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)

Abstract

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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    H. Alt, V. Geffert, and K. Mehlhorn, A lower bound for the nondeterministic space complexity of context-free recognition, IPL 42, 1992, 25–27.Google Scholar
  2. 2.
    H. Alt, and K. Mehlhorn, Lower bounds for the space complexity of context free recognition, Proc. 3. ICALP, 1976, 339–354.Google Scholar
  3. 3.
    J. Chang, O. Ibarra, B. Ravikumar, and L. Berman, Some observations concerning alternating Turing machines using small space, IPL 25, 1987, 1–9.Google Scholar
  4. 4.
    V. Geffert, Nondeterministic computations in sublogarithmic space and space constructability, SIAM J. Comput., 20, 1991, 484–498.Google Scholar
  5. 5.
    V. Geffert, Sublogarithmic Σ2-space is not closed under complement and other separation results, Technical Report, University of Safarik, 1992.Google Scholar
  6. 6.
    J. Hartmanis, and D. Ranjan, Space bounded computations: review and new separation results, Proc. 14. MFCS, 1989, 46–66 (also TCS 80, 1991, 289–302).Google Scholar
  7. 7.
    N. Immerman, Nondeterministic space is closed under complementation, SIAM J. Comput., 17, 1988, 935–938.Google Scholar
  8. 8.
    P. Michel, A survey of space complexity, TCS 101, 1992, 99–132.Google Scholar
  9. 9.
    M. Sipser, Halting space-bounded computations, TCS 10, 1980, 335–338.Google Scholar
  10. 10.
    R. Stearns, J. Hartmanis, and P. Lewis, Hierarchies of memory limited computations, Proc. IEEE Conf. on Switching Circuit Theory and Logical Design, 1965, 179–190.Google Scholar
  11. 11.
    R. Szelépcsenyi, The method of forced enumeration for nondeterministic automata, Acta Informatica, 26, 1988, 279–284.Google Scholar
  12. 12.
    A. Szepietowski, Turing machines with sublogarithmic space, unpubl. manuscript.Google Scholar
  13. 13.
    K. Wagner, and G. Wechsung, Computational Complexity, Reidel, 1986.Google Scholar

Copyright information

© Springer-Verlag 1993

Authors and Affiliations

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

Personalised recommendations