Chapter 4: Decidability

For Your Enjoyment

Chapter 4.2, Undecidability

An Undecidable Problem

Universal Turing Machine

U = "On input <M, w>, where M is a TM and w is a string:

  1. Simulate M on input w.
  2. If M ever enters its accept state, ACCEPT; if M ever enters its reject state, REJECT.

Set Size

Implication of Set Size

ATM is Undecidable

The complement of ATM is Unrecognizable

In-Class Notes

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