XPost: comp.theory, sci.math, comp.lang.prolog   
   XPost: sci.lang, comp.software-eng   
   From: polcott333@gmail.com   
      
   On 2/5/2026 9:23 PM, dart200 wrote:   
   > On 2/5/26 7:11 PM, olcott wrote:   
   >> On 2/5/2026 8:49 PM, dart200 wrote:   
   >>> On 2/5/26 12:20 PM, olcott wrote:   
   >>>> On 2/5/2026 12:06 PM, dart200 wrote:   
   >>>>> On 2/4/26 7:04 PM, olcott wrote:   
   >>>>>> On 2/4/2026 8:52 PM, dart200 wrote:   
   >>>>>>> On 2/4/26 6:50 PM, olcott wrote:   
   >>>>>>>> On 2/4/2026 8:42 PM, dart200 wrote:   
   >>>>>>>>> On 2/4/26 4:00 PM, olcott wrote:   
   >>>>>>>>>> On 2/4/2026 5:43 PM, dart200 wrote:   
   >>>>>>>>>>> On 2/4/26 2:27 PM, olcott wrote:   
   >>>>>>>>>>>> On 2/4/2026 4:19 PM, dart200 wrote:   
   >>>>>>>>>>>>> On 2/4/26 2:15 PM, olcott wrote:   
   >>>>>>>>>>>>>> On 2/4/2026 2:41 PM, dart200 wrote:   
   >>>>>>>>>>>>>>> On 2/1/26 9:35 AM, olcott wrote:   
   >>>>>>>>>>>>>>>> On 2/1/2026 6:11 AM, Richard Damon wrote:   
   >>>>>>>>>>>>>>>>> On 1/31/26 12:49 PM, olcott wrote:   
   >>>>>>>>>>>>>>>>>> Source code of fully operational system   
   >>>>>>>>>>>>>>>>>> https://github.com/plolcott/x86utm/blob/master/Halt7.c   
   >>>>>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>>>>> int DD()   
   >>>>>>>>>>>>>>>>>> {   
   >>>>>>>>>>>>>>>>>>    int Halt_Status = HHH(DD);   
   >>>>>>>>>>>>>>>>>>    if (Halt_Status)   
   >>>>>>>>>>>>>>>>>>      HERE: goto HERE;   
   >>>>>>>>>>>>>>>>>>    return Halt_Status;   
   >>>>>>>>>>>>>>>>>> }   
   >>>>>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>>>>> HHH simulates DD step-by-step according to   
   >>>>>>>>>>>>>>>>>> the semantics of the C programming language.   
   >>>>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>>>> IT CAN'T, as you have been told, as your above program,   
   >>>>>>>>>>>>>>>>> without the C CODE for HHH, has undefined behavior by   
   >>>>>>>>>>>>>>>>> the semantics of the C programming language.   
   >>>>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>> HHH as executed by polcott is exhibiting a classifier   
   >>>>>>>>>>>>>>> interface i'm calling a *partial recognizer*   
   >>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>> (machine) -> {   
   >>>>>>>>>>>>>>>    TRUE iff machine HALTS and DECIDABLE,   
   >>>>>>>>>>>>>>>    FALSE iff machine LOOPS or UNDECIDABLE,   
   >>>>>>>>>>>>>>> }   
   >>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>> it doesn't do so quite so intelligently, but HHH(DD)   
   >>>>>>>>>>>>>>> needs to return FALSE because DD is an UNDECIDABLE input   
   >>>>>>>>>>>>>>> to HHH   
   >>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>> polcott does this by detecting the infinite recursion and   
   >>>>>>>>>>>>>>> returning FALSE because of that   
   >>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>> this approach of returning FALSE upon encountering an   
   >>>>>>>>>>>>>>> infinite recursion on self (which i believe all paradoxes   
   >>>>>>>>>>>>>>> will involve) will either be accurate or inaccurate in   
   >>>>>>>>>>>>>>> regards to actually halting/ not... but it doesn't matter   
   >>>>>>>>>>>>>>> because returning FALSE for halting yet UNDECIDABLE input   
   >>>>>>>>>>>>>>> is acceptable for a *partial recognizer*   
   >>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>> where this wouldn't work is:   
   >>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>> int ND()   
   >>>>>>>>>>>>>>> {   
   >>>>>>>>>>>>>>>      int Halt_Status = HHH(ND);   
   >>>>>>>>>>>>>>>      return Halt_Status;   
   >>>>>>>>>>>>>>> }   
   >>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>> HHH(ND) -> FALSE because HHH(ND) will recognize the   
   >>>>>>>>>>>>>>> infinite recursion and return FALSE ... but that's not an   
   >>>>>>>>>>>>>>> acceptable response for a *partial recognizer* for ND   
   >>>>>>>>>>>>>>> because ND is not an UNDECIDABLE input, and it clearly   
   >>>>>>>>>>>>>>> should HALT   
   >>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>> sorry polcott   
   >>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>   
   >>>>>>>>>>>>>> That is merely a text message that has not been updated.   
   >>>>>>>>>>>>>>   
   >>>>>>>>>>>>>> See my other post:   
   >>>>>>>>>>>>>> When halt provers are allowed to reject bad   
   >>>>>>>>>>>>>> inputs the remaining domain is decidable   
   >>>>>>>>>>>>>>   
   >>>>>>>>>>>>>> A bad input is any input that does not have   
   >>>>>>>>>>>>>> *a well-founded justification tree within Proof*   
   >>>>>>>>>>>>>> *theoretic semantics*   
   >>>>>>>>>>>>>>   
   >>>>>>>>>>>>>> For a simulating halt prover as soon as it detects   
   >>>>>>>>>>>>>> that its simulated input cannot possibly reach its   
   >>>>>>>>>>>>>> own simulated final halt state for any reason   
   >>>>>>>>>>>>>> what-so-ever then this input  a bad input.   
   >>>>>>>>>>>>>>   
   >>>>>>>>>>>>>   
   >>>>>>>>>>>>> so ur just banning self-referential analysis?   
   >>>>>>>>>>>>>   
   >>>>>>>>>>>>   
   >>>>>>>>>>>> When we reject inputs not having   
   >>>>>>>>>>>> *a well-founded justification tree within Proof*   
   >>>>>>>>>>>> *theoretic semantics*   
   >>>>>>>>>>>>   
   >>>>>>>>>>>> Then undecidability utterly ceases to exist.   
   >>>>>>>>>>>   
   >>>>>>>>>>> i agree it's impossible to demonstrated undecidability   
   >>>>>>>>>>> without self- reference,   
   >>>>>>>>>>>   
   >>>>>>>>>>> and filtering out paradoxes is a path to turing complete and   
   >>>>>>>>>>> fully decidable subset of turing machines,   
   >>>>>>>>>>>   
   >>>>>>>>>>> but ND is a halting function, and i don't see a particular   
   >>>>>>>>>>> reason why a more intelligent HHH couldn't return that given   
   >>>>>>>>>>> a more in- depth analysis of how the self-reference   
   >>>>>>>>>>> interplays with the rest of the machine   
   >>>>>>>>>>>   
   >>>>>>>>>>   
   >>>>>>>>>> It cannot do that because that is not what it sees.   
   >>>>>>>>>   
   >>>>>>>>> once it sees the infinite recursion on itself ...   
   >>>>>>>>>   
   >>>>>>>>> why can't it do analysis on the effects of various possible   
   >>>>>>>>> return values for itself ... like what we do when we talk thru it?   
   >>>>>>>>>   
   >>>>>>>>   
   >>>>>>>> The job of a simulating halt prover is to determine   
   >>>>>>>> whether or not it must abort its simulation to prevent   
   >>>>>>>> its own non-termination. If for-any-reason the answer   
   >>>>>>>> is yes then it is always correct to abort and reject   
   >>>>>>>> this input.   
   >>>>>>>>   
   >>>>>>>   
   >>>>>>> it's still a partial recognizer, just with worse power than   
   >>>>>>> perhaps a more optimal one that can do more than just abort it's   
   >>>>>>> simulation, but upon doing so recognize the self-reference and   
   >>>>>>> perform more in- depth analysis beyond pure simulation.   
   >>>>>>>   
   >>>>>>   
   >>>>>> Like I tell the LLM systems it is a partial halt prover   
   >>>>>   
   >>>>> i simple see that a more powerful partial halting recognizer can   
   >>>>> return TRUE to the input ND just fine,   
   >>>>>   
   >>>>   
   >>>> When an input does the opposite of whatever value   
   >>>   
   >>> bro u didn't read what i posted before, please refer to the definition:   
   >>>   
   >>>    int ND()   
   >>>    {   
   >>>         int Halt_Status = HHH(ND);   
   >>>         return Halt_Status;   
   >>>    }   
   >>>   
   >>> *ND* does not do the oppose of whatever HHH(ND) reports 🫩, it halts   
   >>> regardless of what HHH(ND) reports.   
   >>>   
      
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