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Computability and Randomness$
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André Nies

Print publication date: 2009

Print ISBN-13: 9780199230761

Published to Oxford Scholarship Online: May 2009

DOI: 10.1093/acprof:oso/9780199230761.001.0001

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The complexity of sets

The complexity of sets

(p.1) 1 The complexity of sets
Computability and Randomness

André Nies

Oxford University Press

This chapter studies the complexity of sets of natural numbers. There are two interrelated types of complexity, these are computational and descriptive. In both cases, to understand the complexity of sets, this chapter introduces classes of similar complexity, namely, classes of sets sharing a certain complexity property.

Keywords:   computational complexity, descriptive complexity, lowness properties, highness properties, Cantor space, uniform measure

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