Related papers: Relations on words
This paper examines the characterization and learning of grammars defined with enriched representational models. Model-theoretic approaches to formal language theory traditionally assume that each position in a string belongs to exactly one…
We employ the theory of canonical extensions to study residuation algebras whose associated relational structures are functional, i.e., for which the ternary relations associated to the expanded operations admit an interpretation as…
The theory of two binary relations has the strong amalgamation property when the first relation is assumed to be coarser than the second relation, and each relation satisfies a chosen set of properties from the following list: transitivity,…
Convolution is a ubiquitous operation in mathematics and computing. The Kripke semantics for substructural and interval logics motivates its study for quantale-valued functions relative to ternary relations. The resulting notion of…
This is a survey of recent developments in combinatorics. The goal is to give a big picture of its many interactions with other areas of mathematics, such as: group theory, representation theory, commutative algebra, geometry (including…
Compositionality in language refers to how much the meaning of some phrase can be decomposed into the meaning of its constituents and the way these constituents are combined. Based on the premise that substitution by synonyms is…
Analogical proportions compare pairs of items (a, b) and (c, d) in terms of their differences and similarities. They play a key role in the formalization of analogical inference. The paper first discusses how to improve analogical inference…
The complexity of an infinite word can be measured in several ways, the two most common measures being the subword complexity and the abelian complexity. In 2015, Rigo and Salimov introduced a family of intermediate complexities indexed by…
These lecture notes provide an introduction to combinatorics on words and its interactions with dynamics, algebra, and arithmetic. The central theme is the notion of low factor complexity for infinite words. We investigate the following…
Typical arguments for results like Kleene's Second Recursion Theorem and the existence of self-writing computer programs bear the fingerprints of equational reasoning and combinatory logic. In fact, the connection of combinatory logic and…
Dictionaries are inherently circular in nature. A given word is linked to a set of alternative words (the definition) which in turn point to further descendants. Iterating through definitions in this way, one typically finds that…
We consider a language together with the subword relation, the cover relation, and regular predicates. For such structures, we consider the extension of first-order logic by threshold- and modulo-counting quantifiers. Depending on the…
We consider a class of generalized binomials emerging in fractional calculus. After establishing some general properties, we focus on a particular yet relevant case, for which we provide several ready-for-use combinatorial identities,…
This work lists and describes the main recent strategies for building fixed-length, dense and distributed representations for words, based on the distributional hypothesis. These representations are now commonly called word embeddings and,…
The database community lacks a unified relational query language for subset selection and optimisation queries, limiting both user expression and query optimiser reasoning about such problems. Decades of research (latterly under the rubric…
The class of Parikh word representable graphs were recently introduced. In this work, we further develop its general theory beyond the binary alphabet. Our main result shows that this class is equivalent to the class of bipartite…
Word embeddings have been found to capture a surprisingly rich amount of syntactic and semantic knowledge. However, it is not yet sufficiently well-understood how the relational knowledge that is implicitly encoded in word embeddings can be…
We introduce and study a new complexity function in combinatorics on words, which takes into account the smallest second occurrence time of a factor of an infinite word. We characterize the eventually periodic words and the Sturmian words…
Human language defines the most complex outcomes of evolution. The emergence of such an elaborated form of communication allowed humans to create extremely structured societies and manage symbols at different levels including, among others,…
What is the relation between a word and its description, or a word and its embedding? Both descriptions and embeddings are semantic representations of words. But, what information from the original word remains in these representations? Or…