A quick look at Chapter 5

Section 5.1 — Undecidable Problems

• Section 5.1: Undecidable Problems, notes by Adam Whitley

Section 5.2 — PCP – Post Correspondence Problem

We are skipping this one, but you can take a look at Harry Porter’s videos on The Post Correspondence Problem and the Undecidability of the PCP. PCP is the best known non-geeky undecidable langauge.

Section 5.3 — Mapping Reducibility

• Adam Whitley’s Section 5.3 notes
• some artsy slides (See more at the University of North Dakota CSE3015 site)
• Some pictures about mapping reducibility
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• Some theorems about mapping reducibility
  • 5.22: A ≤_m B and B is decidable ⇒ A is decidable
  • 5.23: A ≤_m B and A is undecidable ⇒ B is undecidable
  • 5.28: A ≤_m B and B is Turing-recognizable ⇒ A is Turing-recognizable
  • 5.29: A ≤_m B and A is not Turing-recognizable ⇒ B is not Turing-recognizable