Abstract
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.
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A. Borodin, S.A. Cook, P.W. Dymond, W.L. Ruzzo, M. Tompa: Two applications of complementation via inductive counting, manuscript, Sept. 1987.
S.A. Cook: Characterizations of pushdown machines in terms of timebounded computers, Journ. of the ACM 18, 1(1971): 4–18.
A.K. Chandra, D.C. Kozen, L.J. Stockmeyer: Alternation, Journ. of the ACM 28, 1(1981): 114–133.
J.E. Hopcroft, J.D. Ullman: Introduction to Automata Theory, Languages, and Computation, Addison-Wesley, Reading, Mass., 1979.
N. Immerman: Nondeterministic space is closed under complement, Techn. Report, Yale University, YALEU/DCS/TR 552, July 1987.
K.-J. Lange, B. Jenner, B. Kirsig: The logarithmic alternation hierarchy collapses: AΣ l2 =AΠ l2 , Proc. of the 14th ICALP, Karlsruhe, July 1987, Lect. Notes in Comp. Sci. 267, 531–541.
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.
U. Schöning, K.W. Wagner: Collapsing oracle hierarchies, census functions and logarithmically many queries, Report Nr. 140, Universität Augsburg, May 1987.
L.J. Stockmeyer: The polynomial-time hierarchy, Theoret. Comp. Sci. 3(1976), 1–22.
I.H. Sudborough: On the time and tape complexity of deterministic context-free languages, Journ. of the ACM 25, 3(1978): 405–414.
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© 1988 Springer-Verlag Berlin Heidelberg
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Jenner, B., Kirsig, B. (1988). Characterizing the polynomial Hierarchy by alternating auxiliary pushdown automata. In: Cori, R., Wirsing, M. (eds) STACS 88. STACS 1988. Lecture Notes in Computer Science, vol 294. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0035838
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DOI: https://doi.org/10.1007/BFb0035838
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