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From: dbush <dbush.mobile@gmail.com>
Newsgroups: comp.theory
Subject: Re: Halting Problem: What Constitutes Pathological Input
Date: Tue, 6 May 2025 16:53:19 -0400
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On 5/6/2025 4:49 PM, olcott wrote:
> On 5/6/2025 3:42 PM, dbush wrote:
>> On 5/6/2025 4:33 PM, olcott wrote:
>>> On 5/6/2025 2:38 PM, dbush wrote:
>>>> On 5/6/2025 2:55 PM, olcott wrote:
>>>>> On 5/6/2025 7:12 AM, dbush wrote:
>>>>>> On 5/6/2025 12:55 AM, olcott wrote:
>>>>>>> On 5/5/2025 3:53 PM, Richard Heathfield wrote:
>>>>>>>> On 05/05/2025 20:38, 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?"
>>>>>>>>
>>>>>>>> 20:45GMT, give or take.
>>>>>>>>
>>>>>>>>> is also "undecidable" because it is not a proposition
>>>>>>>>> having a truth value.
>>>>>>>>
>>>>>>>> No, it's computable and therefore decidable. Your computer is 
>>>>>>>> perfectly capable of displaying its interpretation of the time.
>>>>>>>>
>>>>>>>>> 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.
>>>>>>>>
>>>>>>>> But we know that it halts at the full stop.
>>>>>>>>
>>>>>>>>> Can Carol correctly answer “no” to this (yes/no) question?
>>>>>>>>
>>>>>>>> You have, I see, learned that not all yes/no questions are 
>>>>>>>> decidable. Well done! You're coming along nicely.
>>>>>>>>
>>>>>>>>> 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.
>>>>>>>>
>>>>>>>> The question is grammatically and syntactically unremarkable. I 
>>>>>>>> see no grounds for claiming that it's 'incorrect'. It's just 
>>>>>>>> undecidable.
>>>>>>>>
>>>>>>>> You appear to be trying to overturn the Halting Problem by 
>>>>>>>> claiming that Turing somehow cheated. You're entitled to hold 
>>>>>>>> that opinion, but it's not one that will gain any traction with 
>>>>>>>> peer reviewers when you try to publish.
>>>>>>>>
>>>>>>>
>>>>>>> *EVERYONE IGNORES THIS*
>>>>>>> It is very simple the mapping from inputs to outputs
>>>>>>> must have a well defined sequence of steps.
>>>>>>>
>>>>>>
>>>>>> FALSE!!!
>>>>>>
>>>>>> There is no requirement that mappings have steps to compute them.
>>>>>>
>>>>>
>>>>> The requirement is that 
>>>>
>>>> Assuming that an algorithm exists that can compute 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
>>>>
>>>>
>>>>> OUTPUTS must correspond
>>>>> to INPUTS. This requires that outputs must be
>>>>> derived from INPUTS.
>>>>
>>>> And when a contradiction is reached that proves the above assumption 
>>>> false, as Linz and others have proved, and you have *explicitly* 
>>>> admitted is correct.
>>>
>>> As I already said Linz is only correct when the halting
>>> problem proof is construed as 
>>
>> After assuming that an algorithm exists to map the halting function
>>
>>> having an input that can
>>> actually do the opposite of whatever value the termination
>>> analyzer returns. Since this is false,
>>
>> That proves the above assumption false, as Linz and others have proved 
>> and as you have *explicitly* agreed is correct.
>>
> 
> The fundamental basic assumption of all of the halting
> problem proofs is that

An algorithm exists that can compute 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


> THIS ASSUMPTION IS FALSE.

As Linz and others have proved, and as you have *explicitly* agreed is 
correct.