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Structure and importance of logspace-MOD-classes

  • Complexity I
  • Conference paper
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STACS 91 (STACS 1991)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 480))

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Abstract

We refine the techniques of Beigel, Gill, Hertrampf [BGH90] who investigated polynomial time counting classes, in order to make them applicable to the case of logarithmic space. We define the complexity classes MOD k L and demonstrate their significance by proving that all standard problems of linear algebra over the finite rings Z/kZ are complete for these classes. We then define new complexity classes LogFew and LogFew NL and identify them as adequate logspace versions of Few and LogFew and Few P. We show that LogFew and LogFew NL is contained in MODZ k L and that LogFew is contained in MOD k L for all k. Also an upper bound for L #L in terms of computation of integer determinants is given from which we conclude that all logspace counting classes are contained in NC 2.

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Author information

Authors and Affiliations

  1. Institut für Informatik, Universität Würzburg, D-8700, Würzburg, Germany

    Gerhard Buntrock & Ulrich Hertrampf

  2. Sektion Informatik, Humboldt-Universität Berlin, D-1086, Berlin, Germany

    Carsten Damm & Christoph Meinel

Authors
  1. Gerhard Buntrock
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  2. Ulrich Hertrampf
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  3. Carsten Damm
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  4. Christoph Meinel
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Editor information

Christian Choffrut Matthias Jantzen

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© 1991 Springer-Verlag Berlin Heidelberg

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Buntrock, G., Hertrampf, U., Damm, C., Meinel, C. (1991). Structure and importance of logspace-MOD-classes. In: Choffrut, C., Jantzen, M. (eds) STACS 91. STACS 1991. Lecture Notes in Computer Science, vol 480. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0020812

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  • DOI: https://doi.org/10.1007/BFb0020812

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-53709-0

  • Online ISBN: 978-3-540-47002-1

  • eBook Packages: Springer Book Archive

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