Abstract
Two characterizations of the logarithmic alternation hierarchy are given. The first one by bounded quantification of DSPACE(log n)-predicates, where the quantified words are given as one-way input. It is shown that a simple change of the order of the quantified words (w.r.t. the order of the quantifiers) allows the generation of NP-complete sets. The second characterization is by nondeterministic many-one log-space reductions, which fulfill the Ruzzo, Simon, and Tompa - condition.
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References
A. Chandra, D. Kozen, L. Stockmeyer: Alternation, J. Assoc. Comput. Mach. 28 (1981), 114–133.
P. Flajolet, J. Steyaert: Complexity of classes of languages and operators, IRIA Laboria, Rap. de Recherche No. 92, Nov. 1974.
J. Hopcroft, J. Ullman: Introduction to Automata Theory, Languages, and Computation, Addison-Wesley, Reading Mass., 1979.
R. Ladner, N. Lynch: Relativization of questions about log space computability, Math. Systems Theory 10 (1976), 19–32.
R. Ladner, N. Lynch, A. Selman: A comparison of polynomial time reducibilities, Theoret. Comput. Sci. 1 (1975), 103–123.
K.-J. Lange: Nichtdeterministische Reduktionen und Logarithmische Hierarchien, Habilitationsschrift, University of Hamburg, 1985, (in German).
K.-J. Lange: Decomposition of nondeterministic reductions, to be published in the proceedings of ICALP 1986.
N. Lynch: Log space recognition and translation of parenthesis languages, J. Assoc. Compu. Mach. 24 (1977), 583–590.
A. Meyer, L. Stockmeyer: The equivalence problem for regular expressions with squaring requires exponential space, Proc. of the 13th IEEE Symp. on Swi. and Aut. Theory 1972, 125–129.
L. Rosier, H.-C. Yen: Logspace hierarchies, polynomial time and the complexity of fairness problems concerning ω-machines, Proc. of STACS 1986, Springer LNCS 210, 306–320.
W. Ruzzo, J. Simon, M. Tompa: Space-bounded hierarchies and probabilistic computations, J. Comput. System Sci. 28 (1984), 216–230.
L. Stockmeyer: The polynomial-time hierarchy, Theoret. Comput. Sci. 3 (1976), 1–22.
L. Stockmeyer, A. Meyer: Word problems requiring exponential time: preliminary report, Proc. of the 5th ACM Symp. on Theory of Comp., 1973, 1–9.
C. Wrathall: Complete sets and the polynomial hierarchy, Theoret. Comput. Sci. 3 (1976), 23–33.
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© 1986 Springer-Verlag Berlin Heidelberg
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Lange, KJ. (1986). Two characterizations of the logarithmic alternation hierarchy. In: Gruska, J., Rovan, B., Wiedermann, J. (eds) Mathematical Foundations of Computer Science 1986. MFCS 1986. Lecture Notes in Computer Science, vol 233. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0016278
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DOI: https://doi.org/10.1007/BFb0016278
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