XPost: comp.theory, sci.math, comp.theory   
   From: polcott333@gmail.com   
      
   On 12/15/2025 2:53 AM, Mikko wrote:   
   > On 15/12/2025 02:31, olcott wrote:   
   >> Whenever any textbook says that a halt decider   
   >> must compute halting for machine M on input w   
   >> is it wrong. At best it only computes the halting   
   >> of M/w through the proxy of finite strings ⟨M⟩/w.   
   >>   
   >> Turing machine deciders compute the mapping from   
   >> input finite strings to an accept or reject value   
   >> by some criterion measure.   
   >>   
   >> Turing machine halt deciders compute the mapping   
   >> from input finite strings to a halt status on the   
   >> basis of the behavior that these finite strings   
   >> inputs actually specify.   
   >   
   > There are no halt deciders so they don't actually do anything.   
   >   
      
   There are no halt only deciders because they are   
   defined as a category error. The above definition   
   removes that category error.   
      
   No halt decider can possibly report on the behavior   
   of a Turing machine they can only report on the   
   behavior that finite string inputs specify. Within   
   this definition HHH(DD)==0 is correct.   
      
   --   
   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)