Abstract
Synchronous tree-adjoining grammars have been given two types of semantics: one based on bimorphisms and one based on synchronous derivations, in both of which the input and output trees are constructed synchronously. We introduce a third type of semantics that is based on unidirectional derivations. It derives output trees based on a given input tree and thus marks a first step towards conditional probability distributions. We prove that the unidirectional semantics coincides with the bimorphism-based semantics with the help of a strong correspondence to linear and nondeleting extended top-down tree transducers with explicit substitution. In addition, we show that stateful synchronous tree-adjoining grammars admit a normal form in which only adjunction is used. This contrasts the situation encountered in the stateless case.
This is an extended and revised version of: [A. Maletti: A tree transducer model for synchronous tree-adjoining grammars. In Proc. 48th Annual Meeting Association for Computational Linguistics, pages 1067–1076, 2010].
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Aho, A.V., Ullman, J.D.: The Theory of Parsing, Translation, and Compiling. Prentice Hall (1972)
Büchse, M., Nederhof, M.J., Vogler, H.: Tree parsing with synchronous tree-adjoining grammars. In: Proc. Parsing Technologies, pp. 14–25. ACL (2011)
Büchse, M., Nederhof, M.J., Vogler, H.: Tree parsing for tree-adjoining machine translation (submitted, 2012), www.inf.tu-dresden.de/index.php?node_id=1571
Chiang, D.: Hierarchical phrase-based translation. Comput. Linguist. 33(2), 201–228 (2007)
Courcelle, B., Franchi-Zannettacci, P.: Attribute grammars and recursive program schemes I. Theoret. Comput. Sci. 17(2), 163–191 (1982)
DeNeefe, S.: Tree-Adjoining Machine Translation. Ph.D. thesis, University of Southern California (2011)
DeNeefe, S., Knight, K., Vogler, H.: A decoder for probabilistic synchronous tree insertion grammars. In: Proc. Applications of Tree Automata in Natural Language Processing, pp. 10–18. ACL (2010)
Engelfriet, J.: Bottom-up and top-down tree transformations—a comparison. Math. Systems Theory 9(3), 198–231 (1975)
Engelfriet, J.: Some open questions and recent results on tree transducers and tree languages. In: Book, R.V. (ed.) Formal Language Theory—Perspectives and Open Problems, pp. 241–286. Academic Press (1980)
Engelfriet, J., Vogler, H.: Macro tree transducers. J. Comput. System Sci. 31(1), 71–146 (1985)
Fülöp, Z., Maletti, A., Vogler, H.: Preservation of recognizability for synchronous tree substitution grammars. In: Proc. Applications of Tree Automata in Natural Language Processing, pp. 1–9. ACL (2010)
Gécseg, F., Steinby, M.: Tree Automata. Akadémiai Kiadó, Budapest (1984)
Gécseg, F., Steinby, M.: Tree languages. In: Rozenberg and Salomaa [23], ch. 1, pp. 1–68
Graehl, J., Knight, K., May, J.: Training tree transducers. Comput. Linguist. 34(3), 391–427 (2008)
Joshi, A., Schabes, Y.: Tree-adjoining grammars. In: Rozenberg and Salomaa [23], ch. 2, pp. 69–123
Knight, K., Graehl, J.: An Overview of Probabilistic Tree Transducers for Natural Language Processing. In: Gelbukh, A. (ed.) CICLing 2005. LNCS, vol. 3406, pp. 1–24. Springer, Heidelberg (2005)
Koehn, P.: Statistical Machine Translation. Cambridge University Press (2010)
Maletti, A.: Compositions of extended top-down tree transducers. Inform. and Comput. 206(9-10), 1187–1196 (2008)
Maletti, A.: A tree transducer model for synchronous tree-adjoining grammars. In: Proc. Association for Computational Linguistics, pp. 1067–1076. ACL (2010)
Maletti, A., Engelfriet, J.: Strong lexicalization of tree adjoining grammars. In: Proc. Association for Computational Linguistics. ACL (to appear, 2012)
Nesson, R., Shieber, S.M., Rush, A.: Induction of probabilistic synchronous tree-insertion grammars for machine translation. In: Proc. Association for Machine Translation in the Americas (2006)
Rounds, W.C.: Mappings and grammars on trees. Math. Systems Theory 4(3), 257–287 (1970)
Rozenberg, G., Salomaa, A. (eds.): Handbook of Formal Languages, vol. 3. Springer (1997)
Schabes, Y.: Mathematical and Computational Aspects of Lexicalized Grammars. Ph.D. thesis, University of Pennsylvania, Philadelphia (1990)
Shieber, S.M.: Synchronous grammars as tree transducers. In: Proc. Tree Adjoining Grammar and Related Formalisms, pp. 88–95 (2004)
Shieber, S.M.: Unifying synchronous tree adjoining grammars and tree transducers via bimorphisms. In: Proc. European Chapter of the Association for Computational Linguistics, pp. 377–384. ACL (2006)
Shieber, S.M.: Probabilistic synchronous tree-adjoining grammars for machine translation: The argument from bilingual dictionaries. In: Proc. Syntax and Structure in Statistical Translation, pp. 88–95. ACL (2007)
Shieber, S.M., Schabes, Y.: Synchronous tree-adjoining grammars. In: Proc. Computational Linguistics, pp. 253–258. University of Helsinki (1990)
Thatcher, J.W.: Generalized2 sequential machine maps. J. Comput. System Sci. 4(4), 339–367 (1970)
The XTAG Project, www.cis.upenn.edu/~xtag/
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Büchse, M., Maletti, A., Vogler, H. (2012). Unidirectional Derivation Semantics for Synchronous Tree-Adjoining Grammars. In: Yen, HC., Ibarra, O.H. (eds) Developments in Language Theory. DLT 2012. Lecture Notes in Computer Science, vol 7410. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31653-1_33
Download citation
DOI: https://doi.org/10.1007/978-3-642-31653-1_33
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-31652-4
Online ISBN: 978-3-642-31653-1
eBook Packages: Computer ScienceComputer Science (R0)