Effective category and measure in abstract complexity theory

Extended abstract
  • Cristian Calude
  • Marius Zimand
Part of the Lecture Notes in Computer Science book series (LNCS, volume 965)


Strong variants of the Operator Speed-up Theorem, Operator Gap Theorem and Compression Theorem are obtained using an effective version of Baire Category Theorem. It is also shown that all complexity classes of recursive predicates have effective measure zero in the space of recursive predicates and, on the other hand, the class of predicates with almost everywhere complexity above an arbitrary recursive threshold has recursive measure one in the class of recursive predicates.


Complexity measure Operator Speed-up Theorem Operator Gap Theorem Compression Theorem effective Baire classification effective measure 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Cristian Calude
    • 1
  • Marius Zimand
    • 2
  1. 1.Computer Science DepartmentThe University of AucklandAucklandNew Zealand
  2. 2.Department of Computer ScienceUniversity of RochesterNew YorkUSA

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