XPost: comp.theory, sci.logic, sci.math   
   From: polcott333@gmail.com   
      
   On 12/19/2025 5:20 PM, Richard Damon wrote:   
   > On 12/19/25 6:13 PM, olcott wrote:   
   >> On 12/19/2025 4:01 PM, Richard Damon wrote:   
   >>> On 12/19/25 11:13 AM, olcott wrote:   
   >>>   
   >>>> Computations: Transform finite strings by finite   
   >>>> string transformation rules into values or nontermination.   
   >>>>   
   >>>> Deciders: Transform finite strings by finite string   
   >>>> transformation rules into {Accept, Reject}.   
   >>>   
   >>> But XXX Deciders need to transform there finite string to {Accept,   
   >>> Reject} in a manner that MATCHES the XXX function.   
   >>>   
   >>   
   >> Not when there is no transformation from the input   
   >> to the required value.   
   >   
   > In other words, you think UTM don't exist.   
   >   
      
   This boils my whole point down much more succinctly than   
   ever before and it is derived from standard definitions.   
      
   Computations: Transform finite strings by finite   
   string transformation rules into values or non-termination.   
      
   Deciders: Transform finite strings by finite string   
   transformation rules into {Accept, Reject}.   
      
   When UTM(P) and H.UTM(P) vary then it is H.UTM(P)   
   that rules because H is only required to report on   
   the behavior that it actual input actually specifies.   
      
      
   --   
   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)