ACC is Undecidable

• Suppose it were decidable. Let D be a TM that decides it.

• Construct the following TM, named P:

• P:

  • Given input < M > run D on <M, <M> >
  • If D accepts, then REJECT
  • Else (if D rejects), ACCEPT

• P seems harmless enough.

• BUT... what happens when we give P the input <P> ?

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