Abstract
Alternation is a generalized principle of nondeterminism. The alternating turing machine is used to characterize the polynomial hierarchy. In this paper we show, that a hierarchy can be characterized with alternating pushdown automata, which we expect to be strict in contrast to a hierarchy with alternating finite automata or alternating space bounded automata. We describe a similar oracle hierarchy over the context-free languages, for which we construct complete languages. We show, that each level of the hierarchy with alternating pushdown automata is included in the corresponding level of the oracle hierarchy and that the logarithmic closure over both levels is the corresponding level of the polynomial hierarchy with one alternation less.
The principle of the alternation is also transfered to grammars. Hereby we prove, that the hierarchy with alternating context-free grammars is identical with the oracle hierarchy over the context-free languages and that in case of unbounded alternation context-free and context-sensitive grammars have the same power.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
J. Berstel: Transductions and Context-Free Languages, Teubner 1979.
A.K. Chandra, D.C. Kozen, L.J. Stockmeyer; Alternation, Journ. of the ACM 28,1(1981), 114–133.
S.A. Cook: Characterizations of pushdown machines in terms of timebounded computers, Journ. of the ACM 18,1(1971), 4–18
J.E. Hopcroft, J.D. Ullman: Introduction to Automata Theory, Languages and Computation, Addison-Wesley, 1979.
N. Immerman: Nondeterministic space is closed under complementation, SIAM Journ. Comput. 15, 5 (1988), 935–938.
Birgit Jenner, Bernd Kirsig: Characterizing the polynomial hierarchy by alternating auxiliary pushdown automata. Theoretical Informatics and Applications, 1989, 87–99.
A.J. Korenjak, J.E. Hopcroft: Simple deterministic languages, Conf. Rec. 7th Annual IEEE Symp. Switching and Automata Theory (1966), 36–46.
R.E. Ladner,L.J. Stockmeyer,R.J. Lipton: Alternation bounded auxiliary pushdown automata, Information and Control 62(1984), 93–108.
Etsuro Moriya: A grammatical characterization of alternating pushdown automata, TCS 67 (1989) 75–85.
R. Szelepcsenyi: The Method of forced enumeration for nondeterministic automata, Acta Informatica 26(1988), 279–284.
Robert I. Soare: Recursively Enumerable Sets and Degrees, Springer 1987.
L.J. Stockmeyer: The polynomial-time hierarchy, Theoret. Comp. Sci. 3 (1976), 1–22.
I.H. Sudborough: On the tape complexity of deterministic context-free languages, Journ. of the ACM 25, 3 (1978),405–414.
C. Wrathall: Complete sets and the polynomial-time hierarchy, Theoret. Comp. Sci. 3 (1976), 23–33.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1990 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Reinhardt, K. (1990). Hierarchies over the context-free languages. In: Dassow, J., Kelemen, J. (eds) Aspects and Prospects of Theoretical Computer Science. IMYCS 1990. Lecture Notes in Computer Science, vol 464. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-53414-8_44
Download citation
DOI: https://doi.org/10.1007/3-540-53414-8_44
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-53414-3
Online ISBN: 978-3-540-46869-1
eBook Packages: Springer Book Archive