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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: Halting Problem: What Constitutes Pathological Input
Date: Mon, 5 May 2025 19:30:25 -0500
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On 5/5/2025 7:18 PM, dbush wrote:
> On 5/5/2025 8:14 PM, olcott wrote:
>> On 5/5/2025 7:02 PM, dbush wrote:
>>> On 5/5/2025 7:29 PM, olcott wrote:
>>>> On 5/5/2025 5:33 PM, dbush wrote:
>>>>> On 5/5/2025 6:27 PM, olcott wrote:
>>>>>> On 5/5/2025 4:58 PM, dbush wrote:
>>>>>>> On 5/5/2025 5:39 PM, olcott wrote:
>>>>>>>> On 5/5/2025 4:31 PM, dbush wrote:
>>>>>>>>> On 5/5/2025 5:08 PM, olcott wrote:
>>>>>>>>>> On 5/5/2025 3:14 PM, dbush wrote:
>>>>>>>>>>> On 5/5/2025 4:10 PM, olcott wrote:
>>>>>>>>>>>> On 5/5/2025 3:00 PM, dbush wrote:
>>>>>>>>>>>>> On 5/5/2025 3:54 PM, olcott wrote:
>>>>>>>>>>>>>> On 5/5/2025 2:49 PM, dbush wrote:
>>>>>>>>>>>>>>> On 5/5/2025 3:38 PM, olcott wrote:
>>>>>>>>>>>>>>>> On 5/5/2025 2:23 PM, Richard Heathfield wrote:
>>>>>>>>>>>>>>>>> On 05/05/2025 20:20, olcott wrote:
>>>>>>>>>>>>>>>>>> Is "halts" the correct answer for H to return?  NO
>>>>>>>>>>>>>>>>>> Is "does not halt" the correct answer for H to 
>>>>>>>>>>>>>>>>>> return?  NO
>>>>>>>>>>>>>>>>>> Both Boolean return values are the wrong answer
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> Or to put it another way, the answer is undecidable, QED.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> See? You got there in the end.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> Is this sentence true or false: "What time is it?"
>>>>>>>>>>>>>>>> is also "undecidable" because it is not a proposition
>>>>>>>>>>>>>>>> having a truth value.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> Is this sentence true or false: "This sentence is untrue."
>>>>>>>>>>>>>>>> is also "undecidable" because it is not a semantically 
>>>>>>>>>>>>>>>> sound
>>>>>>>>>>>>>>>> proposition having a truth value.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> Can Carol correctly answer “no” to this (yes/no) question?
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> Both Yes and No are the wrong answer proving that
>>>>>>>>>>>>>>>> the question is incorrect when the context of who
>>>>>>>>>>>>>>>> is asked is understood to be a linguistically required
>>>>>>>>>>>>>>>> aspect of the full meaning of the question.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> And "does algorthm X with input Y halt when executed 
>>>>>>>>>>>>>>> directly" has a single well defined answer.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> That is not even the actual question.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> In other words, you don't understand what the halting 
>>>>>>>>>>>>> problem is about, because that is EXACTLY the question.
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> That question is in many textbooks yet is still
>>>>>>>>>>>> wrong because functions computed by models of
>>>>>>>>>>>> computation such as Turing Machines or RASP machines
>>>>>>>>>>>> are only allowed to use actual inputs as their basis.
>>>>>>>>>>>
>>>>>>>>>>> And no Turing machine can compute the following mapping, as 
>>>>>>>>>>> proven by Linz and other and as you have *explicitly* agreed 
>>>>>>>>>>> is correct.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> No TM can compute the square root of a dead rabbit either.
>>>>>>>>>
>>>>>>>>> Strawman.  The square root of a dead rabbit does not exist, but 
>>>>>>>>> the question of whether any arbitrary algorithm X with input Y 
>>>>>>>>> halts when executed directly has a correct answer in all cases.
>>>>>>>>>
>>>>>>>>
>>>>>>>> It has a correct answer that cannot ever be computed
>>>>>>> Excellent!  So you once again *explicitly* agree that the theorem 
>>>>>>> that the halting problem proofs prove is correct.
>>>>>>>
>>>>>>
>>>>>> because
>>>>>
>>>>> The existence of an algorithm that meets those requirements creates 
>>>>> contradictions.
>>>>
>>>> It is the problem incorrect specification that creates
>>>> the contradiction.
>>>
>>> The fact that any arbitrary algorithm X with input Y either halts or 
>>> does not halt when executed directly proves that false.
>>>
>>>>
>>>> Everyone here insists that functions computed
>>>> by models of computation can ignore inputs and
>>>> base their output on something else.
>>>>
>>>> THAT IS VERY STUPIDLY VERY WRONG.
>>>>
>>>
>>> No, we just say that no algorithm can compute the above in all cases, 
>>> as Linz and others have proves and as you have *explicitly* agreed is 
>>> correct.
>>
>> FROM INPUTS --- FROM INPUTS --- FROM INPUTS
>> FROM INPUTS --- FROM INPUTS --- FROM INPUTS
>> FROM INPUTS --- FROM INPUTS --- FROM INPUTS
>> FROM INPUTS --- FROM INPUTS --- FROM INPUTS
>> FROM INPUTS --- FROM INPUTS --- FROM INPUTS
>> FROM INPUTS --- FROM INPUTS --- FROM INPUTS
>> FROM INPUTS --- FROM INPUTS --- FROM INPUTS
>> FROM INPUTS --- FROM INPUTS --- FROM INPUTS
>> FROM INPUTS --- FROM INPUTS --- FROM INPUTS
>> FROM INPUTS --- FROM INPUTS --- FROM INPUTS
>> FROM INPUTS --- FROM INPUTS --- FROM INPUTS
>> FROM INPUTS --- FROM INPUTS --- FROM INPUTS
>> FROM INPUTS --- FROM INPUTS --- FROM INPUTS
>> FROM INPUTS --- FROM INPUTS --- FROM INPUTS
>> FROM INPUTS --- FROM INPUTS --- FROM INPUTS
>> FROM INPUTS --- FROM INPUTS --- FROM INPUTS
>> FROM INPUTS --- FROM INPUTS --- FROM INPUTS
>> FROM INPUTS --- FROM INPUTS --- FROM INPUTS
>> FROM INPUTS --- FROM INPUTS --- FROM INPUTS
>>
>>
> 
> I'll let you respond to yourself:
> 

I keep telling you and conclusively proving
that both the Linz counter example input
and my fully specified termination analyzer
DO COMPUTE THAT THE INPUT IS NON-HALTING
IFF (if and only if) the mapping FROM INPUTS
IS COMPUTED.

The Linz proof also screws up because he does
not require that the halt status be computed
on the basis of the behavior THAT ITS ACTUAL
INPUT ACTUALLY SPECIFIES.

Instead he falsely imagines that the input
can actaully do the opposite of whatever
value its termination analayzer returns.

Until I made every single detail 100%
fully specfied it was possible to simply
imagine things that are not true.
-- 
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer