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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 19:57:04 -0500
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On 5/5/2025 7:49 PM, dbush wrote:
> On 5/5/2025 8:30 PM, olcott wrote:
>> 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
> 
> Which starts with the assumption that an algorithm exists that performs 
> the following mapping:
> 
> 
> Given any algorithm (i.e. a fixed immutable sequence of instructions) X 
> described as <X> with input Y:
> 
> A solution to the halting problem is an algorithm H that computes the 
> following mapping:
> 
> (<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
> 
> 
> 
>> DO COMPUTE THAT THE INPUT IS NON-HALTING
>> IFF (if and only if) the mapping FROM INPUTS
>> IS COMPUTED.
> 
> i.e. it is found to map something other than the above function which is 
> a contradiction.
> 

The above function VIOLATES COMPUTER SCIENCE.
You make no attempt to show how my claim
THAT IT VIOLATES COMPUTER SCIENCE IS INCORRECT
you simply take that same quote from a computer
science textbook as the infallible word-of-God.

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