Separating the lower levels of the sublogarithmic space hierarchy

  • Maciej Liśkiewicz
  • Rüdiger Reischuk
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 665)


For S(n)≥logn it is well known that the complexity classes NSPACE(S) are closed under complementation. Furthermore, the corresponding alternating space hierarchy collapses to the first level. Till now, it is an open problem if these results hold for space complexity bounds between loglogn and logn, too. In this paper we give some partial answer to this question. We show that for each S between loglogn and logn, Σ2SPACE(S) and Σ3SPACE(S) are not closed under complement. This implies the hierarchy Σ1SPACE(S) ⊂Σ2SPACE(S) ⊂Σ3SPACE(S) ⊂Σ4SPACE(S). We also compare the power of weak and strong sublogarithmic space bounded ATMs.


Space Complexity Initial Configuration Memory State Computation Path Space Bound 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Maciej Liśkiewicz
    • 1
  • Rüdiger Reischuk
    • 1
  1. 1.Institut für Theoretische InformatikTechnische Hochschule DarmstadtDarmstadtGermany

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