The alternation hierarchy for machines with sublogarithmic space is infinite

  • Burchard von Braunmühl
  • Romain Gengler
  • Robert Rettinger
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 775)

Abstract

The alternation hierarchy for Turing machines with a space bound between loglog and log is infinite. That applies to all common concepts, especially a) to two-way machines with weak space-bounds, b) to two-way machines with strong space-bounds, and c) to one-way machines with weak space-bounds. In all of these cases the σk− and IIk−classes are not comparable for k ≥ 2. Furthermore the σk−classes are not closed under intersection and the IIkclasses are not closed under union. Thus these classes are not closed under complementation. The hierarchy results also apply to classes determined by an alternation depth which is a function depending on the input rather than on a constant.

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Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • Burchard von Braunmühl
    • 1
  • Romain Gengler
    • 1
  • Robert Rettinger
    • 1
  1. 1.Institut für Informatik IUniversität Bonn Römerstraße 164BonnGermany

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