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Structure and importance of logspace-MOD-classes

  • Gerhard Buntrock
  • Ulrich Hertrampf
  • Carsten Damm
  • Christoph Meinel
Complexity I
Part of the Lecture Notes in Computer Science book series (LNCS, volume 480)

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 MODkL 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 LogFewNL and identify them as adequate logspace versions of Few and LogFew and FewP. We show that LogFew and LogFewNL is contained in MODZkL and that LogFew is contained in MODkL 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 NC2.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Gerhard Buntrock
    • 1
  • Ulrich Hertrampf
    • 1
  • Carsten Damm
    • 2
  • Christoph Meinel
    • 2
  1. 1.Institut für InformatikUniversität WürzburgWürzburgGermany
  2. 2.Sektion InformatikHumboldt-Universität BerlinBerlinGermany

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