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From: "Fred. Zwarts" <F.Zwarts@HetNet.nl>
Newsgroups: comp.theory,sci.logic
Subject: Re: Halting Problem is wrong two different ways
Date: Wed, 5 Jun 2024 10:11:38 +0200
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Op 05.jun.2024 om 04:05 schreef olcott:
> On 6/4/2024 8:48 PM, Richard Damon wrote:
>> On 6/4/24 1:40 PM, olcott wrote:
>>> 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).
>>
>> But strings don't HAVE "Behavior", they only represent things that do.
>>
> 
> Turing Machine descriptions specify behavior to UTMs.
> 
>> And, for a Halt decider, that thing they represent is the program, 
>> whose direct execution specifies the proper behavior of the input.
>>
>> The DEFINITON IS NOT  "as measured by DD correctly simulated by HH", 
>> as deciders, by their definiton, are trying to compute the mapping of 
>> their input according to a defined function, which is a function of 
>> just that input. Since that function doesn't know which "H' is going 
>> to try to decide on it, it can't change its answer based on which H we 
>> ask.
>>
>> Proper Deciders can not be asked "Subjective" questions, unless we 
>> SPECIFICALLY define the mapping to include the decider as one of the 
>> inputs, and at that point, the question actually ceases to be 
>> subjective, as it becomes, what should THAT H say about this input, 
>> which is back to an objective agian (since machines are deterministic, 
>> so the definition of H tells us what H will answer to that question).
>>
>>>
>>> When we go ahead and contradict this definition then the
>>> *HALTING PROBLEM IS STILL WRONG IN A DIFFERENT WAY*
>>
>> Nope, YOU are wrong, because you
>>
>>>
>>> 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.
>>
>> Nope, Just shows how small your mind is.
>>
>> Proven elsewhere.,
>>
>>>
>>> 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.
>>>
>>
>> But the question it asks is an OBJECTIVE question that doesn't depend 
>> on who it is asked of.
>>
> 
> When H is asked about the behavior of a Machine that is programmed
> to do the opposite of whatever it says then the context that it is H
> that is being asked is an inherent aspect of the meaning of this
> question and cannot be correctly ignored.

But that has nothing to do with your simulation result. Your simulation 
does not even reach the part that contradict its result.
Your decider even diagnoses programs as non-halting when they do not 
contradict the result of the decider, as in:

        typedef int (*ptr)();  // ptr is pointer to int function in C

        int H(ptr p, ptr i);

        int main()
        {
          H(main, 0);
        }

It is clear that main does not programmed to do the opposite of what H 
says.

This illustrates that a simulating halt-decider is a bad idea, because 
the decider itself does not halt when simulated by itself and therefore 
its results are often false negatives.