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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: comp.theory
Subject: Re: Halting Problem: What Constitutes Pathological Input
Date: Thu, 8 May 2025 12:35:52 +0300
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On 2025-05-07 20:47:29 +0000, olcott said:

> On 5/7/2025 1:27 PM, dbush wrote:
>> On 5/7/2025 2:24 PM, olcott wrote:
>>> On 5/7/2025 5:58 AM, Richard Damon wrote:
>>>> On 5/6/25 10:00 PM, olcott wrote:
>>>>> On 5/6/2025 5:49 PM, Richard Damon wrote:
>>>>>> On 5/6/25 2:05 PM, olcott wrote:
>>>>>>> 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:
>>>>>>>>>>>> 
>>>>>>>>>>>> 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.
>>>>>>>>>> 
>>>>>>>>>> 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.
>>>>>> 
>>>>>> Right, "Computed by a model of computation", that
>>>>>> 
>>>>>>> 
>>>>>>> HHH(DD) must emulate DD according to the rules
>>>>>>> of the x86 language.
>>>>>> 
>>>>>> Right, which is doesn't do.
>>>>>> 
>>>>>> Remember, your HHH stop processing at a CALL HHH instruction.
>>>>>> 
>>>>> 
>>>>> <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
>>>>> 
>>>>> *input D* // the actual input
>>>> 
>>>> Which calls the original H
>>>> 
>>>>> 
>>>>> *would never stop running unless aborted*
>>>>> // A hypothetical HHH/DD pair where HHH and DD are
>>>>> // exactly the same except that this HHH does not abort.
>>>>> 
>>>>> 
>>>> 
>>>> No, your hypothetical HHH (like  your HHH1) paired with the originl DD 
>>>> which uses the original HHH.
>>>> 
>>> 
>>> That is NOT what this means:
>>> *simulated D would never stop running unless aborted*
>>> 
>>> All simulating halt deciders must
>>> PREDICT WHAT THE BEHAVIOR WOULD BE
>> 
>> If the machine described by its input was executed directly, as per the 
>> requirements of a halt decider:
>> 
>> 
>> 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
> 
> I have proved that everyone has been wrong about this
> for ninety years. Ignoring my proof is not any rebuttal.
> My proof is probably totally over-your-head.

The halting problem defined in the definition 12.1 at
  https://www.liarparadox.org/Linz_Proof.pdf

What dbush said above means the same so is correct.

You have never presented any proof of anything.

-- 
Mikko