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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory,sci.logic
Subject: Re: Halting Problem is wrong two different ways
Date: Thu, 6 Jun 2024 11:44:59 -0500
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On 6/6/2024 11:34 AM, Fred. Zwarts wrote:
> Op 06.jun.2024 om 18:07 schreef olcott:
>> On 6/6/2024 11:01 AM, Fred. Zwarts wrote:
>>> Op 06.jun.2024 om 00:44 schreef olcott:
>>>> On 6/5/2024 1:51 PM, Fred. Zwarts wrote:
>>>>> Op 05.jun.2024 om 15:59 schreef olcott:
>>>>>> On 6/5/2024 3:11 AM, Fred. Zwarts wrote:
>>>>>>> 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. 
>>>>>>
>>>>>> Notice the subject line of this thread.
>>>>>> That HH is being asked an incorrect question is the second
>>>>>> way that the Halting Problem is wrong.
>>>>>>
>>>>>>> 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.
>>>>>>>
>>>>>>
>>>>>> *I was surprised that this worked correctly: here are the details*
>>>>>>
>>>>>> int main()
>>>>>> {
>>>>>>    Output("Input_Halts = ", HH(main,(ptr)0));
>>>>>> }
>>>>>>
>>>>>>   machine   stack     stack     machine    assembly
>>>>>>   address   address   data      code       language
>>>>>>   ========  ========  ========  =========  =============
>>>>>> [00001e42][00103375][00000000] 55         push ebp      ; begin main
>>>>>> [00001e43][00103375][00000000] 8bec       mov ebp,esp
>>>>>> [00001e45][00103371][00000000] 6a00       push +00
>>>>>> [00001e47][0010336d][00001e42] 68421e0000 push 00001e42 ; push main
>>>>>> [00001e4c][00103369][00001e51] e831f5ffff call 00001382 ; call HH
>>>>>> New slave_stack at:103419
>>>>>>
>>>>>> Begin Local Halt Decider Simulation   Execution Trace Stored 
>>>>>> at:113421
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