XPost: comp.theory   
   From: tristan.wibberley+netnews2@alumni.manchester.ac.uk   
      
   On 13/12/2025 05:10, polcott wrote:   
   > On 12/12/2025 10:43 PM, Tristan Wibberley wrote:   
   >> I don't think that's true, a UTM-based halt decider may also use   
   >> properties of the finite string other than it's nominal contracta.   
   >>   
   >   
   > I have no idea what you are saying.   
   > There is apparently only one way to determine   
   > the behavior that the input specifies.   
      
   "contracta" latin plural of "contractum" (I think).   
      
   "contractum" the result of reducing a redex.   
      
   In a reduction system with transitive reduction (all those interesting   
   wrt to halting problems) a program is a redex of a reduction which has a   
   contractum that is a redex of a reduction that has a contractum ... so I   
   say a program has many contracta. I say nominal contracta because a   
   physical TM won't always do as the assumptions programmed into the   
   deciding TM stipulate and I feel that gets the point across.   
      
   Simulation (sense of emulation/virtualisation) works by sequentially   
   enumerating all the contracta.   
      
   Halt-deciding by simulation (sense of emulation/virtualisation) draws   
   inferences from the contracta, but it may draw inferences from the   
   initial program that are, at least in part, not contracta of the initial   
   program.   
      
   --   
   Tristan Wibberley   
      
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