Let's assume there exists hardware that is able to compute the halting function H(n). That is, if you give it the number of a Turing Machine program/input combination, it will output a 1 if the TM halts and a 0 otherwise. “Super Turing Machine” (STM) based on this are constructed that can run “super algorithms.” STMs are ordinary TMs that can call the magic hardware as though it were a subroutine. Super algorithms are therefore ordinary TM programs that can make a call to the function H whenever necessary, and actually get a result. Clearly these are more powerful than ordinary computers, since they can solve the halting problem for ordinary TMs. Can they also solve the halting problem for themselves?
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