XPost: comp.theory, sci.logic, sci.math   
   From: mikko.levanto@iki.fi   
      
   olcott kirjoitti 11.12.2025 klo 4.00:   
   > *It has take me 21 years to boil it down to this*   
   >   
   > When the halting problem requires a halt decider   
   > to report on the behavior of a Turing machine this   
   > is always a category error.   
      
   No, that is not a category error. If the question to be answered   
   is something other than "does this computation halt" then there   
   is not point to call the decider a "halting decider".   
      
   > The corrected halting problem requires a Turing   
   > machine decider to report in the behavior that   
   > its finite string input specifies.   
      
   The usual defintion does the same. But usually the requirement is   
   that the solution to the problem includes encoding rules that   
   specify what the input shall be in order to specify the behaviour   
   asked about.   
      
   It is possible to pose the problem so that encoding rules are a   
   part of the problem specification. For example, the problem nay   
   present a particular unversal Turing machine and require that   
   the halting decider can be given the same input as that universal   
   Turing machine, which then is required to accept if that universal   
   Turing mahine halts with the same input and to reject otherwise.   
      
   --   
   Mikko   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)