XPost: comp.theory, sci.math, comp.theory   
   From: mikko.levanto@iki.fi   
      
   On 15/12/2025 16:01, olcott wrote:   
   > 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 expression "halt only deciders" does not make sense. A decider   
   is a decider of one fieture of the input. It does not decide   
   anything else. What is that "only" intended to mean?   
      
   > The above definition removes that category error.   
      
   It also removes the halting problem.   
      
   > 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.   
      
   The input string specifies the behavour of a Truing machine and a   
   particular input to that Turing machine. Any other inpterpretation   
   is outside of the scope of the halting problem.   
      
   Because no decider can determine about every pair of a Turing   
   machine and input there are no halting deciders.   
      
   --   
   Mikko   
      
   --- SoupGate-Win32 v1.05   
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