Abstract
Linear weighted extended top-down tree transducers with regular look-ahead and with weights from a semiring are formal models that are used in syntax-based statistical machine translation. The composition hierarchies of some restricted versions of such weighted tree transducers (also without regular look-ahead) are considered. In particular, combinations of the restrictions of \(\varepsilon \)-freeness (all rules consume input), nondeletion, and strictness (all rules produce output) are considered. The composition hierarchy is shown to be finite for all but one \(\varepsilon \)-free variant of these weighted transducers over any commutative semiring.
Z. Fülöp—Supported by NKFI grant K 108 448 and by grant 20391-3/2018/FEKUSTRAT of the Ministry of Human Capacities, Hungary.
A. Maletti—Partially supported by the DFG research training group 1763 ‘QuantLA’.
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Arnold, A., Dauchet, M.: Morphismes et bimorphismes d’arbres. Theor. Comput. Sci. 20(1), 33–93 (1982). https://doi.org/10.1016/0304-3975(82)90098-6
Benedikt, M., Engelfriet, J., Maneth, S.: Determinacy and rewriting of functional top-down and MSO tree transformations. J. Comput. Syst. Sci. 85, 57–73 (2017). https://doi.org/10.1016/j.jcss.2016.11.001
Chiang, D.: An introduction to synchronous grammars. In: Calzolari, N., Cardie, C., Isabelle, P. (eds.) Proceedings of 44th Annual Meeting ACL. Association for Computational Linguistics (2006). Part of a tutorial given with Kevin Knight. https://www3.nd.edu/~dchiang/papers/synchtut.pdf
Engelfriet, J.: Top-down tree transducers with regular look-ahead. Math. Syst. Theory 10(1), 289–303 (1977). https://doi.org/10.1007/BF01683280
Engelfriet, J.: On tree transducers for partial functions. Inf. Process. Lett. 7(4), 170–172 (1978). https://doi.org/10.1016/0020-0190(78)90060-1
Engelfriet, J., Fülöp, Z., Maletti, A.: Composition closure of linear extended top-down tree transducers. Theory Comput. Syst. 60(2), 129–171 (2017). https://doi.org/10.1007/s00224-015-9660-2
Fülöp, Z., Maletti, A., Vogler, H.: Weighted extended tree transducers. Fund. Inform. 111(2), 163–202 (2011). https://doi.org/10.3233/FI-2011-559
Gécseg, F., Steinby, M.: Tree Automata, 2nd edn. Akadémiai Kiadó, Budapest (1984). https://arxiv.org/abs/1509.06233
Golan, J.S.: Semirings and Their Applications. Kluwer Academic, Dordrecht (1999). https://doi.org/10.1007/978-94-015-9333-5
Graehl, J., Knight, K., May, J.: Training tree transducers. Comput. Linguist. 34(3), 391–427 (2008). https://doi.org/10.1162/coli.2008.07-051-R2-03-57
Hebisch, U., Weinert, H.J.: Semirings - Algebraic Theory and Applications in Computer Science. Series in Algebra. World Scientific, Singapore (1998). https://doi.org/10.1142/3903
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). https://doi.org/10.1007/978-3-540-30586-6_1
Lagoutte, A., Maletti, A.: Survey: weighted extended top-down tree transducers part III—composition. In: Kuich, W., Rahonis, G. (eds.) Algebraic Foundations in Computer Science. LNCS, vol. 7020, pp. 272–308. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-24897-9_13
Maletti, A.: The power of weighted regularity-preserving multi bottom-up tree transducers. Int. J. Found. Comput. Sci. 26(7), 987–1005 (2015). https://doi.org/10.1142/S0129054115400109
Maletti, A.: Compositions of tree-to-tree statistical machine translation models. In: Brlek, S., Reutenauer, C. (eds.) DLT 2016. LNCS, vol. 9840, pp. 293–305. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53132-7_24
Maletti, A., Graehl, J., Hopkins, M., Knight, K.: The power of extended top-down tree transducers. SIAM J. Comput. 39(2), 410–430 (2009). https://doi.org/10.1137/070699160
May, J., Knight, K., Vogler, H.: Efficient inference through cascades of weighted tree transducers. In: Hajič, J., Carberry, S., Clark, S., Nivre, J. (eds.) Proceedings of 48th Annual Meeting ACL, pp. 1058–1066. Association for Computational Linguistics (2010). http://www.aclweb.org/anthology/P10-1108
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Fülöp, Z., Maletti, A. (2019). Composition Closure of Linear Weighted Extended Top-Down Tree Transducers. In: Hospodár, M., Jirásková, G. (eds) Implementation and Application of Automata. CIAA 2019. Lecture Notes in Computer Science(), vol 11601. Springer, Cham. https://doi.org/10.1007/978-3-030-23679-3_11
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