XPost: comp.theory, sci.math, comp.lang.prolog   
   XPost: sci.lang, comp.software-eng   
   From: polcott333@gmail.com   
      
   On 2/5/2026 11:22 PM, dart200 wrote:   
   > On 2/5/26 9:01 PM, olcott wrote:   
   >> On 2/5/2026 10:36 PM, dart200 wrote:   
   >>> On 2/5/26 8:31 PM, olcott wrote:   
   >>>> On 2/5/2026 10:15 PM, dart200 wrote:   
   >>>>> On 2/5/26 8:08 PM, olcott wrote:   
   >>>>>> 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   
      
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