Corollary: DOESN’T-HALT is unrecognizable

• Again, we’ll use a reduction.

• Suppose DOESN’T-HALT were recognizable. Say Turing Machine DH recognizes it.

• Say H recognizes HALT.

• Define another TM, named D by

• D: On input < M, w >:

  • Run H and DH simultaneously.
  • If H accepts, ACCEPT
  • If DH accepts, REJECT

• Then D decides HALT!!

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