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International Symposium on Fundamentals of Computation Theory

FCT 2003: Fundamentals of Computation Theory pp 321–332Cite as

Dimension- and Time-Hierarchies for Small Time Bounds

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2751))

Abstract

Recently, infinite time hierarchies of separated complexity classes in the range between real time and linear time have been shown. This result is generalized to arbitrary dimensions. Furthermore, for fixed time complexities of the form id+r, where r ∈ o(id) is a sublinear function, proper dimension hierarchies are presented. The hierarchy results are established by counting arguments. For an equivalence relation and a family of witness languages the number of induced equivalence classes is compared to the number of equivalence classes distinguishable by the model in question. By contradiction the properness of the inclusions is proved.

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Author information

Authors and Affiliations

  1. Institute of Informatics, University of Giessen, Arndtstr. 2, D-35392, Giessen, Germany

    Martin Kutrib

Authors
  1. Martin Kutrib
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Lund University, 22100, Lund, Sweden

    Andrzej Lingas

  2. School of Technology and Society, Malmö University, SE-205 06, Malmö, Sweden

    Bengt J. Nilsson

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© 2003 Springer-Verlag Berlin Heidelberg

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Kutrib, M. (2003). Dimension- and Time-Hierarchies for Small Time Bounds. In: Lingas, A., Nilsson, B.J. (eds) Fundamentals of Computation Theory. FCT 2003. Lecture Notes in Computer Science, vol 2751. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45077-1_30

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  • DOI: https://doi.org/10.1007/978-3-540-45077-1_30

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40543-6

  • Online ISBN: 978-3-540-45077-1

  • eBook Packages: Springer Book Archive

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