XPost: comp.theory, comp.software-eng, sci.math   
   From: polcott333@gmail.com   
      
   On 1/7/2026 6:05 AM, Mikko wrote:   
   > On 06/01/2026 09:47, dart200 wrote:   
   >   
   >    ...   
   >   
   >> i think the actual problem is the TM computing is not sufficient to   
   >> describe all computable relationships.   
   >   
   > It is not. Although we don't know any way compute what is not Turing   
   > computable,   
      
   In computability theory, a decider is a Turing machine   
   that halts for every input.[1] A decider is also called   
   a total Turing machine[2] as it represents a total function.   
      
   Because it always halts, such a machine is able to   
   decide whether a given string is a member of a formal   
   language. The class of languages that can be decided   
   by such machines is the set of recursive languages.   
      
   Given an arbitrary Turing machine, determining whether   
   it is a decider is an undecidable problem. This is a   
   variant of the halting problem, which asks for whether   
   a Turing machine halts on a specific input.   
   https://en.wikipedia.org/wiki/Decider_(Turing_machine)   
      
   That seems a little silly because a TM that simply   
   halts on all inputs including the empty string is   
   said to have accepted that input. The "decision" in   
   this case is "don't make any decision, just accept".   
      
   *Here is a better definition by a*   
   https://yuvalfilmus.cs.technion.ac.il/   
   *PhD computer science Associate Professor*   
   Yuval Filmus   
      
   Intuitively, a decider should be a Turing machine that   
   given an input, halts and either accepts or rejects,   
   relaying its answer in one of many equivalent ways,   
   such as halting at an ACCEPT or REJECT state, or leaving   
   its answer on the output tape.   
   https://cs.stackexchange.com/questions/84433/what-is-decider   
      
   Here is my own generalization across models   
   of computation.   
      
   All deciders essentially: Transform finite string   
   inputs by finite string transformation rules into   
   {Accept, Reject} values.   
      
   Thus the simple way to determine what is not   
   computable is that any required result that   
   cannot be derived by applying finite string   
   transformation rules to specific inputs is   
   outside the scope of computation.   
      
    From this frame-of-reference "undecidability"   
   is not actual weakness or limit to computation.   
   It is merely forming a requirement that exceeds   
   the boundary of the scope of computation.   
      
      
   > we can image a machine that can compute what a Turing   
   > machine can't. Such machine can use a tape as an input and output   
   > device as well as working storage just like Turing machine but has   
   > additional instructions for operations that are not Turring computable.   
   > While it is possible to imagine a halting decider for TUring machines   
   > implemented with an extended machine, a halting decider for all such   
   > machines still requires that the decider can compute something that   
   > none of the machines in its input domain can.   
   >   
      
      
   --   
   Copyright 2026 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-DOS v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)