Context-Free Path Querying with Structural Representation of Result

Graph data model and graph databases are very popular in various areas such as bioinformatics, semantic web, and social networks. One specific problem in the area is a path querying with constraints formulated in terms of formal grammars. The query in this approach is written as grammar, and paths querying is graph parsing with respect to given grammar. There are several solutions to it, but how to provide structural representation of query result which is practical for answer processing and debugging is still an open problem. In this paper we propose a graph parsing technique which allows one to build such representation with respect to given grammar in polynomial time and space for arbitrary context-free grammar and graph. Proposed algorithm is based on generalized LL parsing algorithm, while previous solutions are based mostly on CYK or Earley algorithms, which reduces time complexity in some cases.Comment: Evaluation extende

Efficient Analysis of Complex Diagrams using Constraint-Based Parsing

This paper describes substantial advances in the analysis (parsing) of diagrams using constraint grammars. The addition of set types to the grammar and spatial indexing of the data make it possible to efficiently parse real diagrams of substantial complexity. The system is probably the first to demonstrate efficient diagram parsing using grammars that easily be retargeted to other domains. The work assumes that the diagrams are available as a flat collection of graphics primitives: lines, polygons, circles, Bezier curves and text. This is appropriate for future electronic documents or for vectorized diagrams converted from scanned images. The classes of diagrams that we have analyzed include x,y data graphs and genetic diagrams drawn from the biological literature, as well as finite state automata diagrams (states and arcs). As an example, parsing a four-part data graph composed of 133 primitives required 35 sec using Macintosh Common Lisp on a Macintosh Quadra 700.Comment: 9 pages, Postscript, no fonts, compressed, uuencoded. Composed in MSWord 5.1a for the Mac. To appear in ICDAR '95. Other versions at ftp://ftp.ccs.neu.edu/pub/people/futrell

Features and Algorithms for Visual Parsing of Handwritten Mathematical Expressions

Math expressions are an essential part of scientific documents. Handwritten math expressions recognition can benefit human-computer interaction especially in the education domain and is a critical part of document recognition and analysis. Parsing the spatial arrangement of symbols is an essential part of math expression recognition. A variety of parsing techniques have been developed during the past three decades, and fall into two groups. The first group is graph-based parsing. It selects a path or sub-graph which obeys some rule to form a possible interpretation for the given expression. The second group is grammar driven parsing. Grammars and related parameters are defined manually for different tasks. The time complexity of these two groups parsing is high, and they often impose some strict constraints to reduce the computation. The aim of this thesis is working towards building a straightforward and effective parser with as few constraints as possible. First, we propose using a line of sight graph for representing the layout of strokes and symbols in math expressions. It achieves higher F-score than other graph representations and reduces search space for parsing. Second, we modify the shape context feature with Parzen window density estimation. This feature set works well for symbol segmentation, symbol classification and symbol layout analysis. We get a higher symbol segmentation F-score than other systems on CROHME 2014 dataset. Finally, we develop a Maximum Spanning Tree (MST) based parser using Edmonds\u27 algorithm, which extracts an MST from the directed line of sight graph in two passes: first symbols are segmented, and then symbols and spatial relationship are labeled. The time complexity of our MST-based parsing is lower than the time complexity of CYK parsing with context-free grammars. Also, our MST-based parsing obtains higher structure rate and expression rate than CYK parsing when symbol segmentation is accurate. Correct structure means we get the structure of the symbol layout tree correct, even though the label of the edge in the symbol layout tree might be wrong. The performance of our math expression recognition system with MST-based parsing is competitive on CROHME 2012 and 2014 datasets. For future work, how to incorporate symbol classifier result and correct segmentation error in MST-based parsing needs more research

If the Current Clique Algorithms are Optimal, so is Valiant's Parser

The CFG recognition problem is: given a context-free grammar $\mathcal{G}$ and a string $w$ of length $n$, decide if $w$ can be obtained from $\mathcal{G}$. This is the most basic parsing question and is a core computer science problem. Valiant's parser from 1975 solves the problem in $O(n^{\omega})$ time, where $\omega<2.373$ is the matrix multiplication exponent. Dozens of parsing algorithms have been proposed over the years, yet Valiant's upper bound remains unbeaten. The best combinatorial algorithms have mildly subcubic $O(n^3/\log^3{n})$ complexity. Lee (JACM'01) provided evidence that fast matrix multiplication is needed for CFG parsing, and that very efficient and practical algorithms might be hard or even impossible to obtain. Lee showed that any algorithm for a more general parsing problem with running time $O(|\mathcal{G}|\cdot n^{3-\varepsilon})$ can be converted into a surprising subcubic algorithm for Boolean Matrix Multiplication. Unfortunately, Lee's hardness result required that the grammar size be $|\mathcal{G}|=\Omega(n^6)$. Nothing was known for the more relevant case of constant size grammars. In this work, we prove that any improvement on Valiant's algorithm, even for constant size grammars, either in terms of runtime or by avoiding the inefficiencies of fast matrix multiplication, would imply a breakthrough algorithm for the $k$-Clique problem: given a graph on $n$ nodes, decide if there are $k$ that form a clique. Besides classifying the complexity of a fundamental problem, our reduction has led us to similar lower bounds for more modern and well-studied cubic time problems for which faster algorithms are highly desirable in practice: RNA Folding, a central problem in computational biology, and Dyck Language Edit Distance, answering an open question of Saha (FOCS'14)

Synchronous Context-Free Grammars and Optimal Linear Parsing Strategies

Synchronous Context-Free Grammars (SCFGs), also known as syntax-directed translation schemata, are unlike context-free grammars in that they do not have a binary normal form. In general, parsing with SCFGs takes space and time polynomial in the length of the input strings, but with the degree of the polynomial depending on the permutations of the SCFG rules. We consider linear parsing strategies, which add one nonterminal at a time. We show that for a given input permutation, the problems of finding the linear parsing strategy with the minimum space and time complexity are both NP-hard

Interaction Grammars

Interaction Grammar (IG) is a grammatical formalism based on the notion of polarity. Polarities express the resource sensitivity of natural languages by modelling the distinction between saturated and unsaturated syntactic structures. Syntactic composition is represented as a chemical reaction guided by the saturation of polarities. It is expressed in a model-theoretic framework where grammars are constraint systems using the notion of tree description and parsing appears as a process of building tree description models satisfying criteria of saturation and minimality

Parsing Expression Grammars Made Practical

Parsing Expression Grammars (PEGs) define languages by specifying recursive-descent parser that recognises them. The PEG formalism exhibits desirable properties, such as closure under composition, built-in disambiguation, unification of syntactic and lexical concerns, and closely matching programmer intuition. Unfortunately, state of the art PEG parsers struggle with left-recursive grammar rules, which are not supported by the original definition of the formalism and can lead to infinite recursion under naive implementations. Likewise, support for associativity and explicit precedence is spotty. To remedy these issues, we introduce Autumn, a general purpose PEG library that supports left-recursion, left and right associativity and precedence rules, and does so efficiently. Furthermore, we identify infix and postfix operators as a major source of inefficiency in left-recursive PEG parsers and show how to tackle this problem. We also explore the extensibility of the PEG paradigm by showing how one can easily introduce new parsing operators and how our parser accommodates custom memoization and error handling strategies. We compare our parser to both state of the art and battle-tested PEG and CFG parsers, such as Rats!, Parboiled and ANTLR.Comment: "Proceedings of the International Conference on Software Language Engineering (SLE 2015)" - 167-172 (ISBN : 978-1-4503-3686-4

Tabular Parsing

This is a tutorial on tabular parsing, on the basis of tabulation of nondeterministic push-down automata. Discussed are Earley's algorithm, the Cocke-Kasami-Younger algorithm, tabular LR parsing, the construction of parse trees, and further issues.Comment: 21 pages, 14 figure