XPost: comp.theory, sci.math, comp.ai.philosophy   
   From: mikko.levanto@iki.fi   
      
   olcott kirjoitti 10.12.2025 klo 18.27:   
   > On 12/10/2025 4:14 AM, Mikko wrote:   
   >> olcott kirjoitti 8.12.2025 klo 21.00:   
   >>> On 12/8/2025 3:04 AM, Mikko wrote:   
   >>>> olcott kirjoitti 8.12.2025 klo 5.14:   
   >>>>> Turing machine deciders only compute a mapping from   
   >>>>> their [finite string] inputs to an accept or reject   
   >>>>> state on the basis that this [finite string] input   
   >>>>> specifies or fails to specify a semantic or syntactic   
   >>>>> property.   
   >>>>   
   >>>>> Within the verified truth of the above paragraph   
   >>>>> *that took me three years to write* the halting   
   >>>>> problem is proved to be incorrect in that it requires   
   >>>>> that halting be computed from behavior other than   
   >>>>> the actual behavior that the actual input actually   
   >>>>> specifies as measured by a UTM based halt decider.   
   >>>>   
   >>>> The halting problem as usually posed asks for a method to determine   
   >>>> about every computation whether it halts or runs forever. Some   
   >>>> formulations specify further that the solution shall be expressed   
   >>>> as a Turing machine that can be given a description of the computation.   
   >>>   
   >>> The mistake that I have fully elaborated many dozens   
   >>> of times and so far everyone has ignored is that the   
   >>> halting problem as specified requires a halt decider   
   >>> to report on a behavior that differs from the behavior   
   >>> that its actual finite string input actually specifies.   
   >>   
   >> When you start with a false claim you can infer nore false claims.   
   >> But false claims are false no matter what you said about them.   
   >   
   > *You cannot possibly find any mistake with this*   
   > *You cannot possibly find any mistake with this*   
   > *You cannot possibly find any mistake with this*   
   >   
   > int DD()   
   > {   
   >    int Halt_Status = HHH(DD);   
   >    if (Halt_Status)   
   >      HERE: goto HERE;   
   >    return Halt_Status;   
   > }   
   >   
   > After many very extensive discussions with LLM   
   > systems there are two principles that prove that   
   > I have correctly refuted the halting problem itself.   
   >   
   > (1) Turing Machine based Computable functions   
   > only transform input finite strings into some value   
   > on the basis of a semantric of syntatic property   
   > that this finite string specifies.   
   >   
   > (2) the behavior that an input DD specifies to halt   
   > decider HHH is the sequence of steps of DD   
   > simulated by HHH according to the semantics of   
   > the C programming language.   
   >   
   > Computable functions are the basic objects of study   
   > in computability theory. Informally, a function is   
   > computable if there is an algorithm that computes   
   > the value of the function for every value of its argument.   
   > https://en.wikipedia.org/wiki/Computable_function   
   >   
   > 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.   
      
   --   
   Mikko   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)