4.C: Rice’s Theorem and reductions via computation histories
Course week(s)
Week 4
Course subject(s)
4: Reducibility
Description: Rice’s theorem says “non-trivial sets of Turing machines sharing a property about input-output behaviour are undecidable”. Its proof by mapping reduction is surprisingly simple. A new reduction technique using computational histories is introduced. It is used to prove the undecidability of the Post correspondence problem.
Book: Introduction to the Theory of Computation, Chaper 5, pp. 196-209.
Exercises: 5.19, 5.21, 5.29, 5.30.
Key concepts:
- DiTheorem of Rice
- Reduction via Computation Histories
- Post Correspondence Problem
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