3.B: Decidable problems, the Halting Problem and its undecidability, and Universal Turing Machines

Course week(s) Week 3
Course subject(s) 3: Decidabillity

Description: Some decidability results concerning finite automata and context-free languages are discussed. An informal proof of the undecidability of the Halting Problem is presented. The acceptance problem is introduced and its undecidability is demonstrated. Here the notion of Universal Turing Machine is (implicitly) used: a Turing machine can execute programmes stored with their application data on its input tape.

Book: Introduction to the Theory of Computability, Chapter 4, pp. 167-176, 181-184.

Exercises: 4.1 (abcef), 4.3-4.9, 4.16-4.18 and 4.18.

Key concepts:

  • Decidable Problems concerning Regular Languages and Context-free Languages
  • Halting Problem
  • Acceptability Problem
  • Universal Turing Machines
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