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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: comp.theory
Subject: Re: Halting Problem is wrong two different ways
Date: Wed, 5 Jun 2024 10:13:59 +0300
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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.

-- 
Mikko