Standard Article


  1. S. Barry Cooper

Published Online: 16 MAR 2009

DOI: 10.1002/9780470050118.ecse539

Wiley Encyclopedia of Computer Science and Engineering

Wiley Encyclopedia of Computer Science and Engineering

How to Cite

Cooper, S. B. 2009. Computability. Wiley Encyclopedia of Computer Science and Engineering. 490–500.

Author Information

  1. University of Leeds, Leeds, United Kingdom

Publication History

  1. Published Online: 16 MAR 2009


The history of the computer is unusual, in that the theory in the form of the Universal Turing Machine preceded its physical embodiment by around 10 years. Computability as a research area grew out of the work of pioneers such as Alan Turing in the 1930s, and it is still very much defined by the interests of Turing, with his keen curiosity about patterns and underlying theory, but theory firmly tied to a real-world context. This article reviews some main contemporary research directions with new developments strongly featured. A particular focus is the development and investigation of deep and mathematically interesting computational structures, which tell us more about what can and cannot be computed. Turing's notion of an oracle computing machine provides a natural model of computationally complex environments, structuring information, and hence the real world, in remarkably informative ways. Other important topics include randomness and computability of structures. A useful reading list is given.


  • computability;
  • relative computation;
  • computability and information;
  • computable enumerability;
  • enumeration reducibility;
  • Turing reducibility;
  • randomness;
  • degree structures;
  • computable models;
  • Turing definability, invariance