Abstract
Measures of relative complexity such as Turing reducibility, wtt-reducibility, and so on have proven to be central tools in computability theory. The resulting degree structures have been widely studied, and there has been considerable interplay between structural results and insights informing our understanding of the concept of computability and its application to such areas as effective mathematics and reverse mathematics. In this chapter, we examine reducibilities that can act as measures of relative complexity, and hence perform a similar role in the theory of algorithmic randomness.
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© 2010 Springer Science+Business Media, LLC
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Downey, R.G., Hirschfeldt, D.R. (2010). Measures of Relative Randomness. In: Algorithmic Randomness and Complexity. Theory and Applications of Computability. Springer, New York, NY. https://doi.org/10.1007/978-0-387-68441-3_9
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DOI: https://doi.org/10.1007/978-0-387-68441-3_9
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Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-95567-4
Online ISBN: 978-0-387-68441-3
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