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Re: Simulating Halt Decider Applied to the Halting Theorem [new abstract]

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On Sat, 5 Nov 2022 17:05:35 -0500
olcott <polcott2@gmail.com> wrote:

> On 11/5/2022 4:57 PM, Mr Flibble wrote:
> > On Sat, 5 Nov 2022 16:42:22 -0500
> > olcott <polcott2@gmail.com> wrote:
> >   
> >> On 11/5/2022 4:02 PM, Mr Flibble wrote:  
> >>> On Sat, 5 Nov 2022 13:10:54 -0500
> >>> olcott <polcott2@gmail.com> wrote:
> >>>      
> >>>> On 11/5/2022 12:05 PM, Mr Flibble wrote:  
> >>>>> On Sat, 5 Nov 2022 09:47:27 -0500
> >>>>> olcott <polcott2@gmail.com> wrote:
> >>>>>         
> >>>>>> The novel concept of a simulating halt decider enables C
> >>>>>> function H to correctly determine the halt status of C function
> >>>>>> D that implements the halting theorem's "impossible" input.
> >>>>>> When D is correctly simulated by H it remains stuck in
> >>>>>> recursive simulation until H aborts this simulation. D cannot
> >>>>>> do the opposite of the return value from H because this return
> >>>>>> value is unreachable by every simulated D. This same result is
> >>>>>> derived in Turing machine based proofs.
> >>>>>>
> >>>>>> On 11/4/2022 9:33 AM, olcott wrote:  
> >>>>>>> Can you see that simulating halt decider H correctly
> >>>>>>> determines the halt status of the halting problem's
> >>>>>>> "impossible" input D?
> >>>>>>>
> >>>>>>> void D(void (*x)())
> >>>>>>> {
> >>>>>>>       int Halt_Status = H(x, x);
> >>>>>>>       if (Halt_Status)
> >>>>>>>         HERE: goto HERE;
> >>>>>>>       return;
> >>>>>>> }
> >>>>>>>
> >>>>>>> int main()
> >>>>>>> {
> >>>>>>>       Output("Input_Halts = ", H(D, D));
> >>>>>>> }
> >>>>>>>
> >>>>>>> https://www.researchgate.net/publication/364657019_Simulating_Halt_Decider_Applied_to_the_Halting_Theorem
> >>>>>>>            
> >>>>>>        
> >>>>>
> >>>>> As I said before it is sufficient to detect nested simulation to
> >>>>> assert the presence of a category error; trying to map that to a
> >>>>> valid halting decision of non-halting muddies the water and
> >>>>> implies no such category error exists which is wrong: nested
> >>>>> simulation PREVENTS a halting decision being made because of the
> >>>>> category error present in [Strachey 1965] and the proofs
> >>>>> predicated on it. Again: you don't have to abort simulation or
> >>>>> give an artificial halting decision of non-halting to refute the
> >>>>> halting problem proofs, the simple presence of the category
> >>>>> error does that.
> >>>>>
> >>>>> /Flibble
> >>>>>         
> >>>>
> >>>> Unlike with Gödel's incompleteness theorem and the Tarski
> >>>> undefinability theorem with mathematical formulas that can only
> >>>> just sit on the page, TM's have intelligence and can take
> >>>> corrective action for what would otherwise simply be a category
> >>>> error.  
> >>>
> >>> There is no corrective action for a category error; the category
> >>> error can be used to directly refute the halting problem proofs
> >>> without recourse to creating an actual simulating halt decider
> >>> that gives an artificial result of non-halting.
> >>>
> >>> /Flibble
> >>>
> >>>      
> >>
> >> It is not an artificial result.  
> >   
> > It is an artificial result because the category error means the
> > input is INVALID; a halt decider shouldn't be able to give a
> > traditional decision result for INVALID input.
> > 
> > /Flibble  
> 
> Your assumption of category error is correct for non simulating halt 
> deciders. In this case the input would contradict any value that its 
> decider returns.

The category error is not due to the contradiction, the category error
is due to the input referencing the decider.

> 
> For simulating halt decider H it is impossible for its correctly 
> simulated D to do the opposite of whatever H returns because this
> return value is unreachable by every simulated D. Every simulated D
> remains stuck in infinite recursion until aborted by each element of
> its corresponding simulating halt deciders.
> 

/Flibble

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Simulating Halt Decider Applied to the Halting Theorem olcott <polcott2@gmail.com> - 2022-11-04 09:33 -0500
  Re: Simulating Halt Decider Applied to the Halting Theorem Mr Flibble <flibble@reddwarf.jmc.corp> - 2022-11-04 15:09 +0000
    Re: Simulating Halt Decider Applied to the Halting Theorem olcott <polcott2@gmail.com> - 2022-11-04 10:28 -0500
  Re: Simulating Halt Decider Applied to the Halting Theorem [new abstract] olcott <polcott2@gmail.com> - 2022-11-05 09:47 -0500
    Re: Simulating Halt Decider Applied to the Halting Theorem [new abstract] Mr Flibble <flibble@reddwarf.jmc.corp> - 2022-11-05 17:05 +0000
      Re: Simulating Halt Decider Applied to the Halting Theorem [new abstract] olcott <polcott2@gmail.com> - 2022-11-05 13:10 -0500
        Re: Simulating Halt Decider Applied to the Halting Theorem [new abstract] Mr Flibble <flibble@reddwarf.jmc.corp> - 2022-11-05 21:02 +0000
          Re: Simulating Halt Decider Applied to the Halting Theorem [new abstract] olcott <polcott2@gmail.com> - 2022-11-05 16:42 -0500
            Re: Simulating Halt Decider Applied to the Halting Theorem [new abstract] Mr Flibble <flibble@reddwarf.jmc.corp> - 2022-11-05 21:57 +0000
              Re: Simulating Halt Decider Applied to the Halting Theorem [new abstract] olcott <polcott2@gmail.com> - 2022-11-05 17:05 -0500
                Re: Simulating Halt Decider Applied to the Halting Theorem [new abstract] Mr Flibble <flibble@reddwarf.jmc.corp> - 2022-11-06 01:13 +0000
                Re: Simulating Halt Decider Applied to the Halting Theorem [new abstract] Richard Damon <Richard@Damon-Family.org> - 2022-11-05 21:54 -0400
                Re: Simulating Halt Decider Applied to the Halting Theorem [new abstract] Mr Flibble <flibble@reddwarf.jmc.corp> - 2022-11-06 14:09 +0000
                Re: Simulating Halt Decider Applied to the Halting Theorem [new abstract] Richard Damon <Richard@Damon-Family.org> - 2022-11-06 09:34 -0500
                Re: Simulating Halt Decider Applied to the Halting Theorem [new abstract] Mr Flibble <flibble@reddwarf.jmc.corp> - 2022-11-06 23:09 +0000
                Re: Simulating Halt Decider Applied to the Halting Theorem [new abstract] Richard Damon <Richard@Damon-Family.org> - 2022-11-06 18:24 -0500
                Re: Simulating Halt Decider Applied to the Halting Theorem [new abstract] Mr Flibble <flibble@reddwarf.jmc.corp> - 2022-11-07 18:28 +0000
                Re: Simulating Halt Decider Applied to the Halting Theorem [new abstract] olcott <polcott2@gmail.com> - 2022-11-07 13:03 -0600
                Re: Simulating Halt Decider Applied to the Halting Theorem [new abstract] olcott <polcott2@gmail.com> - 2022-11-06 08:40 -0600
        Re: Simulating Halt Decider Applied to the Halting Theorem [new abstract] Richard Damon <Richard@Damon-Family.org> - 2022-11-05 17:06 -0400

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