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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory,sci.logic
Subject: Re: Halting Problem is wrong two different ways
Date: Wed, 5 Jun 2024 19:46:28 -0400
Organization: i2pn2 (i2pn.org)
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On 6/5/24 9:59 AM, olcott wrote:
> 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
> [00001e42][0011340d][00113411] 55         push ebp      ; begin main
> [00001e43][0011340d][00113411] 8bec       mov ebp,esp
> [00001e45][00113409][00000000] 6a00       push +00
> [00001e47][00113405][00001e42] 68421e0000 push 00001e42 ; push main
> [00001e4c][00113401][00001e51] e831f5ffff call 00001382 ; call HH
> New slave_stack at:14de41
> [00001e42][0015de35][0015de39] 55         push ebp      ; begin main
> [00001e43][0015de35][0015de39] 8bec       mov ebp,esp
> [00001e45][0015de31][00000000] 6a00       push +00
> [00001e47][0015de2d][00001e42] 68421e0000 push 00001e42 ; push main
> [00001e4c][0015de29][00001e51] e831f5ffff call 00001382 ; call HH
> Local Halt Decider: Infinite Recursion Detected Simulation Stopped
> 
> [00001e51][00103375][00000000] 83c408     add esp,+08
> [00001e54][00103371][00000000] 50         push eax
> [00001e55][0010336d][00000743] 6843070000 push 00000743
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