XPost: comp.theory, comp.theory   
   From: mikko.levanto@iki.fi   
      
   On 14/12/2025 17:34, polcott wrote:   
   > On 12/14/2025 2:59 AM, joes wrote:   
   >> Am Sat, 13 Dec 2025 14:19:01 -0600 schrieb olcott:   
   >>> On 12/13/2025 1:17 PM, Richard Damon wrote:   
   >>>> On 12/11/25 8:48 PM, olcott wrote:   
   >>>>   
   >>>>> Turing machine deciders compute functions from finite strings to   
   >>>>> {accept, reject}.   
   >>>>> The halting problem itself requires that deciders compute the behavior   
   >>>>> of executing machines, thus category error flat out and simple.   
   >>>>   
   >>>> Why do you say that?   
   >>>>   
   >>> All of the textbooks require halt deciders to report on the behavior of   
   >>> machine M on input w.   
   >>> Since no Turing machine ever takes any Machine M as an input this  a   
   >>> category error even when this make no difference.   
   >>> We correct this error by saying that halt deciders must report on the   
   >>> basis of the behavior specified by their input finite string.   
   >>   
   >> TMs don't take numbers as input either but can still do arithmetic.   
   >   
   > A syntactic versus semantic property.   
   >   
   > When a TM adds two numbers it adds the numbers   
   > that its finite string inputs specify.   
      
   What numbers does the input string   
      101+110   
   specify in the input language of a Turing adder?   
      
   What input string specifies the numbers 21 and 15 in the input laugauge   
   of that Turing adder?   
      
   --   
   Mikko   
      
   --- SoupGate-Win32 v1.05   
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