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, Σ2 SPACE(S) and Σ3 SPACE(S) are not closed under complement. This implies the hierarchy Σ1 SPACE(S) ⊂Σ2 SPACE(S) ⊂Σ3 SPACE(S) ⊂Σ4 SPACE(S). We also compare the power of weak and strong sublogarithmic space bounded ATMs.
On leave of Institute of Computer Science, University of Wrocław supported by the Alexander-von-Humboldt-Stiftung
This is a preview of subscription content, log in via an institution.
Preview
Unable to display preview. Download preview PDF.
References
H. Alt, V. Geffert, and K. Mehlhorn, A lower bound for the nondeterministic space complexity of context-free recognition, IPL 42, 1992, 25–27.
H. Alt, and K. Mehlhorn, Lower bounds for the space complexity of context free recognition, Proc. 3. ICALP, 1976, 339–354.
J. Chang, O. Ibarra, B. Ravikumar, and L. Berman, Some observations concerning alternating Turing machines using small space, IPL 25, 1987, 1–9.
V. Geffert, Nondeterministic computations in sublogarithmic space and space constructability, SIAM J. Comput., 20, 1991, 484–498.
V. Geffert, Sublogarithmic Σ2-space is not closed under complement and other separation results, Technical Report, University of Safarik, 1992.
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).
N. Immerman, Nondeterministic space is closed under complementation, SIAM J. Comput., 17, 1988, 935–938.
P. Michel, A survey of space complexity, TCS 101, 1992, 99–132.
M. Sipser, Halting space-bounded computations, TCS 10, 1980, 335–338.
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.
R. Szelépcsenyi, The method of forced enumeration for nondeterministic automata, Acta Informatica, 26, 1988, 279–284.
A. Szepietowski, Turing machines with sublogarithmic space, unpubl. manuscript.
K. Wagner, and G. Wechsung, Computational Complexity, Reidel, 1986.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1993 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Liśkiewicz, M., Reischuk, R. (1993). Separating the lower levels of the sublogarithmic space hierarchy. In: Enjalbert, P., Finkel, A., Wagner, K.W. (eds) STACS 93. STACS 1993. Lecture Notes in Computer Science, vol 665. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56503-5_4
Download citation
DOI: https://doi.org/10.1007/3-540-56503-5_4
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-56503-1
Online ISBN: 978-3-540-47574-3
eBook Packages: Springer Book Archive