XPost: comp.theory, sci.math, comp.theory   
   From: mikko.levanto@iki.fi   
      
   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.   
      
   --   
   Mikko   
      
   --- SoupGate-Win32 v1.05   
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