XPost: comp.theory, sci.logic, sci.math   
   From: polcott333@gmail.com   
      
   On 12/21/2025 6:41 PM, Richard Damon wrote:   
   > On 12/21/25 7:15 PM, olcott wrote:   
   >> On 12/21/2025 5:40 PM, Richard Damon wrote:   
   >>> On 12/21/25 6:19 PM, olcott wrote:   
   >>>> On 6/12/2024 11:50 AM, olcott wrote:   
   >>>>>   
   >>>>> When we compute the mapping from the input to H(D,D) this   
   >>>>> must apply a set of finite string transformation rules   
   >>>>> (specified by the semantics of the x86 language) to this input.   
   >>>>>   
   >>>>   
   >>>> The above is my first use applying this term to a halt decider.   
   >>>>   
   >>>> My first documented use of the term   
   >>>> "finite string transformation rules"   
   >>>> https://groups.google.com/g/comp.theory/c/TFXhleKnHmY/m/lqhDVnvUBgAJ   
   >>>>   
   >>>> *This is the basis for my unique definition of a generic decider*   
   >>>>   
   >>>> Deciders: Transform finite string inputs by finite   
   >>>> string transformation rules into {Accept, Reject} values.   
   >>>>   
   >>>>   
   >>>   
   >>> And is just wrong.   
   >>>   
   >>> For instance, a RASP based decider uses no strings, but might use a   
   >>> numeric representatio of a string.   
   >>>   
   >>   
   >> That may be an actual exception yet over-complicates   
   >> the essence that I need to convey.   
   >   
   > It is a GENERAL exception, so it can't be the rule.   
   >   
   >>   
   >>> And in the more generic version of the theory, are not restricted to   
   >>> just Accepting or Rejecting the input.   
   >>>   
   >>   
   >> Decider seems to be limited to deciding.   
   >   
   > Nope, they started out that way, but there use expanded. That is the   
   > problem of working blind, you can't know what you are doing.   
   >   
   > "Seems" is an admittion that you don't actually know.   
   >   
   > Remember the definition on wikipedia, "A Decider is a Turing Machine   
   > that halts on every input"   
   >   
   > That doesn't limit it to machines with two output states.   
   >   
   > Yes, it means the term has outgrown its roots, but that happens with   
   > languages.   
   >   
      
   Turing machine deciders: Transform finite string   
   inputs by finite string transformation rules into   
   {Accept, Reject} values.   
      
   *Here is how I first said that On 6/10/2017 1:32 PM*   
    > Basically I formalize the entire set of all   
    > knowledge (mathematical and otherwise) simply   
    > as finite string transformation rules.   
   https://groups.google.com/g/comp.theory/c/TFXhleKnHmY/m/lqhDVnvUBgAJ   
      
   *I said this in a much more precise way now*   
   For the entire body of knowledge it is only   
   "finite string transformation rules" that validate   
   "true on the basis of meaning expressed in language"   
      
      
      
   --   
   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)