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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 17:27:31 -0500
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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 no Turing Machine can take the direct execution
of another Turing Machine as an input.

Likewise the square root of a dead rabbit cannot be computed.

-- 
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer