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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory,sci.logic
Subject: Re: Halting Problem is wrong two different ways
Date: Wed, 5 Jun 2024 08:18:24 -0500
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On 6/5/2024 2:13 AM, Mikko wrote:
> On 2024-06-04 17:40:47 +0000, olcott said:
> 
>> On 6/4/2024 3:28 AM, Mikko wrote:
>>> On 2024-06-03 18:14:39 +0000, olcott said:
>>>
>>>> On 6/3/2024 9:27 AM, Mikko wrote:
>>>>> On 2024-06-03 12:20:01 +0000, olcott said:
>>>>>
>>>>>> On 6/3/2024 4:42 AM, Ben Bacarisse wrote:
>>>>>>> Mike Terry <news.dead.person.stones@darjeeling.plus.com> writes:
>>>>>>>
>>>>>>>> PO's D(D) halts, as illustrated in various traces that have been 
>>>>>>>> posted here.
>>>>>>>> PO's H(D,D) returns 0 : [NOT halting] also as illustrated in 
>>>>>>>> various traces.
>>>>>>>> i.e. exactly as the Linz proof claims.  PO has acknowledged both 
>>>>>>>> these
>>>>>>>> results.  Same for the HH/DD variants.
>>>>>>>>
>>>>>>>> You might imagine that's the end of the matter - PO failed.  :)
>>>>>>>>
>>>>>>>> That's right, but PO just carries on anyway!
>>>>>>>
>>>>>>> He has quite explicitly stated that false (0) is the correct 
>>>>>>> result for
>>>>>>> H(D,D) "even though D(D) halts".  I am mystified why anyone 
>>>>>>> continues to
>>>>>>> discuss the matter until he equally explicitly repudiates that 
>>>>>>> claim.
>>>>>>>
>>>>>>
>>>>>> Deciders only compute the mapping *from their inputs* to their own
>>>>>> accept or reject state.
>>>>>
>>>>> That does not restrict what a problem statement can specify.
>>>>> If the computed mapping differs from the specified one the
>>>>> decider does not solve the problem.
>>>>
>>>> int sum(int x, int y) { return x + y; }
>>>> sum(2,3) cannot return the sum of 5 + 6.
>>>
>>> That does not restrict what a problem statement can specify.
>>> If the mapping computed by sum differs from the specified one
>>> the program sum does not solve the problem.
>>>
>>
>> On 6/3/2024 9:53 PM, Richard Damon wrote:
>>  > Because you keep on mentioning about DD Halting,
>>  > which IS about the direct execution of DD
>>
>> Only when one contradicts the definition of a decider that must
>> compute the mapping FROM ITS INPUTS BASED ON THE ACTUAL BEHAVIOR
>> OF THESE INPUTS (as measured by DD correctly simulated by HH).
>>
>> When we go ahead and contradict this definition then the
>> *HALTING PROBLEM IS STILL WRONG IN A DIFFERENT WAY*
>>
>> When D is defined to do the opposite of whatever yes/no
>> an answer that H provides then the counter-example input
>> is precisely isomorphic to the question:
>> Is this sentence: "This sentence is not true." true or false?
>> Thus that question and the HP question are both incorrect
>> because both yes and no are the wrong answer.
>>
>> The theory of computation may be ignorant of the details of
>> how the context of who is asked a question changes the meaning
>> of this question, none-the-less this cannot be ignored.
>> It is and remains incorrect for the theory of computation
>> to ignore this.
> 
> Nice to see that you don't disagree with my observation that
> your statement
> 
>>>>>> Deciders only compute the mapping *from their inputs* to their own
>>>>>> accept or reject state.
> 
> does not restrict what a problem statement can specify.
> 

Sure it does.
int sum(int x, int y) { return x + y; }
sum(3,4) cannot correctly return the sum of 5 + 6.

H(D,D) cannot possibly return the halt status of D(D) because
D calls H in recursive simulation thus forcing the behavior of
D correctly simulated by H to be different than the behavior of
the directly executed D(D).

Requiring H(D,D) to return the halt status of D(D) is exactly
the same as requiring sum(3,4) to return the sum of 5 + 6.

*This unequivocally proves the behavior of DD correctly simulated by HH*
https://liarparadox.org/DD_correctly_simulated_by_HH_is_Proven.pdf


-- 
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer