The HOM-problem asks whether the image of a regular tree language under a given tree homomorphism is again regular. It was recently shown to be decidable by Godoy, Giménez, Ramos, and Àlvarez. In this paper, the ℕ-weighted version of this problem is considered and its decidability is proved. More precisely, it is decidable in polynomial time whether the image of a regular ℕ-weighted tree language under a nondeleting, nonerasing tree homomorphism is regular.

Abstract The HOM problem, which asks whether the image of a regular tree language under a given tree homomorphism is again regular, is known to be decidable [Godoy & Giménez: The HOM problem is decidable. JACM 60(4), 2013]. However, the problem remains open for regular weighted tree languages. It is demonstrated that the main notion used in the unweighted setting, the tree automaton with equality and inequality constraints , can straightforwardly be generalized to the weighted setting and can represent the image of any regular weighted tree language under any nondeleting and nonerasing tree homomorphism. Several closure properties as well as decision problems are also investigated for the weighted tree languages generated by weighted tree automata with constraints.

The generative capacity of combinatory categorial grammars (CCGs) as generators of tree languages is investigated. It is demonstrated that the tree languages generated by CCGs can also be generated by simple monadic context-free tree grammars. However, the important subclass of pure combinatory categorial grammars cannot even generate all regular tree languages. Additionally, the tree languages generated by combinatory categorial grammars with limited rule degrees are characterized: If only application rules are allowed, then these grammars can generate only a proper subset of the regular tree languages, whereas they can generate exactly the regular tree languages once first-degree composition rules are permitted.

Tree-adjoining grammar (TAG) and combinatory categorial grammar (CCG) are two well-established mildly context-sensitive grammar formalisms that are known to have the same expressive power on strings (i.e., generate the same class of string languages). It is demonstrated that their expressive power on trees also essentially coincides. In fact, CCG without lexicon entries for the empty string and only first-order rules of degree at most 2 are sufficient for its full expressive power.

The generative capacity of combinatory categorial grammars as acceptors of tree languages is investigated. It is demonstrated that the such obtained tree languages can also be generated by simple monadic context-free tree grammars. However, the subclass of pure combinatory categorial grammars cannot even accept all regular tree languages. Additionally, the tree languages accepted by combinatory categorial grammars with limited rule degrees are characterized: If only application rules are allowed, then they can accept only a proper subset of the regular tree languages, whereas they can accept exactly the regular tree languages once first degree composition rules are permitted.

Yining Chen, Sorcha Gilroy, Andreas Maletti, Jonathan May, Kevin Knight. Proceedings of the 2018 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, Volume 1 (Long Papers). 2018.

Nina Seemann, Fabienne Braune, Andreas Maletti. Proceedings of the 53rd Annual Meeting of the Association for Computational Linguistics and the 7th International Joint Conference on Natural Language Processing (Volume 1: Long Papers). 2015.

Harry Bunt, Andreas Maletti, Joakim Nivre; Grammars, Parsers and Recognizers, Journal of Logic and Computation, Volume 24, Issue 2, 1 April 2014, Pages 309

Weighted extended tree transducers (wxtts) over countably complete semirings are systematically explored. It is proved that the extension in the left-hand sides of a wxtt can be simulated by the inverse of a linear and nondeleting tree homomorphism. In addition, a characterization of the class of weighted tree transformations computable by bottom-up wxtts in terms of bimorphisms is provided. Backward and forward application to recognizable weighted tree languages are standard operations for wxtts. It is shown that the backward application of a linear wxtt preserves recognizability and that the domain of an arbitrary bottom-up wxtt is recognizable. Examples demonstrate that neither backward nor forward application of arbitrary wxtts preserves recognizability. Finally, a HASSE diagram relates most of the important subclasses of weighted tree transformations computable by wxtts.

In this second part of the survey, we present the application of weighted extended top-down tree transducers in machine translation, which is the automatic translation of natural language texts. We present several formal properties that are relevant to machine translation and evaluate the weighted extended top-down tree transducer along those criteria. In addition, we demonstrate how to extract rules for an extended top-down tree transducer from existing linguistic data and how to obtain suitable rule weights automatically from similar information. Overall, the aim of the survey is twofold. It should provide a synopsis that illustrates how theory (tree transducers) and practice (machine translation) interact on this particular example. Secondly, it presents a uniform and simplified treatment of the rule extraction and training algorithms that is accessible to the nonexpert. Additional details can be found in the original results that are referenced throughout the text.

Abstract Synchronous tree substitution grammars (stsg) are a (formal) tree transformation model that is used in the area of syntax-based machine translation. A competitor that is at least as expressive as stsg is proposed and compared to stsg. The competitor is the extended multi bottom-up tree transducer (mbot), which is the bottom-up analogue with the additional feature that states have non-unary ranks. Unweighted mbot have already been investigated with respect to their basic properties, but the particular properties of the constructions that are required in the machine translation task are largely unknown. stsg and mbot are compared with respect to binarization, regular restriction, and application. Particular attention is paid to the complexity of the constructions.

Several models of automata are available that operate unranked trees. Two well-known examples are the stepwise unranked tree automaton (suta) and the parallel unranked tree automaton (puta). By adding a weight, taken from some semiring, to every transition we generalise these two qualitative automata models to quantitative models, thereby obtaining weighted stepwise unranked tree automata (wsuta) and weighted parallel unranked tree automata (wputa); the qualitative automata models are reobtained by choosing the BOOLEAN semiring. The weighted versions have applications in natural language processing, XML-based data management and quantitative information retrieval. We address the minimisation problem of wsuta and wputa by using (forward and backward) bisimulations and we prove the following results: (1) for every wsuta an equivalent forward (resp. backward) bisimulation minimal wsuta can be computed in time O(mn) where n is the number of states and m is the number of transitions of the given wsuta; (2) the same result is proved for wputa instead of wsuta; (3) if the semiring is additive cancellative or the BOOLEAN semiring, then the bound can be improved to O(mlog n) for both wsuta and wputa; (4) for every deterministic puta we can compute a minimal equivalent deterministic puta in time O(mlog n); (5) the automata models wsuta, wputa, and weighted unranked tree automaton have the same computational power.

Extended top-down tree transducers (transducteurs généralisés descendants; see [A. Arnold and M. Dauchet, Bi-transductions de forêts, in Proceedings of the 3rd International Colloquium on Automata, Languages and Programming, Edinburgh University Press, Edinburgh, 1976, pp. 74–86]) received renewed interest in the field of natural language processing. Here those transducers are extensively and systematically studied. Their main properties are identified and their relation to classical top-down tree transducers is exactly characterized. The obtained properties completely explain the Hasse diagram of the induced classes of tree transformations. In addition, it is shown that most interesting classes of transformations computed by extended top-down tree transducers are not closed under composition.