Description: Enumerability is introduced as an alternative to recognisability: the Turing machine as an enumerator instead of as a recogniser. The proof of equivalence of both notions uses the so-called technique of “dove tailing”. A first, seemingly simple, undecidable language is presented: Hilbert’s tenth problem.

Book: Introduction to the Theory of Computation, Chapter 3, pp. 154-157.

Exercises: 3.15 and 3.16.

Key concepts:

• Equivalence Enumerability and Recognizability