Measures of Relative Randomness

  • Rodney G. Downey
  • Denis R. Hirschfeldt
Part of the Theory and Applications of Computability book series (THEOAPPLCOM)


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.


Initial Segment Computable Function Minimal Pair Splitting Node Expansionary Stage 
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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.School of Mathematics, Statistics and Operations ResearchVictoria University of WellingtonWellingtonNew Zealand
  2. 2.Department of MathematicsUniversity of ChicagoChicagoUSA

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