Synchronous grammars as tree transducers

Tree transducer formalisms were developed in the formal language theory community as generalizations of finite-state transducers from strings to trees. Independently, synchronous tree-substitution and -adjoining grammars arose in the computational linguistics community as a means to augment strictly syntactic formalisms to provide for parallel semantics. We present the first synthesis of these two independently developed approaches to specifying tree relations, unifying their respective literatures for the first time, by using the framework of bimorphisms as the generalizing formalism in which all can be embedded. The central result is that synchronous tree-substitution grammars are equivalent to bimorphisms where the component homomorphisms are linear and complete.Engineering and Applied Science

Bimorphisms and synchronous grammars

We tend to think of the study of language as proceeding by characterizing the strings and structures of a language, and we think of natural language processing as using those structures to build systems of utility in manipulating the language. But many language-related problems are more fruitfully viewed as requiring the specification of a relation between two languages, rather than the specification of a single language. We provide a synthesis and extension of work that unifies two approaches to such language relations: the automata-theoretic approach based on tree transducers that transform trees to their counterparts in the relation, and the grammatical approach based on synchronous grammars that derive pairs of trees in the relation. In particular, we characterize synchronous tree-substitution grammars and synchronous tree-adjoining grammars in terms of bimorphisms, which have previously been used to characterize tree transducers. In the process, we provide new approaches to formalizing the various concepts: a metanotation for describing varieties of tree automata and transducers in equational terms; a rigorous formalization of tree-adjoining and tree-substitution grammars and their synchronous counterparts, using trees over ranked alphabets; and generalizations of tree-adjoining grammar allowing multiple adjunction.Engineering and Applied Science

Multiple Context-Free Tree Grammars: Lexicalization and Characterization

Multiple (simple) context-free tree grammars are investigated, where "simple" means "linear and nondeleting". Every multiple context-free tree grammar that is finitely ambiguous can be lexicalized; i.e., it can be transformed into an equivalent one (generating the same tree language) in which each rule of the grammar contains a lexical symbol. Due to this transformation, the rank of the nonterminals increases at most by 1, and the multiplicity (or fan-out) of the grammar increases at most by the maximal rank of the lexical symbols; in particular, the multiplicity does not increase when all lexical symbols have rank 0. Multiple context-free tree grammars have the same tree generating power as multi-component tree adjoining grammars (provided the latter can use a root-marker). Moreover, every multi-component tree adjoining grammar that is finitely ambiguous can be lexicalized. Multiple context-free tree grammars have the same string generating power as multiple context-free (string) grammars and polynomial time parsing algorithms. A tree language can be generated by a multiple context-free tree grammar if and only if it is the image of a regular tree language under a deterministic finite-copying macro tree transducer. Multiple context-free tree grammars can be used as a synchronous translation device.Comment: 78 pages, 13 figure

Unifying synchronous tree-adjoining grammars and tree transducers via bimorphisms.

We place synchronous tree-adjoining grammars and tree transducers in the single overarching framework of bimorphisms, continuing the unification of synchronous grammars and tree transducers initiated by Shieber (2004). Along the way, we present a new definition of the tree-adjoining grammar derivation relation based on a novel direct inter-reduction of TAG and monadic macro tree transducers.Engineering and Applied Science

Restricting the Weak-Generative Capacity of Synchronous Tree-Adjoining Grammars

The formalism of synchronous tree-adjoining grammars, a variant of standard tree-adjoining grammars (TAG), was intended to allow the use of TAGs for language transduction in addition to language specification. In previous work, the definition of the transduction relation defined by a synchronous TAG was given by appeal to an iterative rewriting process. The rewriting definition of derivation is problematic in that it greatly extends the expressivity of the formalism and makes the design of parsing algorithms difficult if not impossible. We introduce a simple, natural definition of synchronous tree-adjoining derivation, based on isomorphisms between standard tree-adjoining derivations, that avoids the expressivity and implementability problems of the original rewriting definition. The decrease in expressivity, which would otherwise make the method unusable, is offset by the incorporation of an alternative definition of standard tree-adjoining derivation, previously proposed for completely separate reasons, thereby making it practical to entertain using the natural definition of synchronous derivation. Nonetheless, some remaining problematic cases call for yet more flexibility in the definition; the isomorphism requirement may have to be relaxed. It remains for future research to tune the exact requirements on the allowable mappings.Comment: 21 pages, uses lingmacros.sty, psfig.sty, fullname.sty; minor typographical changes onl

Rule-restricted Automaton-grammar transducers: Power and Linguistic Applications

This paper introduces the notion of a new transducer as a two-component system, which consists of a nite automaton and a context-free grammar. In essence, while the automaton reads its input string, the grammar produces its output string, and their cooperation is controlled by a set, which restricts the usage of their rules. From a theoretical viewpoint, the present paper discusses the power of this system working in an ordinary way as well as in a leftmost way. In addition, the paper introduces an appearance checking, which allows us to check whether some symbols are present in the rewritten string, and studies its e ect on the power. It achieves the following three main results. First, the system generates and accepts languages de ned by matrix grammars and partially blind multi-counter automata, respectively. Second, if we place a leftmost restriction on derivation in the context-free grammar, both accepting and generating power of the system is equal to generative power of context-free grammars. Third, the system with appearance checking can accept and generate all recursively enumerable languages. From more pragmatical viewpoint, this paper describes several linguistic applications. A special attention is paid to the Japanese-Czech translation

Graph-to-Sequence Learning using Gated Graph Neural Networks

Many NLP applications can be framed as a graph-to-sequence learning problem. Previous work proposing neural architectures on this setting obtained promising results compared to grammar-based approaches but still rely on linearisation heuristics and/or standard recurrent networks to achieve the best performance. In this work, we propose a new model that encodes the full structural information contained in the graph. Our architecture couples the recently proposed Gated Graph Neural Networks with an input transformation that allows nodes and edges to have their own hidden representations, while tackling the parameter explosion problem present in previous work. Experimental results show that our model outperforms strong baselines in generation from AMR graphs and syntax-based neural machine translation.Comment: ACL 201

Tree edit distance as a baseline approach for paraphrase representation

Finding an adequate paraphrase representation formalism is a challenging issue in Natural Language Processing. In this paper, we analyse the performance of Tree Edit Distance as a paraphrase representation baseline. Our experiments using Edit Distance Textual Entailment Suite show that, as Tree Edit Distance consists of a purely syntactic approach, paraphrase alternations not based on structural reorganizations do not find an adequate representation. They also show that there is much scope for better modelling of the way trees are aligned