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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: Halt Deciders must be computable functions --- dbush was always
 wrong
Date: Tue, 25 Mar 2025 07:40:08 -0500
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On 3/25/2025 4:33 AM, Mikko wrote:
> On 2025-03-24 14:21:01 +0000, olcott said:
> 
>> On 3/24/2025 3:00 AM, Mikko wrote:
>>> On 2025-03-23 20:08:25 +0000, olcott said:
>>>
>>>> On 3/23/2025 4:49 AM, Mikko wrote:
>>>>> On 2025-03-22 15:47:03 +0000, olcott said:
>>>>>
>>>>>> On 3/22/2025 9:57 AM, Mikko wrote:
>>>>>>> On 2025-03-21 15:25:09 +0000, olcott said:
>>>>>>>
>>>>>>>> On 3/21/2025 10:00 AM, olcott wrote:
>>>>>>>>> On 3/21/2025 9:44 AM, dbush wrote:
>>>>>>>>>> On 3/17/2025 11:29 PM, olcott wrote:
>>>>>>>>>>> On 3/17/2025 8:25 PM, dbush wrote:
>>>>>>>>>>>> On 3/17/2025 9:18 PM, olcott wrote:
>>>>>>>>>>>>> On 3/17/2025 7:48 PM, dbush wrote:
>>>>>>>>>>>>>> On 3/17/2025 8:44 PM, olcott wrote:
>>>>>>>>>>>>>>> On 3/17/2025 7:22 PM, dbush wrote:
>>>>>>>>>>>>>>>> On 3/17/2025 8:18 PM, olcott wrote:
>>>>>>>>>>>>>>>>> On 3/17/2025 7:00 PM, dbush wrote:
>>>>>>>>>>>>>>>>>> On 3/17/2025 7:51 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>> On 3/17/2025 5:15 PM, dbush wrote:
>>>>>>>>>>>>>>>>>>>> On 3/17/2025 6:10 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> The halt decider does not and cannot possibly
>>>>>>>>>>>>>>>>>>>>> compute the mapping from the actual behavior
>>>>>>>>>>>>>>>>>>>>> of an executing process.
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> No one claimed it should.  What it must do is 
>>>>>>>>>>>>>>>>>>>> determine what would happen in the hypothetical case 
>>>>>>>>>>>>>>>>>>>> that a direct execution is done.
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> It can only do that when it assumes that the behavior
>>>>>>>>>>>>>>>>>>> specified by the semantics of its input machine language
>>>>>>>>>>>>>>>>>>> exactly matches this behavior. Its only basis is this
>>>>>>>>>>>>>>>>>>> input finite string.
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> i.e. the semantics of the x86 language when those 
>>>>>>>>>>>>>>>>>> actual instructions are actually executed on an actual 
>>>>>>>>>>>>>>>>>> x86 processor.
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> A termination analyzer has no access to that.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> The input is required to be a complete description of 
>>>>>>>>>>>>>>>> the program that can be used to determine its full 
>>>>>>>>>>>>>>>> behavior.  In the case of DD, that description is the 
>>>>>>>>>>>>>>>> code of the function DD, the code of the function HHH, 
>>>>>>>>>>>>>>>> and everything that HHH calls down to the OS level.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> It does do that and this behavior does specify
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Halting behavior when executed directly, which is what is 
>>>>>>>>>>>>>> to be reported on as per the requirements:
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> It has always been incorrectly assumed that the input
>>>>>>>>>>>>> finite string is a perfect proxy for the behavior
>>>>>>>>>>>>> of the direct execution.
>>>>>>>>>>>>
>>>>>>>>>>>> False.  The input finite string is REQUIRED to be a perfect 
>>>>>>>>>>>> proxy for direct execution, as per the requirements:
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> It looks like you simply don't understand that a
>>>>>>>>>>> counter-factual requirement is necessarily incorrect.
>>>>>>>>>>
>>>>>>>>>> Category error.  Requirements can't be false.  They can 
>>>>>>>>>> however be impossible to satisfy.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> When the definition of a [HALT decider] contradicts the 
>>>>>>>>> definition of a [decider] in the same field of inquiry at least 
>>>>>>>>> one of them is incorrect.
>>>>>>>
>>>>>>> No, there is nothing incorrect there. It simply means a halpt 
>>>>>>> decider
>>>>>>> is not a decider,
>>>>>>
>>>>>> It has always been stipulated that a [halt decider] is a type
>>>>>> of [decider]. This means that every halt decider only has the
>>>>>> behavior that its finite string input specifies as its only basis.
>>>>>
>>>>> No, it has not. "Halting decider" can be defined without mentioning
>>>>> "decider" and some authors do so.
>>>>
>>>> I forgot that the notion of computable function already proves my point
>>>
>>> Maybe, if you have a point. But it does not prove your false claim 
>>> above.
>>
>> No Turing Machine computation can report on the behavior
>> of any directly executing Turing Machine because no directly
>> executing Turing machine is a finite string input.
>>
>>   given an input of the function domain it
>>   can return the corresponding output.
>> https://en.wikipedia.org/wiki/Computable_function
> 
> Ia that your "point"? At least that was not what you were talking about
> when you falsely claimed that "It has always been stipulated that a 
> [halt decider] is a type of [decider]" and is therefore irrelevant to that
> message and the discussion after that.
> 

A halt decider <is> and has always been a type of decider.
The nothing of computable function  proves my point another way.

All Turing computable functions compute the mapping from an
input finite string on the basis of something that this finite
string specifies. No TM every has any psychic ability.


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