Finite Automata for the Sub- and Superword Closure of CFLs: Descriptional and Computational Complexity

We answer two open questions by (Gruber, Holzer, Kutrib, 2009) on the state-complexity of representing sub- or superword closures of context-free grammars (CFGs): (1) We prove a (tight) upper bound of $2^{\mathcal{O}(n)}$ on the size of nondeterministic finite automata (NFAs) representing the subword closure of a CFG of size $n$. (2) We present a family of CFGs for which the minimal deterministic finite automata representing their subword closure matches the upper-bound of $2^{2^{\mathcal{O}(n)}}$ following from (1). Furthermore, we prove that the inequivalence problem for NFAs representing sub- or superword-closed languages is only NP-complete as opposed to PSPACE-complete for general NFAs. Finally, we extend our results into an approximation method to attack inequivalence problems for CFGs

Abstract syntax as interlingua: Scaling up the grammatical framework from controlled languages to robust pipelines

Syntax is an interlingual representation used in compilers. Grammatical Framework (GF) applies the abstract syntax idea to natural languages. The development of GF started in 1998, first as a tool for controlled language implementations, where it has gained an established position in both academic and commercial projects. GF provides grammar resources for over 40 languages, enabling accurate generation and translation, as well as grammar engineering tools and components for mobile and Web applications. On the research side, the focus in the last ten years has been on scaling up GF to wide-coverage language processing. The concept of abstract syntax offers a unified view on many other approaches: Universal Dependencies, WordNets, FrameNets, Construction Grammars, and Abstract Meaning Representations. This makes it possible for GF to utilize data from the other approaches and to build robust pipelines. In return, GF can contribute to data-driven approaches by methods to transfer resources from one language to others, to augment data by rule-based generation, to check the consistency of hand-annotated corpora, and to pipe analyses into high-precision semantic back ends. This article gives an overview of the use of abstract syntax as interlingua through both established and emerging NLP applications involving GF

Genie: A Generator of Natural Language Semantic Parsers for Virtual Assistant Commands

To understand diverse natural language commands, virtual assistants today are trained with numerous labor-intensive, manually annotated sentences. This paper presents a methodology and the Genie toolkit that can handle new compound commands with significantly less manual effort. We advocate formalizing the capability of virtual assistants with a Virtual Assistant Programming Language (VAPL) and using a neural semantic parser to translate natural language into VAPL code. Genie needs only a small realistic set of input sentences for validating the neural model. Developers write templates to synthesize data; Genie uses crowdsourced paraphrases and data augmentation, along with the synthesized data, to train a semantic parser. We also propose design principles that make VAPL languages amenable to natural language translation. We apply these principles to revise ThingTalk, the language used by the Almond virtual assistant. We use Genie to build the first semantic parser that can support compound virtual assistants commands with unquoted free-form parameters. Genie achieves a 62% accuracy on realistic user inputs. We demonstrate Genie's generality by showing a 19% and 31% improvement over the previous state of the art on a music skill, aggregate functions, and access control.Comment: To appear in PLDI 201

Computer-Aided Derivation of Multi-scale Models: A Rewriting Framework

We introduce a framework for computer-aided derivation of multi-scale models. It relies on a combination of an asymptotic method used in the field of partial differential equations with term rewriting techniques coming from computer science. In our approach, a multi-scale model derivation is characterized by the features taken into account in the asymptotic analysis. Its formulation consists in a derivation of a reference model associated to an elementary nominal model, and in a set of transformations to apply to this proof until it takes into account the wanted features. In addition to the reference model proof, the framework includes first order rewriting principles designed for asymptotic model derivations, and second order rewriting principles dedicated to transformations of model derivations. We apply the method to generate a family of homogenized models for second order elliptic equations with periodic coefficients that could be posed in multi-dimensional domains, with possibly multi-domains and/or thin domains.Comment: 26 page

Statistical Parsing by Machine Learning from a Classical Arabic Treebank

Research into statistical parsing for English has enjoyed over a decade of successful results. However, adapting these models to other languages has met with difficulties. Previous comparative work has shown that Modern Arabic is one of the most difficult languages to parse due to rich morphology and free word order. Classical Arabic is the ancient form of Arabic, and is understudied in computational linguistics, relative to its worldwide reach as the language of the Quran. The thesis is based on seven publications that make significant contributions to knowledge relating to annotating and parsing Classical Arabic. Classical Arabic has been studied in depth by grammarians for over a thousand years using a traditional grammar known as i’rāb (إعغاة ). Using this grammar to develop a representation for parsing is challenging, as it describes syntax using a hybrid of phrase-structure and dependency relations. This work aims to advance the state-of-the-art for hybrid parsing by introducing a formal representation for annotation and a resource for machine learning. The main contributions are the first treebank for Classical Arabic and the first statistical dependency-based parser in any language for ellipsis, dropped pronouns and hybrid representations. A central argument of this thesis is that using a hybrid representation closely aligned to traditional grammar leads to improved parsing for Arabic. To test this hypothesis, two approaches are compared. As a reference, a pure dependency parser is adapted using graph transformations, resulting in an 87.47% F1-score. This is compared to an integrated parsing model with an F1-score of 89.03%, demonstrating that joint dependency-constituency parsing is better suited to Classical Arabic. The Quran was chosen for annotation as a large body of work exists providing detailed syntactic analysis. Volunteer crowdsourcing is used for annotation in combination with expert supervision. A practical result of the annotation effort is the corpus website: http://corpus.quran.com, an educational resource with over two million users per year