Alternation for two-way machines with sublogarithmic space

  • Burchard von Braunmühl
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 665)

Abstract

The alternation hierarchy for two-way Turing machines with a space bound in o(log) does not collapse below level five.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [BM88]
    L. Babai and S. Moran. Arthur-Merlin games: a randomized proof-system, and a hierarchy of complexity classes. Journal of Computer and System Sciences 36 (1988) 254–276, 36:254–276, 1988.Google Scholar
  2. [Bra91]
    B. v. Braunmühl. Alternationshierarchien von Turingmaschinen mit kleinem Speicher. Informatik Berichte 83, Inst. für Informatik, Universität Bonn, 1991.Google Scholar
  3. [Has86]
    J. Hastad. Almost optimal lower bounds for small depth circuits. In Proc. 18. STOC, pages 6–20, 1986.Google Scholar
  4. [Hem87]
    L. A. Hemachandra. The strong exponential hierarchy collapses. In Proc. 19th. STOC Conference, pages 110–122, 1987.Google Scholar
  5. [IIT87]
    A. Ito, K. Inoue, and I. Takanami. A note on alternating Turing machines using small space. The Transactions of the IEICE, E 70 no. 10:990–996, 1987.Google Scholar
  6. [Imm88]
    N. Immerman. NSPACE is closed under complement. SIAM J. Comput., 17:935–938, 1988.Google Scholar
  7. [LL89]
    M. Liśkiewicz and K. Loryś. On reversal complexity for alternating Turing machines. In Proc. 30st Ann. Symp. on Foundations of Computer Science, pages 618–623, 1989.Google Scholar
  8. [LSH65]
    P. M. Lewis, R. E. Stearns, and J. Hartmanis. Memory bounds for recognition of context-free and context-sensitive languages. In IEEE Conf. Switch. Circuit Theory and Logic Design, pages 191–202, 1965.Google Scholar
  9. [SW88]
    U. Schöning and K. W. Wagner. Collapsing oracle hierarchies, census functions and logarithmically many queries. In Proc. 5th. STACS 88, LNCS 294, pages 91–97, 1988.Google Scholar
  10. [Sze88]
    R. Szelepcsényi. The method of forced enumeration for nondeterministic automata. Acta Informatica, 26:279–284, 1988.Google Scholar
  11. [Yao85]
    A. Yao. Separating the polynomial time hierarchy by oracles. In Proc. 26th. FoCS, pages 1–10, 1985.Google Scholar

Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • Burchard von Braunmühl
    • 1
  1. 1.Institut für Informatik IUniversität BonnBonn 1

Personalised recommendations