XPost: comp.theory, sci.math, comp.theory   
   From: mikko.levanto@iki.fi   
      
   On 15/12/2025 11:14, Richard Heathfield wrote:   
   > On 15/12/2025 08:53, 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.   
   >   
   >   
   > Halt deciders are ten a penny.   
   >   
   > This one, for example, works 99% of the time, +/-:   
   >   
   > int halts(char *prgfilename, void *input)   
   > {   
   >    return 1;   
   > }   
   >   
   > If you meant to claim that there are no *universal* halt deciders, then   
   > of course I agree.   
      
   The usual meaning of "halt decider" and "halting decider" is that   
   it answers correctly every time. One that may fail to answer   
   correctly is called a "partial halt decider".   
      
   More generally, a "decider" is a Turing machine that for every   
   input either accepts or rejects.   
      
   --   
   Mikko   
      
   --- SoupGate-Win32 v1.05   
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