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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: comp.theory
Subject: Re: Halt Deciders must be computable functions --- dbush was always wrong
Date: Mon, 24 Mar 2025 10:00:38 +0200
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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.

-- 
Mikko