Unlike other mildly context-sensitive formalisms, Combinatory Categorial Grammar (CCG) cannot be parsed in polynomial time when the size of the grammar is taken into account. Refining this result, we show that the parsing complexity of CCG is exponential only in the maximum degree of composition. When that degree is fixed, parsing can be carried out in polynomial time. Our finding is interesting from a linguistic perspective because a bounded degree of composition has been suggested as a universal constraint on natural language grammar. Moreover, ours is the first complexity result for a version of CCG that includes substitution rules, which are used in practical grammars but have been ignored in theoretical work.

We present algorithms for extracting Hyperedge Replacement Grammar (HRG) rules from a graph along with a vertex order. Our algorithms are based on finding a tree decomposition of smallest width, relative to the vertex order, and then extracting one rule for each node in this structure. The assumption of a fixed order for the vertices of the input graph makes it possible to solve the problem in polynomial time, in contrast to the fact that the problem of finding optimal tree decompositions for a graph is NP-hard. We also present polynomial-time algorithms for parsing based on our HRGs, where the input is a vertex sequence and the output is a graph structure. The intended application of our algorithms is grammar extraction and parsing for semantic representation of natural language. We apply our algorithms to data annotated with Abstract Meaning Representations and report on the characteristics of the resulting grammars.

We propose a formal model for translating unranked syntactic trees, such as dependency trees, into semantic graphs. These tree-to-graph transducers can serve as a formal basis of transition systems for semantic parsing which recently have been shown to perform very well, yet hitherto lack formalization. Our model features “extended” rules and an arc-factored normal form, comes with an efficient translation algorithm, and can be equipped with weights in a straightforward manner.

In this paper, we present a sequence-to-sequence based approach for mapping natural language sentences to AMR semantic graphs. We transform the sequence to graph mapping problem to a word sequence to transition action sequence problem using a special transition system called a cache transition system. To address the sparsity issue of neural AMR parsing, we feed feature embeddings from the transition state to provide relevant local information for each decoder state. We present a monotonic hard attention model for the transition framework to handle the strictly left-to-right alignment between each transition state and the current buffer input focus. We evaluate our neural transition model on the AMR parsing task, and our parser outperforms other sequence-to-sequence approaches and achieves competitive results in comparison with the best-performing models.

Motivated by the task of semantic parsing, we describe a transition system that generalizes standard transition-based dependency parsing techniques to generate a graph rather than a tree. Our system includes a cache with fixed size m, and we characterize the relationship between the parameter m and the class of graphs that can be produced through the graph-theoretic concept of tree decomposition. We find empirically that small cache sizes cover a high percentage of sentences in existing semantic corpora.

Graphs have a variety of uses in natural language processing, particularly as representations of linguistic meaning. A deficit in this area of research is a formal framework for creating, combining, and using models involving graphs that parallels the frameworks of finite automata for strings and finite tree automata for trees. A possible starting point for such a framework is the formalism of directed acyclic graph (DAG) automata, defined by Kamimura and Slutzki and extended by Quernheim and Knight. In this article, we study the latter in depth, demonstrating several new results, including a practical recognition algorithm that can be used for inference and learning with models defined on DAG automata. We also propose an extension to graphs with unbounded node degree and show that our results carry over to the extended formalism.

We study the parsing complexity of Combinatory Categorial Grammar (CCG) in the formalism of Vijay-Shanker and Weir (1994). As our main result, we prove that any parsing algorithm for this formalism will take in the worst case exponential time when the size of the grammar, and not only the length of the input sentence, is included in the analysis. This sets the formalism of Vijay-Shanker and Weir (1994) apart from weakly equivalent formalisms such as Tree Adjoining Grammar, for which parsing can be performed in time polynomial in the combined size of grammar and input sentence. Our results contribute to a refined understanding of the class of mildly context-sensitive grammars, and inform the search for new, mildly context-sensitive versions of CCG.

Abstract Meaning Representation (AMR) is a semantic representation for natural language that embeds annotations related to traditional tasks such as named entity recognition, semantic role labeling, word sense disambiguation and co-reference resolution. We describe a transition-based parser for AMR that parses sentences left-to-right, in linear time. We further propose a test-suite that assesses specific subtasks that are helpful in comparing AMR parsers, and show that our parser is competitive with the state of the art on the LDC2015E86 dataset and that it outperforms state-of-the-art parsers for recovering named entities and handling polarity.

We develop parsing oracles for two transition-based dependency parsers, including the arc-standard parser, solving a problem that was left open in (Goldberg and Nivre, 2013). We experimentally show that using these oracles during training yields superior parsing accuracies on many languages.

We present a polynomial-time parsing algorithm for CCG, based on a new decomposition of derivations into small, shareable parts. Our algorithm has the same asymptotic complexity, O(n6), as a previous algorithm by Vijay-Shanker and Weir (1993), but is easier to understand, implement, and prove correct.

Head splitting techniques have been successfully exploited to improve the asymptotic runtime of parsing algorithms for projective dependency trees, under the arc-factored model. In this article we extend these techniques to a class of non-projective dependency trees, called well-nested dependency trees with block-degree at most 2, which has been previously investigated in the literature. We define a structural property that allows head splitting for these trees, and present two algorithms that improve over the runtime of existing algorithms at no significant loss in coverage.

The EVALITA 2007 Parsing Task has been the first contest among parsing systems for Italian. It is the first attempt to compare the approaches and the results of the existing parsing systems specific for this language using a common treebank annotated using both a dependency and a constituency-based format. The development data set for this parsing competition was taken from the Turin University Treebank, which is annotated both in dependency and constituency format. The evaluation metrics were those standardly applied in CoNLL and PARSEVAL. The results of the parsing results are very promising and higher than the state-of-the-art for dependency parsing of Italian. An analysis of such results is provided, which takes into account other experiences in treebank-driven parsing for Italian and for other Romance languages (in particular, the CoNLL X & 2007 shared tasks for dependency parsing). It focuses on the characteristics of data sets, i.e. type of annotation and size, parsing paradigms and approaches applied also to languages other than Italian.

We show that a well-known algorithm to compute the intersection of a context-fre language and a regular language can be extended to apply to a probabilistic context-free grammar and a probabilistic finite automaton, provided the two probabilistic models are combined through multiplication. The result is a probabilistic context-free grammar that contains joint information about the original grammar and automaton.

We present a new formalism, partially ordered multiset context-free grammars (poms-CFG), along with an Earley-style parsing algorithm. The formalism, which can be thought of as a generalization of context-free grammars with partially ordered right-hand sides, is of interest in its own right, and also as infrastructure for obtaining tighter complexity bounds for more expressive context-free formalisms intended to express free or multiple word-order, such as ID/LP grammars. We reduce ID/LP grammars to poms-grammars, thereby getting finer-grained bounds on the parsing complexity of ID/LP grammars. We argue that in practice, the width of attested ID/LP grammars is small, yielding effectively polynomial time complexity for ID/LP grammar parsing.

In automatic speech recognition the use of language models improves performance. Stochastic language models fit rather well the uncertainty created by the acoustic pattern matching. These models are used to score theories corresponding to partial interpretations of sentences. Algorithms have been developed to compute probabilities for theories that grow in a strictly left-to-right fashion. In this paper we consider new relations to compute probabilities of partial interpretations of sentences. We introduce theories containing a gap corresponding to an uninterpreted signal segment. Algorithms can be easily obtained from these relations. Computational complexity of these algorithms is also derived.