XPost: comp.theory, sci.logic, sci.math   
   From: mikko.levanto@iki.fi   
      
   olcott kirjoitti 8.12.2025 klo 5.14:   
   > Turing machine deciders only compute a mapping from   
   > their [finite string] inputs to an accept or reject   
   > state on the basis that this [finite string] input   
   > specifies or fails to specify a semantic or syntactic   
   > property.   
      
   > Within the verified truth of the above paragraph   
   > *that took me three years to write* the halting   
   > problem is proved to be incorrect in that it requires   
   > that halting be computed from behavior other than   
   > the actual behavior that the actual input actually   
   > specifies as measured by a UTM based halt decider.   
      
   The halting problem as usually posed asks for a method to determine   
   about every computation whether it halts or runs forever. Some   
   formulations specify further that the solution shall be expressed   
   as a Turing machine that can be given a description of the computation.   
      
   The halting problem does not require that the halting be computed   
   from behaviour other that the acrual input acutally specifies.   
   If the input does not specify the computation that is asked about   
   then the input is wrong and another input should be used instead.   
   If no input that can be given specifies the behaviour asked about   
   then the decider is not a nalting decider.   
      
   The measure of the actual behaviour that the actual input actually   
   specifies is not a UTM based halt decider. Instead the measure is   
   whether the computation asked about halts. If the designer has not   
   specified encoding rules that ensure that the input actually   
   specifies the computation asked about then the halting problem is   
   not solved.   
      
   --   
   Mikko   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)