XPost: comp.theory, comp.lang.c, comp.lang.c++   
   From: polcott333@gmail.com   
      
   On 12/15/2025 3:20 AM, Mikko wrote:   
   > On 15/12/2025 02:15, olcott wrote:   
   >> On 12/14/2025 4:46 AM, Mikko wrote:   
   >>> On 11/12/2025 16:38, olcott wrote:   
   >>>> On 12/11/2025 2:53 AM, Mikko wrote:   
   >>>>> olcott kirjoitti 10.12.2025 klo 18.27:   
   >>>>>>   
   >>>>>> DD() executed from main() calls HHH(DD) thus is   
   >>>>>> not one-and-the-same-thing as an argument to HHH.   
   >>>>>   
   >>>>> If the last sentence is true then this is not the counter exmaple   
   >>>>> mentioned in certain proofs of noncomputability of halting and   
   >>>>> therefore not relevant in that context. The halting problem reuqires   
   >>>>> that HHH can determine whether the counter example halts. That is,   
   >>>>> you must be able to replace "???" in   
   >>>>>   
   >>>>>    #include  // or your replacement   
   >>>>>    int main (void)   
   >>>>>    {   
   >>>>>      int Halt_Status = HHH(???); // put the correct argument here   
   >>>>>      printf("HHH says: %s\n", Halt_Status ? "halts" : "does not   
   >>>>> halt");   
   >>>>>      return Halt_Status;   
   >>>>>    }   
   >>>>>   
   >>>>> with whatever specifies the behaviour of DD to HHH. If you can't   
   >>>>> do this then HHH is not a halt decider nor a partial halt decider.   
   >>>   
   >>>> When the halting problem requires a halt decider   
   >>>> to report on the behavior of a Turing machine this   
   >>>> is always a category error.   
   >>>   
   >>> That you don't know what "category error" means does not justify your   
   >>> claim. Apparently you can't apply definitions.   
   >>   
   >> Turing machines only compute functions from finite   
   >> strings they never compute functions from Turing   
   >> machines.   
   >   
   > True, but irrelevant to questions about category errors.   
   >   
   >> A halt decider can at best compute the behavior of   
   >> a Turing machine through the proxy of a finite   
   >> string machine description it never computes it   
   >> directly from another Turing machine.   
   >>   
   >> Whenever any textbook says that a halt decider   
   >> must compute halting for machine M on input w   
   >> is it wrong.   
   >   
   > Which textbook actually says "must"? It is not wrong to say "must" in   
   > the sense that any decider that does not compute whether machine M   
   > halts on input w is not a halt decider. But using "must" is not the   
   > clearest way to say it because the word "must" other meanings.   
   >   
   >  > It actually computes halting that this input pair specifies (⟨M⟩, w).   
   >   
   > There is an unbalanced parenthesis above.   
   >   
      
   No halt decider ever computes the halt status   
   of a machine except through the proxy of finite   
   strings.   
      
   Because all computation only transforms finite   
   strings the result of this transformation is the   
   ultimate correct answer.   
      
   If the machine description is defined to have   
   a dependency on a specific decider and this   
   dependency changes the sequence of steps relative   
   to other execution contexts then it is this   
   changed behavior that must be reported on.   
      
   --   
   Copyright 2025 Olcott

   
      
   My 28 year goal has been to make 
   
   "true on the basis of meaning expressed in language"
   
   reliably computable.

   
      
   This required establishing a new foundation
   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)