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From: "Fred. Zwarts" <F.Zwarts@HetNet.nl>
Newsgroups: comp.theory
Subject: Re: Halting Problem: What Constitutes Pathological Input
Date: Wed, 7 May 2025 17:43:57 +0200
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Op 07.mei.2025 om 17:31 schreef olcott:
> On 5/7/2025 5:55 AM, Richard Damon wrote:
>> On 5/6/25 10:09 PM, olcott wrote:
>>> On 5/6/2025 5:52 PM, Richard Damon wrote:
>>>> On 5/6/25 4:37 PM, olcott wrote:
>>>>> On 5/6/2025 3:22 PM, joes wrote:
>>>>>> Am Tue, 06 May 2025 13:05:15 -0500 schrieb olcott:
>>>>>>> On 5/6/2025 5:59 AM, Richard Damon wrote:
>>>>>>>> On 5/5/25 10:18 PM, olcott wrote:
>>>>>>>>> On 5/5/2025 8:59 PM, dbush wrote:
>>>>>>>>>> On 5/5/2025 8:57 PM, olcott wrote:
>>>>>>>>>>> On 5/5/2025 7:49 PM, dbush wrote:
>>>>>>
>>>>>>>>>>>>> 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.
>>>>>> What does it violate?
>>>>>>
>>>>>>>>>> All you are doing is showing that you don't understand proof by
>>>>>>>>>> contradiction,
>>>>>>>>> Not at all. The COMPUTER SCIENCE of your requirements IS WRONG!
>>>>>>>> No, YOU don't understand what Computer Science actually is talking
>>>>>>>> about.
>>>>>>> Every function computed by a model of computation must apply a 
>>>>>>> specific
>>>>>>> sequence of steps that are specified by the model to the actual 
>>>>>>> finite
>>>>>>> string input.
>>>>>
>>>>>> You are very confused. An algorithm or program computes a function.
>>>>>>
>>>>>
>>>>> Nothing computes a function unless it applies a specific
>>>>> set of rules to its actual input to derive its output.
>>>>> Anything that ignores its input is not computing a function.
>>>>>
>>>>
>>>> Right, so HHH needs to apply the rules that it was designed with.
>>>>
>>>> And that means it breaks the criteria that you say it needs to do to 
>>>> get the right answer,
>>>>
>>>> And thus it gets the wrong answer.
>>>>
>>>
>>> It needs to emulate DD according to the rules of
>>> the x86 language. This includes emulating itself
>>> emulating DD until it recognizes that if it kept
>>> doing this that DD would never halt.
>>
>> No, to be a correct emulator it needs to continue until it reaches the 
>> end,
>>
>> It can get the right answer if it emulates the input to the point that 
>> it can show that a
>>
>>
>>>
>>> <MIT Professor Sipser agreed to ONLY these verbatim words 10/13/2022>
>>>      If simulating halt decider H correctly simulates its
>>>      input D until H correctly determines that its simulated D
>>>      *would never stop running unless aborted* then
>>
>> Right, that UTM(D) would never halt.
>>
>>>
>>> *would never stop running unless aborted*
>>> Is the hypothetical HHH/DD pair where HHH does not abort.
>>
>>
>> Nope, can't change DD, it is your hypothetical HHH, which has become 
>> UTM, when given the ORIGINAL DD, which calls the ORIGINAL HHH, as that 
>> code was part of the definition of DD.
> 
> HHH bases its decision on what the behavior of DD
> would be if a hypothetical version of its own self
> never aborted.
> 

That is indeed what makes HHH incorrect.
Just as  SUM(2,3) returning 7 is incorrect when it uses hypothetical 
inputs 2 and 4.