain to a codomain, neither of which are required to be 
>>>>> strings. Functions don't involve finite string operations at all.
>>>>>
>>>>
>>>> All Turing Machine based computation applies the/
>>>> finite string transformations specified by the TM
>>>> language to the input finite string.
>>>
>>> Turing machines and computable functions are not the same thing. You 
>>> keep conflating the two. The point of my post was to try to get you 
>>> to be more careful with your terminology.
>>>
>>> André
>>>
>>
>> Yes so I must correct my words to say
>>
>> All Turing Machine based *Computable Functions* apply the
>>  >> finite string transformations specified by the TM
>>  >> language to the input finite string.
> 
> Which is just as mangled as your earlier usage. Maybe learn what these 
> things mean...
> 
> André
> 

When HHH emulates DD once and then emulates itself
emulating DD according to the finite string transformation
rules specified by the x86 language then HHH has complete
proof that DD correctly emulated by HHH cannot possibly
reach its final halt state even after an infinite number
of steps of correct emulation.


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