On the relationship between the complexity, the degree, and the extension of a computable set

  • Wolfgang Maass
  • Theodore A. Slaman
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1432)


We consider the equivalence relation A =c B (“A and B have the same time complexity”) ⇔ (for all time constructible f : ADTIME(f)BDTIME(f)). In this paper we give a survey of the known relationships between this equivalence relation and degree theoretic and extensional properties of sets. Furthermore we illustrate the proof techniques that have been used for this analysis, with emphasis on those arguments that are of interest from the point of view of recursion theory. Finally we will discuss in the last section some open problems and directions for further research on this topic.


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Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • Wolfgang Maass
    • 1
  • Theodore A. Slaman
    • 2
  1. 1.Dept. of Math., Stat., and Comp. Sci.University of Illinois at ChicagoChicago
  2. 2.Dept. of MathematicsUniversity of ChicagoChicago

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