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From: dbush <dbush.mobile@gmail.com>
Newsgroups: comp.theory
Subject: Re: Halting Problem: What Constitutes Pathological Input
Date: Wed, 7 May 2025 14:27:20 -0400
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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