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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 VERIFIED FACT
Date: Tue, 29 Apr 2025 10:36:28 -0400
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On 4/29/2025 7:57 AM, dbush wrote:
> On 4/29/2025 12:57 AM, olcott wrote:
>> On 4/28/2025 10:00 PM, dbush wrote:
>>> On 4/28/2025 10:50 PM, olcott wrote:
>>>> On 4/28/2025 3:13 PM, Richard Heathfield wrote:
>>>>> On 28/04/2025 19:30, olcott wrote:
>>>>>> On 4/28/2025 11:38 AM, Richard Heathfield wrote:
>>>>>>> On 28/04/2025 16:01, olcott wrote:
>>>>>>>> On 4/28/2025 2:33 AM, Richard Heathfield wrote:
>>>>>>>>> On 28/04/2025 07:46, Fred. Zwarts wrote:
>>>>>>>>>
>>>>>>>>> <snip>
>>>>>>>>>
>>>>>>>>>> So we agree that no algorithm exists that can determine for 
>>>>>>>>>> all possible inputs whether the input specifies a program that 
>>>>>>>>>> (according to the semantics of the machine language) halts 
>>>>>>>>>> when directly executed.
>>>>>>>>>> Correct?
>>>>>>>>>
>>>>>>>>> Correct. We can, however, construct such an algorithm just as 
>>>>>>>>> long as we can ignore any input we don't like the look of.
>>>>>>>>>
>>>>>>>>
>>>>>>>> The behavior of the direct execution of DD cannot be derived
>>>>>>>> by applying the finite string transformation rules specified
>>>>>>>> by the x86 language to the input to HHH(DD). This proves that
>>>>>>>> this is the wrong behavior to measure.
>>>>>>>>
>>>>>>>> It is the behavior THAT IS derived by applying the finite
>>>>>>>> string transformation rules specified by the x86 language
>>>>>>>> to the input to HHH(DD) proves that THE EMULATED DD NEVER HALTS.
>>>>>>>
>>>>>>> The x86 language is neither here nor there. 
>>>>>>
>>>>>> Computable functions are the formalized analogue
>>>>>> of the intuitive notion of algorithms, in the sense
>>>>>> that a function is computable if there exists an
>>>>>> algorithm that can do the job of the function, i.e.
>>>>>> *given an input of the function domain it*
>>>>>> *can return the corresponding output*
>>>>>> https://en.wikipedia.org/wiki/Computable_function
>>>>>>
>>>>>> *Outputs must correspond to inputs*
>>>>>>
>>>>>> *This stipulates how outputs must be derived*
>>>>>> Every Turing Machine computable function is
>>>>>> only allowed to derive outputs by applying
>>>>>> finite string transformation rules to its inputs.
>>>>>
>>>>> In your reply to my article, you forgot to address what I actually 
>>>>> wrote. I'm not sure you understand what 'reply' means.
>>>>>
>>>>> Still, I'm prepared to give you another crack at it. Here's what I 
>>>>> wrote before:
>>>>>
>>>>> What matters is whether a TM can be constructed that can accept an 
>>>>> arbitrary TM tape P and an arbitrary input tape D and correctly 
>>>>> calculate whether, given D as input, P would halt. Turing proved 
>>>>> that such a TM cannot be constructed.
>>>>>
>>>>> This is what we call the Halting Problem.
>>>>>
>>>>
>>>> Yet it is H(P,D) and NOT P(D) that must be measured.
>>>
>>> Not if it's the behavior of P(D) we want to know about, which it is.
>>>
>>
>> Wanting the square root of a rotten egg would do as well.
> 
> In other words, you're claiming that there's an algorithm, i.e. a fixed 
> immutable sequence of instructions, that when given a particular input 
> neither halts nor not halts when executed directly.
> 
> Show it.
> 
> Failure to do so will in your next reply, or within one hour of your 
> next post on this newsgroup, be taken as you on-the-record admission 
> that there is nothing incorrect about the halting question asking 
> whether any arbitrary algorithm X with input Y will halt when executed 
> directly.


Let The Record Show that Peter Olcott made the following post in this 
newsgroup:

On 4/29/2025 9:11 AM, olcott wrote:
 > No H can possibly see the behavior of P(D)
 > when-so-ever D has defined a pathological
 > relationship with H this changes the behavior
 > of P so that it is not the same as P(D).

And that over 80 minutes has passed without a response to this message. 
Therefore, as per the above criteria, Peter Olcott has admitted that all 
algorithms X with input Y either halt or do not halt when executed 
directly, and therefore that the below halting criteria is *valid*:


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