Related papers: Two-dimensional Dyck words
The picture-hanging puzzle, popularized by Demaine et al. (2014), asks for a way to wrap a wire around $n$ nails such that the picture hangs as long as fewer than $k$ nails are removed, but falls as soon as any $k$ are removed. Solutions…
This paper reviews some results regarding symbolic dynamics, correspondence between languages of dynamical systems and combinatorics. Sturmian sequences provide a pattern for investigation of one-dimensional systems, in particular interval…
Given a string $\sigma$ over alphabet $\Sigma$ and a grammar $G$ defined over the same alphabet, how many minimum number of repairs: insertions, deletions and substitutions are required to map $\sigma$ into a valid member of $G$ ? We…
This paper concerns the structure of meanings within natural language. Earlier, a framework named DisCoCirc was sketched that (1) is compositional and distributional (a.k.a. vectorial); (2) applies to general text; (3) captures linguistic…
Visual Entailment with natural language explanations aims to infer the relationship between a text-image pair and generate a sentence to explain the decision-making process. Previous methods rely mainly on a pre-trained vision-language…
Representation is a core issue in artificial intelligence. Humans use discrete language to communicate and learn from each other, while machines use continuous features (like vector, matrix, or tensor in deep neural networks) to represent…
Cover-inclusive Dyck tilings are tilings of skew Young diagrams with ribbon tiles shaped like Dyck paths, in which tiles are no larger than the tiles they cover. These tilings arise in the study of certain statistical physics models and…
We study subshift that arise by excluding words of length two from Dyck shifts. The words that are to be excluded are taken from a finite set that is not literal-uniform.
Motivated by independent results of Bizley and Duchon, we study rational Dyck paths and their subset of factor-free elements. On the one hand, we give a bijection between rational Dyck paths and regular Dyck paths with ascents colored by…
Recently it has shown that the policy-gradient methods for reinforcement learning have been utilized to train deep end-to-end systems on natural language processing tasks. What's more, with the complexity of understanding image content and…
The dictionary matching problem preprocesses a set of patterns and finds all occurrences of each of the patterns in a text when it is provided. We focus on the dynamic setting, in which patterns can be inserted to and removed from the…
In recent years, concepts and methods of complex networks have been employed to tackle the word sense disambiguation (WSD) task by representing words as nodes, which are connected if they are semantically similar. Despite the increasingly…
Covering arrays for words of length $t$ over a $d$ letter alphabet are $k \times n$ arrays with entries from the alphabet so that for each choice of $t$ columns, each of the $d^t$ $t$-letter words appears at least once among the rows of the…
As the first step in automated natural language processing, representing words and sentences is of central importance and has attracted significant research attention. Different approaches, from the early one-hot and bag-of-words…
Dyck paths (also balanced brackets and Dyck words) are among the most heavily studied Catalan families. This paper is a continuation of [2, 3, 4]. In the paper we are dealing with the numbering of Dyck paths, with the resulting numbers, the…
It is shown how to endow a hierarchy of sets of binary patterns with the structure of an abstract,normed C*-algebra. In the course we also recover an intermediate connection with the words of a Dyck language and Tempereley-Lieb algebras for…
Recent studies have been revisiting whole words as the basic modelling unit in speech recognition and query applications, instead of phonetic units. Such whole-word segmental systems rely on a function that maps a variable-length speech…
Several old and recent classes of picture grammars, that variously extend context-free string grammars in two dimensions, are based on rules that rewrite arrays of pixels. Such grammars can be unified and extended using a tiling based…
In recent years, deep dictionary learning (DDL)has attracted a great amount of attention due to its effectiveness for representation learning and visual recognition.~However, most existing methods focus on unsupervised deep dictionary…
Indexed languages are a generalization of context-free languages and form a proper subset of context-sensitive languages. We propose to generalize to indexed languages several well known characterizations of context-free languages: namely,…