XPost: comp.theory   
   From: tristan.wibberley+netnews2@alumni.manchester.ac.uk   
      
   On 13/12/2025 14:35, Richard Damon wrote:   
   > On 12/12/25 11:36 PM, Tristan Wibberley wrote:   
   >> On 12/12/2025 04:01, olcott wrote:   
   >>> Principle 1: Turing machine deciders compute functions   
   >>> from finite strings to {accept, reject} according to   
   >>                           ^^^^^^^^^^^^^^^^   
   >> "some binary classification"   
   >>   
   >> however, {accept, reject implies a specific human purpose that is not   
   >> intrinsic to the decider, so I think it's not appropriate for a general   
   >> statement.   
   >>   
   >>   
   >   
   > Perhaps you missed that the classic definition of a "Decider" was to   
   > test if a string fit within a given "grammar"   
      
   Yes, I did.   
      
      
   > The decider would "accept" machines that fit, and "reject" things that   
   > didn't.   
   >   
   > THe "grammar" for the halting problem was if the string was a   
   > description of a Turing Machine/Input that would halt.   
      
   Is that a classic definition of "grammar", too? We're talking about   
   before Chomsky's hierarchy. If my memory serves, even after that there   
   isn't a definition of "grammar" that covers halting semantics is there?   
      
      
   > Thus, his Principle 1 is a correct statement for THAT definition of   
   > decider. There are others, going to the point that one definition is   
   > that it is any machine that will always halt no matter what input you   
   > give it. That is, it computes a complete function of all possible input   
   > to some set of output tapes/final states.   
      
   I understood that "to decide" from the time was defined for propositions   
   whereupon one classifies them true or false and that merely extends to   
   the proposition that "string X fits grammar Y". Not the other way around.   
      
      
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   Tristan Wibberley   
      
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