Abstract
Coupled-Context-Free Grammars are a natural generalization of context-free ones obtained by combining nonterminals to corresponding parentheses which can only be substituted simultaneously. Refering to their generative capacity we obtain an infinite hierarchy of languages that comprises the context-free ones as the first and all those generated by Tree Adjoining Grammars (TAGs) as the second element. Here, we present a completely new approach to analyse this language hierarchy. It solves the word problem for the class of languages generated by TAGs in time O(n 6), n length of the input, by reducing it to the analysis of sequences of parentheses.
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References
A. Abbeillé: Parsing French with Tree Adjoining Grammars: Some Linguistic Accounts. In Proc. of the 12th Conf. on Comput. Linguistics 1988, pp. 7–12
J. Bresnan, R. Kaplan, P. Peters, A. Zaenen: Cross-serial Dependencies in Dutch. Linguistic Inquiry 13 (1982), pp. 613–635
N. Chomsky, N. Schützenberger: The Algebraic Theory of Context-Free Languages. In “Computer Programming and Formal Systems” Amsterdam, North Holland 1963
J. Dassow, G. PĂun: Regulated Rewriting in Formal Language Theory. Springer 1989
Y. Guan, G. Hotz, A. Reichert: Tree Grammars with multilinear Interpretation. Technical Report, Univ. of Saarbrücken 1992
Y. Guan: Klammergrammatiken, Netzgrammatiken und Interpretationen von Netzen. PhD thesis, Univ. of Saarbrücken 1992
G. Hotz, T. Kretschmer: The Power of the Greibach Normal Form. EIK 25 (1989), pp. 507–512
G. Hotz, G. Pitsch: Fast Uniform Analysis of Coupled-Context-Free Grammars. In Proc. of ICALP 1994, pp. 412–423
G. Hotz, G. Pitsch: A Representation Theorem for Coupled-Context-Free Grammars. In Proc. of Conf. on Semigroups, Automata, and Languages, Porto 1994, pp. 88–91
A.K. Joshi, L.S. Levy, M. Takahashi: Tree Adjunct Grammars. J. Comput. Syst. Sci. 10 (1975), pp. 136–163
T. Kroch, A.K. Joshi. The Linguistic Relevance of Tree Adjoining Grammars. Technical Report MS-CIS-85-16, Univ. of Pennsylvania, Philadelphia 1985
G. Pitsch: Analyse von Klammergrammatiken. PhD thesis, Univ. of Saarbrücken 1993. also Technical Report 10/1994, Univ. of Saarbrücken, 1994.
G. Pitsch: LL(k)-Parsing of Coupled-Context-Free Grammars. Comput. Intelligence 10, pp. 563–578
D.J. Rosenkrantz. Matrix Equations and Normal Forms for Context-Free Grammars. J. ACM 14 (1967), pp. 501–507
E. Shamir. A Representation Theorem for Algebraic and Context-Free Power Series in Noncommuting Variables. Information and Control 11 (1967), pp. 239–254
S. Shieber: Evidence against Context-Freeness of Natural Language. Linguistics and Philosophy 8 (1986), pp. 333–343
Y. Schabes, A.K. Joshi. An Early-Type Parsing Algorithm for Tree Adjoining Grammars. In Proc. of the 26th Meeting of the Assoc. for Comput. Linguistics 1988
K. Vijay-Shanker, A.K. Joshi. Some Computational Properties of Tree Adjoining Grammars. In Proc. of the 23th Meeting of the Assoc. for Comput. Linguistics 1985, pp. 82–93
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© 1995 Springer-Verlag Berlin Heidelberg
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Hotz, G., Pitsch, G. (1995). A new approach to analyse Coupled-Context-Free languages. In: Wiedermann, J., Hájek, P. (eds) Mathematical Foundations of Computer Science 1995. MFCS 1995. Lecture Notes in Computer Science, vol 969. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60246-1_141
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DOI: https://doi.org/10.1007/3-540-60246-1_141
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