XPost: comp.theory, comp.software-eng   
   From: news.x.richarddamon@xoxy.net   
      
   On 1/27/26 5:07 PM, Chris M. Thomasson wrote:   
   > On 1/25/2026 2:36 PM, Richard Damon wrote:   
   > [...]   
   >   
   >> An actual algorithm being an actual sequence of finite atomic steps,   
   >> and using bounded loops.   
   >   
   > Why must an algorithm use bounded loops? It can run and run...   
   > generating results along the way...   
   >   
   > [...]   
      
   The classic definition of finitie compuations require the computation to   
   finish, as it is allowed to overwrite its interim results.   
      
   THere is a second definition for infinite computations, where the   
   machine can write unerasable partial results that can be used even while   
   the machine is continuing to produce more results. This is used for   
   computations that produce "Real" results.   
      
   The "Halting Problem" as normally stated is about the first type.   
      
   The second type of machine typically just never halts, and its   
   equivalent to the halting problem would be to determine if a machine   
   just gets to a point where it fails to progress and write another digit   
   to the output. If the calculation ends up producing a result that could   
   be expressed in a finite length real number, these machines are supposed   
   to just "end" in a loop that just continues to emit "0", not just stop.   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)