Generalizing input-driven languages: theoretical and practical benefits

Regular languages (RL) are the simplest family in Chomsky's hierarchy. Thanks to their simplicity they enjoy various nice algebraic and logic properties that have been successfully exploited in many application fields. Practically all of their related problems are decidable, so that they support automatic verification algorithms. Also, they can be recognized in real-time. Context-free languages (CFL) are another major family well-suited to formalize programming, natural, and many other classes of languages; their increased generative power w.r.t. RL, however, causes the loss of several closure properties and of the decidability of important problems; furthermore they need complex parsing algorithms. Thus, various subclasses thereof have been defined with different goals, spanning from efficient, deterministic parsing to closure properties, logic characterization and automatic verification techniques. Among CFL subclasses, so-called structured ones, i.e., those where the typical tree-structure is visible in the sentences, exhibit many of the algebraic and logic properties of RL, whereas deterministic CFL have been thoroughly exploited in compiler construction and other application fields. After surveying and comparing the main properties of those various language families, we go back to operator precedence languages (OPL), an old family through which R. Floyd pioneered deterministic parsing, and we show that they offer unexpected properties in two fields so far investigated in totally independent ways: they enable parsing parallelization in a more effective way than traditional sequential parsers, and exhibit the same algebraic and logic properties so far obtained only for less expressive language families

Constituent Parsing as Sequence Labeling

We introduce a method to reduce constituent parsing to sequence labeling. For each word w_t, it generates a label that encodes: (1) the number of ancestors in the tree that the words w_t and w_{t+1} have in common, and (2) the nonterminal symbol at the lowest common ancestor. We first prove that the proposed encoding function is injective for any tree without unary branches. In practice, the approach is made extensible to all constituency trees by collapsing unary branches. We then use the PTB and CTB treebanks as testbeds and propose a set of fast baselines. We achieve 90.7% F-score on the PTB test set, outperforming the Vinyals et al. (2015) sequence-to-sequence parser. In addition, sacrificing some accuracy, our approach achieves the fastest constituent parsing speeds reported to date on PTB by a wide margin.Comment: EMNLP 2018 (Long Papers). Revised version with improved results after fixing evaluation bu

A Tractable Extension of Linear Indexed Grammars

It has been shown that Linear Indexed Grammars can be processed in polynomial time by exploiting constraints which make possible the extensive use of structure-sharing. This paper describes a formalism that is more powerful than Linear Indexed Grammar, but which can also be processed in polynomial time using similar techniques. The formalism, which we refer to as Partially Linear PATR manipulates feature structures rather than stacks.Comment: 8 pages LaTeX, uses eaclap.sty, to appear in EACL-9

Mathematical Formula Recognition and Automatic Detection and Translation of Algorithmic Components into Stochastic Petri Nets in Scientific Documents

A great percentage of documents in scientific and engineering disciplines include mathematical formulas and/or algorithms. Exploring the mathematical formulas in the technical documents, we focused on the mathematical operations associations, their syntactical correctness, and the association of these components into attributed graphs and Stochastic Petri Nets (SPN). We also introduce a formal language to generate mathematical formulas and evaluate their syntactical correctness. The main contribution of this work focuses on the automatic segmentation of mathematical documents for the parsing and analysis of detected algorithmic components. To achieve this, we present a synergy of methods, such as string parsing according to mathematical rules, Formal Language Modeling, optical analysis of technical documents in forms of images, structural analysis of text in images, and graph and Stochastic Petri Net mapping. Finally, for the recognition of the algorithms, we enriched our rule based model with machine learning techniques to acquire better results

A format for phylogenetic placements

We have developed a unified format for phylogenetic placements, that is, mappings of environmental sequence data (e.g. short reads) into a phylogenetic tree. We are motivated to do so by the growing number of tools for computing and post-processing phylogenetic placements, and the lack of an established standard for storing them. The format is lightweight, versatile, extensible, and is based on the JSON format which can be parsed by most modern programming languages. Our format is already implemented in several tools for computing and post-processing parsimony- and likelihood-based phylogenetic placements, and has worked well in practice. We believe that establishing a standard format for analyzing read placements at this early stage will lead to a more efficient development of powerful and portable post-analysis tools for the growing applications of phylogenetic placement.Comment: Documents version 3 of the forma

Pushdown automata in statistical machine translation

This article describes the use of pushdown automata (PDA) in the context of statistical machine translation and alignment under a synchronous context-free grammar. We use PDAs to compactly represent the space of candidate translations generated by the grammar when applied to an input sentence. General-purpose PDA algorithms for replacement, composition, shortest path, and expansion are presented. We describe HiPDT, a hierarchical phrase-based decoder using the PDA representation and these algorithms. We contrast the complexity of this decoder with a decoder based on a finite state automata representation, showing that PDAs provide a more suitable framework to achieve exact decoding for larger synchronous context-free grammars and smaller language models. We assess this experimentally on a large-scale Chinese-to-English alignment and translation task. In translation, we propose a two-pass decoding strategy involving a weaker language model in the first-pass to address the results of PDA complexity analysis. We study in depth the experimental conditions and tradeoffs in which HiPDT can achieve state-of-the-art performance for large-scale SMT. </jats:p

Toward a theory of input-driven locally parsable languages

If a context-free language enjoys the local parsability property then, no matter how the source string is segmented, each segment can be parsed independently, and an efficient parallel parsing algorithm becomes possible. The new class of locally chain parsable languages (LCPLs), included in the deterministic context-free language family, is here defined by means of the chain-driven automaton and characterized by decidable properties of grammar derivations. Such automaton decides whether to reduce or not a substring in a way purely driven by the terminal characters, thus extending the well-known concept of input-driven (ID) alias visibly pushdown machines. The LCPL family extends and improves the practically relevant Floyd's operator-precedence (OP) languages which are known to strictly include the ID languages, and for which a parallel-parser generator exists