Turing and randomness

  title={Turing and randomness},
  author={R. Downey},
  booktitle={The Turing Guide},
  • R. Downey
  • Published in The Turing Guide 2017
  • Computer Science, Mathematics
In an unpublished manuscript, Turing anticipated the basic ideas behind the theory of algorithmic randomness. He did so by nearly 30 years. Turing used a computationally constrained version of “measure theory” to answer a question of Borel in number theory. This question concerned constructing what are called “absolutely normal” numbers. In this article, I will try to explain what these mysterious terms mean, and what Turing did. 1 Borel, number theory and normality 1.1 Repeated decimals in… Expand
2 Citations
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Turing's Normal Numbers: Towards Randomness
  • V. Becher
  • Mathematics, Computer Science
  • CiE
  • 2012
An algorithm that produces real numbers normal to every integer base is given that proves the existence of computable normal numbers and it is the best solution to date to Borel's problem on giving examples of normal numbers. Expand
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  • Computer Science, Psychology
  • Texts and Monographs in Computer Science
  • 1993
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