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Quantitative Aspects of Speed-Up and Gap Phenomena

  • Conference paper
Theory and Applications of Models of Computation (TAMC 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5532))

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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].

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References

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Author information

Authors and Affiliations

  1. Institut für Informatik, University of Heidelberg, D-69120, Heidelberg, Germany

    Klaus Ambos-Spies & Thorsten Kräling

Authors
  1. Klaus Ambos-Spies
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  2. Thorsten Kräling
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, Texas A&M University, College Station, 77843, Texas, USA

    Jianer Chen

  2. School of Mathematics, University of Leeds, LS2 9JT, U.K.

    S. Barry Cooper

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© 2009 Springer-Verlag Berlin Heidelberg

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Ambos-Spies, K., Kräling, T. (2009). Quantitative Aspects of Speed-Up and Gap Phenomena. In: Chen, J., Cooper, S.B. (eds) Theory and Applications of Models of Computation. TAMC 2009. Lecture Notes in Computer Science, vol 5532. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02017-9_12

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  • DOI: https://doi.org/10.1007/978-3-642-02017-9_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02016-2

  • Online ISBN: 978-3-642-02017-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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