Home Courses Theory of Computation Course materials Lectures 2.E: The entscheidungsproblem, the Church-turing thesis, and the coding of Turing machines and problems

2.E: The entscheidungsproblem, the Church-turing thesis, and the coding of Turing machines and problems

Course week(s) Week 2
Course subject(s) 2: Turing Machines and the Church-Turing Thesis

Description: Hilbert’s Entscheidungsproblem is undecidable! The common belief that the intuitive notion of computability is adequately modelled by the formal notion of Turing machine (defined by Alan Turing) or by the lambda calculus (invented by Alonzo Church) is called the Church-Turing Thesis. Turing machines and problems can be coded as natural numbers (or otherwise): a programme is a natural number!

Book: Introduction to the Theory of Computation, Chapter 3, pp. 157-161.

Exercises: 3.17, 3.18 and 3.19

Key concepts:

  • Hilbert’s Problems
  • Church-Turing Thesis
  • Encoding of TM’s
Module 2D and E
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