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Quantitative Aspects of Speed-Up and Gap Phenomena

  • Klaus Ambos-Spies
  • Thorsten Kräling
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5532)

Abstract

We show that, for any abstract complexity measure in the sense of Blum and for any computable function f (or computable operator F), the class of problems which are f-speedable (or F-speedable) does not have effective measure 0. On the other hand, for sufficiently fast growing f (or F), the class of the nonspeedable problems does not have effective measure 0 too. These results answer some questions raised by Calude and Zimand in [CZ96] and [Zim06]. We also give a short quantitative analysis of Borodin and Trakhtenbrot’s Gap Theorem which corrects a claim in [CZ96] and [Zim06].

Keywords

Quantitative Aspect Computable Function Category Concept Baire Space Abstract Complexity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Klaus Ambos-Spies
    • 1
  • Thorsten Kräling
    • 1
  1. 1.Institut für InformatikUniversity of HeidelbergHeidelbergGermany

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