Corollary: HALT is undecidable

• We’ll show this via a reduction.

• Suppose that HALT were decidable. Say H decides it.

• Define another TM, named A by

• A: On input < M, w >:

  • Run H on input < M, w >.
  • If H rejects, then REJECT
  • Else, simulate M on input w.
    • If M accepts, ACCEPT
    • If M rejects, REJECT

• A decides ACC!!

Previous slide

Next slide

Back to first slide

View graphic version