Characterizing the polynomial Hierarchy by alternating auxiliary pushdown automata

  • Birgit Jenner
  • Bernd Kirsig
Contributed Papers Complexity
Part of the Lecture Notes in Computer Science book series (LNCS, volume 294)


An alternating auxiliary pushdown hierarchy is defined by extending the machine model of the Logarithmic Alternation Hierarchy by a pushdown store while keeping a polynomial time bound. Although recently it was proven by Borodin et al. that the class of languages accepted by nondeterministic logarithmic space bounded auxiliary pushdown automata with a polynomial time bound is closed under complement [Bo et al], it is shown that, surprisingly, the further levels of this alternating auxiliary pushdown hierarchy coincide level by level with the Polynomial Hierarchy. Furthermore, it is shown that PSPACE can be characterized by simultaneously logarithmic space and polynomial time bounded auxiliary pushdown automata with unbounded alternation.


Polynomial Time Conjunctive Normal Form Boolean Formula Logarithmic Space Polynomial Hierarchy 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [Bo et al]
    A. Borodin, S.A. Cook, P.W. Dymond, W.L. Ruzzo, M. Tompa: Two applications of complementation via inductive counting, manuscript, Sept. 1987.Google Scholar
  2. [Co]
    S.A. Cook: Characterizations of pushdown machines in terms of timebounded computers, Journ. of the ACM 18, 1(1971): 4–18.Google Scholar
  3. [Cha Ko Sto]
    A.K. Chandra, D.C. Kozen, L.J. Stockmeyer: Alternation, Journ. of the ACM 28, 1(1981): 114–133.Google Scholar
  4. [Ho Ull]
    J.E. Hopcroft, J.D. Ullman: Introduction to Automata Theory, Languages, and Computation, Addison-Wesley, Reading, Mass., 1979.Google Scholar
  5. [Im]
    N. Immerman: Nondeterministic space is closed under complement, Techn. Report, Yale University, YALEU/DCS/TR 552, July 1987.Google Scholar
  6. [La Je Ki]
    K.-J. Lange, B. Jenner, B. Kirsig: The logarithmic alternation hierarchy collapses: AΣ2l=AΠ2l, Proc. of the 14th ICALP, Karlsruhe, July 1987, Lect. Notes in Comp. Sci. 267, 531–541.Google Scholar
  7. [La Li Sto]
    R.E. Ladner, R.J. Lipton, L.J. Stockmeyer: Alternating pushdown automata, Proc. of the 19th IEEE Symp. on Foundations of Comp. Sci., Ann Arbor, Mich., 1978, 92–106.Google Scholar
  8. [Schö Wa]
    U. Schöning, K.W. Wagner: Collapsing oracle hierarchies, census functions and logarithmically many queries, Report Nr. 140, Universität Augsburg, May 1987.Google Scholar
  9. [Sto]
    L.J. Stockmeyer: The polynomial-time hierarchy, Theoret. Comp. Sci. 3(1976), 1–22.Google Scholar
  10. [Sud]
    I.H. Sudborough: On the time and tape complexity of deterministic context-free languages, Journ. of the ACM 25, 3(1978): 405–414.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • Birgit Jenner
    • 1
  • Bernd Kirsig
    • 1
  1. 1.Universität Hamburg, Fachbereich InformatikHamburg 13

Personalised recommendations