Parsing Unary Boolean Grammars Using Online Convolution

In contrast to context-free grammars, the extension of these grammars by explicit conjunction, the so-called conjunctive grammars can generate (quite complicated) non-regular languages over a single-letter alphabet (DLT 2007). Given these expressibility results, we study the parsability of Boolean grammars, an extension of context-free grammars by conjunction and negation, over a unary alphabet and show that they can be parsed in time O(|G| log^2(n) M(n)) where M(n) is the time to multiply two n-bit integers. This multiplication algorithm is transformed into a convolution algorithm which in turn is converted to an online convolution algorithm which is used for the parsing

Advances and applications of automata on words and trees : abstracts collection

From 12.12.2010 to 17.12.2010, the Dagstuhl Seminar 10501 "Advances and Applications of Automata on Words and Trees" was held in Schloss Dagstuhl - Leibniz Center for Informatics. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

MathLex: A Web-Based Mathematical Entry System

Mathematical formulas are easy to convey in handwritten media, but how should they be represented in electronic format? Unfortunately, mathematical content has not been as well-implemented on the Web as images and video. There are two sides to this problem: display and input. The former has been solved in multiple ways by representing formulas as images, MathML, or LaTeX (via MathJax). Representing math input is much more difficult and is the subject of this thesis. The goal is to enable users to enter complex formulas. Unfortunately, existing languages either are too complex for an average user (difficult to learn and/or read), only work in a particular environment (they have system and browser compatibility issues), or lack certain math concepts. Some do not even retain mathematical meaning. This thesis presents MathLex, an intuitive, easy-to-type, unambiguous, mathematically faithful input language and processing system intended for representing math input (and potentially display) on the web. It aims to mimic handwritten math as much as possible while maintaining semantic meaning

Representation Learning for Shape Decomposition, By Shape Decomposition

The ability to parse 3D objects into their constituent parts is essential for humans to understand and interact with the surrounding world. Imparting this skill in machines is important for various computer graphics, computer vision, and robotics tasks. Machines endowed with this skill can better interact with its surroundings, perform shape editing, texturing, recomposing, tracking, and animation. In this thesis, we ask two questions. First, how can machines decompose 3D shapes into their fundamental parts? Second, does the ability to decompose the 3D shape into these parts help learn useful 3D shape representations? In this thesis, we focus on parsing the shape into compact representations, such as parametric surface patches and Constructive Solid Geometry (CSG) primitives, which are also widely used representations in 3D modeling in computer graphics. Inspired by the advances in neural networks for 3D shape processing, we develop neural network approaches to tackle shape decomposition. First, we present CSGNet, a network architecture to parse shapes into CSG programs, which is trained using combination of supervised and reinforcement learning. Second, we present ParSeNet, a network architecture to decompose a shape into parametric surface patches (B-Spline) and geometric primitives (plane, cone, cylinder and sphere), trained on a large set of CAD models using supervised learning. The training of deep neural network architectures for 3D recognition and generation tasks requires a large amount of labeled datasets. We explore ways to alleviate this problem by relying on shape decomposition methods to guide the learning process. Towards that end, we first study the use of freely available metadata, albeit inconsistent, from shape repositories to learn 3D shape features. Later we show that learning to decompose a 3D shape into geometric primitives also helps in learning shape representations useful for semantic segmentation tasks. Finally, since most 3D shapes encountered in real life are textured, consisting of several fine-grained semantic parts, we propose a method to learn fine-grained representations for textured 3D shapes in a self-supervised manner by incorporating 3D geometric priors