Abstract
The expressive power of synchronous forest (tree-sequence) substitution grammars (SFSG) is studied in relation to multi bottom-up tree transducers (MBOT). It is proved that SFSG have exactly the same expressive power as compositions of an inverse MBOT with an MBOT. This result is used to derive complexity results for SFSG and the fact that compositions of an MBOT with an inverse MBOT can compute tree translations that cannot be computed by any SFSG, although the class of tree translations computable by MBOT is closed under composition.
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
Arnold, A., Dauchet, M.: Morphismes et bimorphismes d’arbres. Theor. Comput. Sci. 20(1), 33–93 (1982)
Chiang, D.: An introduction to synchronous grammars. In: Proc. 44th ACL. Association for Computational Linguistics (2006), Part of a tutorial given with K. Knight
Dauchet, M.: Transductions de forêts — Bimorphismes de magmoïdes. Première thèse, Université de Lille (1977)
Engelfriet, J., Lilin, E., Maletti, A.: Composition and decomposition of extended multi bottom-up tree transducers. Acta Informatica 46(8), 561–590 (2009)
Fülöp, Z., Kühnemann, A., Vogler, H.: A bottom-up characterization of deterministic top-down tree transducers with regular look-ahead. Inf. Process. Lett. 91(2), 57–67 (2004)
Fülöp, Z., Kühnemann, A., Vogler, H.: Linear deterministic multi bottom-up tree transducers. Theor. Comput. Sci. 347(1-2), 276–287 (2005)
Gécseg, F., Steinby, M.: Tree Automata. Akadémiai Kiadó, Budapest (1984)
Gécseg, F., Steinby, M.: Tree languages. In: Rozenberg, G., Salomaa, A. (eds.) Handbook of Formal Languages, vol. 3, pp. 1–68. Springer (1997)
Gildea, D.: On the string translations produced by multi bottom-up tree transducers. Computational Linguistics 38(3), 673–693 (2012)
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)
Lilin, E.: Propriétés de clôture d’une extension de transducteurs d’arbres déterministes. In: Astesiano, E., Böhm, C. (eds.) CAAP 1981. LNCS, vol. 112, pp. 280–289. Springer, Heidelberg (1981)
Maletti, A.: Compositions of extended top-down tree transducers. Inform. and Comput. 206(9-10), 1187–1196 (2008)
Maletti, A.: Why synchronous tree substitution grammars? In: Proc. HLT-NAACL. Association for Computational Linguistics, pp. 876–884 (2010)
Maletti, A.: An alternative to synchronous tree substitution grammars. J. Nat. Lang. Engrg. 17(2), 221–242 (2011)
Maletti, A.: How to train your multi bottom-up tree transducer. In: Proc. 49th ACL, pp. 825–834. Association for Computational Linguistics (2011)
Radmacher, F.G.: An automata theoretic approach to rational tree relations. In: Geffert, V., Karhumäki, J., Bertoni, A., Preneel, B., Návrat, P., Bieliková, M. (eds.) SOFSEM 2008. LNCS, vol. 4910, pp. 424–435. Springer, Heidelberg (2008)
Raoult, J.C.: Rational tree relations. Bull. Belg. Math. Soc. Simon Stevin 4(1), 149–176 (1997)
Seki, H., Matsumura, T., Fujii, M., Kasami, T.: On multiple context-free grammars. Theoretical Computer Science 88(2), 191–229 (1991)
Sun, J., Zhang, M., Tan, C.L.: A non-contiguous tree sequence alignment-based model for statistical machine translation. In: Proc. 47th ACL, pp. 914–922. Association for Computational Linguistics (2009)
Vijay-Shanker, K., Weir, D.J., Joshi, A.K.: Characterizing structural descriptions produced by various grammatical formalisms. In: Proc. 25th ACL, pp. 104–111. Association for Computational Linguistics (1987)
Zhang, M., Jiang, H., Aw, A., Li, H., Tan, C.L., Li, S.: A tree sequence alignment-based tree-to-tree translation model. In: Proc. 46th ACL, pp. 559–567. Association for Computational Linguistics (2008)
Zhang, M., Jiang, H., Li, H., Aw, A., Li, S.: Grammar comparison study for translational equivalence modeling and statistical machine translation. In: Proc. 22nd CoLing, pp. 1097–1104. Association for Computational Linguistics (2008)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Maletti, A. (2013). Synchronous Forest Substitution Grammars. In: Muntean, T., Poulakis, D., Rolland, R. (eds) Algebraic Informatics. CAI 2013. Lecture Notes in Computer Science, vol 8080. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40663-8_22
Download citation
DOI: https://doi.org/10.1007/978-3-642-40663-8_22
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-40662-1
Online ISBN: 978-3-642-40663-8
eBook Packages: Computer ScienceComputer Science (R0)