Abstract
Extended multi bottom–up tree transducers are defined and investigated. They are an extension of multi bottom–up tree transducers by arbitrary, not just shallow, left-hand sides of rules; this includes rules that do not consume input. It is shown that such transducers, even linear ones, can compute all transformations that are computed by linear extended top–down tree transducers, which are a theoretical model for syntax-based machine translation. Moreover, the classical composition results for bottom–up tree transducers are generalized to extended multi bottom–up tree transducers. Finally, characterizations in terms of extended top–down tree transducers and tree bimorphisms are presented.
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Aho A.V., Ullman J.D.: Syntax directed translations and the pushdown assembler. J. Comput. Syst. Sci. 3(1), 37–56 (1969)
Allauzen, C., Riley, M., Schalkwyk, J., Skut, W., Mohri, M.: OpenFst: A General and Efficient Weighted Finite-state Transducer Library. In: CIAA, Lecture Notes in Computer Science, vol. 4783, pp. 11–23. Springer, Berlin (2007)
Arnold, A., Dauchet, M.: Transductions inversibles de forêts. Thèse 3ème cycle M. Dauchet, Université de Lille (1975)
Arnold, A., Dauchet, M.: Bi-transductions de forêts. In: ICALP, pp. 74–86. Edinburgh University Press, Edinburgh (1976)
Arnold A., Dauchet M.: Morphismes et bimorphismes d’arbres. Theor. Comput. Sci. 20(1), 33–93 (1982)
Baker B.S.: Composition of top-down and bottom-up tree transductions. Inf. Control 41(2), 186–213 (1979)
Berstel J.: Transductions and Context-free Languages. Teubner, Stuttgart (1979)
Bloem R., Engelfriet J.: A comparison of tree transductions defined by monadic second-order logic and by attribute grammars. J. Comput. Syst. Sci. 61(1), 1–50 (2000)
Courcelle B., Franchi-Zannettacci P.: Attribute grammars and recursive program schemes. Theor. Comput. Sci. 17, 163–191, 235–257 (1982)
DeNeefe, S., Knight, K., Wang, W., Marcu, D.: What can syntax-based MT learn from phrase-based MT? In: EMNLP & CoNLL, pp. 755–763. The Association for Computational Linguistics, Stroudsburg (2007)
Engelfriet J.: Bottom-up and top-down tree transformations: a comparison. Math. Syst. Theory 9(3), 198–231 (1975)
Engelfriet J.: Top-down tree transducers with regular look-ahead. Math. Syst. Theory 10(1), 289–303 (1977)
Engelfriet, J.: Tree transducers and syntax-directed semantics. Technical Report Memorandum 363, Technische Hogeschool Twente, 1981. In: Proceedings of 7th CAAP, pp. 82–107 (1982)
Engelfriet J.: Context-free graph grammars. In: Rozenberg, G., Salomaa, A. (eds) Handbook of Formal Languages, vol. 3, chap. 3, pp. 125–213. Springer, Berlin (1997)
Engelfriet, J., Lilin, E., Maletti, A.: Extended multi bottom-up tree transducers. In: DLT, Lecture Notes in Computer Science, vol. 5257, pp. 289–300. Springer, Berlin (2008)
Engelfriet J., Maneth S.: Macro tree transducers, attribute grammars, and MSO definable tree translations. Inf. Comput. 154(1), 34–91 (1999)
Engelfriet J., Rozenberg G., Slutzki G.: Tree transducers, L systems, and two-way machines. J. Comput. Syst. Sci. 20(2), 150–202 (1980)
Fülöp Z.: On attributed tree transducers. Acta Cybern. 5, 261–279 (1981)
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)
Ganzinger H.: Increasing modularity and language-independency in automatically generated compilers. Sci. Comput. Prog. 3(3), 223–278 (1983)
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, chap. 1., pp. 1–68. Springer, Berlin (1997)
Giegerich R.: Composition and evaluation of attribute coupled grammars. Acta Inf. 25(4), 355–423 (1988)
Graehl, J.: Carmel. ISI/USC. http://www.isi.edu/licensed-sw/carmel (1997)
Graehl, J., Knight, K.: Training tree transducers. In: HLT-NAACL, pp. 105–112. The Association for Computational Linguistics, Stroudsburg (2004) (see also [27])
Graehl J., Knight K., May J.: Training tree transducers. Comput. Linguist. 34(3), 391–427 (2008)
Hopcroft J.E., Ullman J.D.: Introduction to Automata Theory, Languages, and Computation. Addison-Wesley, Reading (1979)
Knight, K., Graehl, J.: An overview of probabilistic tree transducers for natural language processing. In: CICLing, Lecture Notes in Computer Science, vol. 3406, pp 1–24. Springer, Berlin (2005)
Kühnemann, A.: Berechnungsstärken von Teilklassen primitiv-rekursiver Programmschemata. PhD thesis, Technische Universität Dresden (1997)
Kühnemann, A.: Benefits of tree transducers for optimizing functional programs. In: FSTTCS. Lecture Notes in Computer Science, vol. 1530, pp. 146–157. Springer, Berlin (1998)
Lilin, E.: Une généralisation des transducteurs d’états finis d’arbres: les S-transducteurs. Thèse 3ème cycle, Université de Lille (1978)
Lilin, E.: Propriétés de clôture d’une extension de transducteurs d’arbres déterministes. In: CAAP, Lecture Notes in Computer Science, vol. 112, pp. 280–289. Springer, Berlin (1981)
Maletti A.: Compositions of extended top-down tree transducers. Inf. Comput. 206(9–10), 1187–1196 (2008)
Maletti A., Graehl J., Hopkins M., Knight K.: The power of extended top-down tree transducers. SIAM J. Comput. 39(2), 410–430 (2009)
Rambow O., Satta G.: Independent parallelism in finite copying parallel rewriting systems. Theor. Comput. Sci. 223(1–2), 87–120 (1999)
Raoult J.C.: Rational tree relations. Bull. Belg. Math. Soc. 4, 149–176 (1997)
Rounds W.C.: Mappings and grammars on trees. Math. Syst. Theory 4(3), 257–287 (1970)
Seki H., Matsumura T., Fujii M., Kasami T.: On multiple context-free grammars. Theor. Comput. Sci. 88(2), 191–229 (1991)
Shabes, Y.: Mathematical and computational aspects of lexicalized grammars. Ph.D. thesis, University of Pennsylvania (1990)
Shieber, S.M.: Unifying synchronous tree adjoining grammars and tree transducers via bimorphisms. In: EACL, pp. 377–384. The Association for Computational Linguistics, Stroudsburg (2006)
Shieber, S.M., Shabes, Y.: Synchronous tree-adjoining grammars. In: COLING, pp. 1–6. The Association for Computational Linguistics, Stroudsburg (1990)
Steinby, M., Tîrnăucă, C.I.: Syntax-directed translations and quasi-alphabetic tree bimorphisms. In: CIAA, Lecture Notes in Computer Science, vol. 4783, pp. 265–276. Springer, Berlin (2007)
Thatcher J.W.: Generalized2 sequential machine maps. J. Comput. Syst. Sci. 4(4), 339–367 (1970)
Thatcher J.W.: Tree automata: An informal survey. In: Aho, A.V. (eds) Currents in the Theory of Computing, pp. 143–172. Prentice-Hall, Englewood Cliffs (1973)
Weir, D.J.: Linear context-free rewriting systems and deterministic tree-walking transducers. In: ACL, pp. 136–143. The Association for Computational Linguistics, Stroudsburg (1992)
Yamada, K., Knight, K.: A decoder for syntax-based statistical MT. In: ACL, pp. 303–310. The Association for Computational Linguistics, Stroudsburg (2002)
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This is an extended and revised version of: J. Engelfriet, E. Lilin, A. Maletti. Extended Multi Bottom–up Tree Transducers. Proc. 12th Int. Conf. Developments in Language Theory. LNCS 5257, 289–300, Springer-Verlag 2008.
A. Maletti was supported by a fellowship within the Postdoc-Programme of the German Academic Exchange Service (DAAD) and by the Ministerio de Educación y Ciencia (MEC) grant JDCI-2007-760.
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Engelfriet, J., Lilin, E. & Maletti, A. Extended multi bottom–up tree transducers. Acta Informatica 46, 561–590 (2009). https://doi.org/10.1007/s00236-009-0105-8
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DOI: https://doi.org/10.1007/s00236-009-0105-8