XPost: comp.theory, sci.logic   
   From: polcott333@gmail.com   
      
   On 12/13/2025 5:02 PM, Richard Damon wrote:   
   > On 12/13/25 5:41 PM, olcott wrote:   
   >> On 12/13/2025 3:32 PM, olcott wrote:   
   >>> All of the textbooks require halt deciders to   
   >>> report on the behavior of machine M on input w.   
   >>> This may be easy to understand yet not precisely   
   >>> accurate.   
   >>>   
   >>> Since no Turing machine ever takes any Machine   
   >>> M as an input this  a category error even   
   >>> when this makes no functional difference.   
   >>>   
   >>> They simply glossed over this key detail because   
   >>> they thought that it made no difference.   
   >>>   
   >>> *Defining a halt decider with perfect accuracy*   
   >>> Turing machine halt deciders compute the mapping   
   >>> from input finite strings to an {accept, reject}   
   >>> value on the basis of the behavior that this   
   >>> input finite string specifies.   
   >>>   
   >>   
   >> By simply adding more detail we can make the   
   >> original definition more precise:   
   >>   
   >> A Turing machine based halt decider reports on the   
   >> behavior of machine M on input w thorough the   
   >> proxy of the finite string machine description of   
   >> ⟨M⟩ on input w.   
   >>   
   >> The above seems to be more precisely accurate   
   >> than any published proof. It includes a key   
   >> detail that all of them seem to leave out.   
   >>   
   >> If you know of any published proof that directly   
   >> refers to the idea of a proxy, please let me know.   
   >>   
   >   
   > And the use of a string proxy is just normally assumed by the theory, as   
   > that is how Turing Machine work.   
   >   
      
   See that three agreements in one day.   
   That may be more than we have ever had.   
      
   Because none of the textbooks ever directly said   
   that the finite string input is only a proxy for   
   the behavior everyone always took the proxy to be   
   exactly one-and-the-same thing as the actual behavior.   
      
   > They almost ALWAYS work by a string representation proxy, as very few   
   > real questions are based on the "arbitrary" symbol set of the Turing   
   > Machines native operation.   
   >   
   > If you had bothered to learn the basics of the field, you would have   
   > understood that.   
   >   
   > Most works assume the basic knowledge of the field.   
   >   
   > Note, even the Linz proof you mention explicitly talks about giving the   
   > decider a representation of the machine in question, the Wm as the proxy   
   > for giving it M.   
   >   
   > So, why did you not understand the use of a proxy.   
   >   
   > Sometimes the problem when expressed for lay people will talk about the   
   > decider being given a description or representation of the machine.   
   >   
   > You just reject those as you think it too vague, when it is a well   
   > defined term, and even the general meaning is applicable, you just need   
   > to remember that it must be a SUFFICIENT description to convey the   
   > needed details of the machine.   
      
      
   --   
   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)