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9 - Resource bounded randomness and its applications

Published online by Cambridge University Press:  07 May 2020

Johanna N. Y. Franklin
Affiliation:
Hofstra University, New York
Christopher P. Porter
Affiliation:
Drake University, Iowa
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Summary

The field of algorithmic randomness studies the various ways to define the inherent randomness of individual points in a space (for example, the Cantor space or Euclidean space). Classically, this quest seems quixotic. However, the theory of computing allows us to give mathematically meaningful notions of random points. In the past few decades, algorithmic randomness has been extended to make use of resource-bounded (e.g., time or space) computation. In this survey we survey these developments as well as their applications to other parts of mathematics.

Type
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Algorithmic Randomness
Progress and Prospects
, pp. 301 - 348
Publisher: Cambridge University Press
Print publication year: 2020

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