Related papers: A Language Hierarchy of Binary Relations
We give a finite axiomatization for the variety generated by relational, integral ordered monoids. As a corollary we get a finite axiomatization for the language interpretation as well.
Binary multirelations generalise binary relations by associating elements of a set to its subsets. We study the structure and algebra of multirelations under the operations of union, intersection, sequential and parallel composition, as…
We study the role of the second language in bilingual word embeddings in monolingual semantic evaluation tasks. We find strongly and weakly positive correlations between down-stream task performance and second language similarity to the…
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…
This paper considers the word problem for free inverse monoids of finite rank from a language theory perspective. It is shown that no free inverse monoid has context-free word problem; that the word problem of the free inverse monoid of…
A monoid is called special if it admits a presentation in which all defining relations are of the form $w = 1$. Every group is special, but not every monoid is special. In this article, we describe the language-theoretic properties of the…
For every fixed class of regular languages, there is a natural hierarchy of increasingly more general problems: Firstly, the membership problem asks whether a given language belongs to the fixed class of languages. Secondly, the separation…
Most languages use the relative order between words to encode meaning relations. Languages differ, however, in what orders they use and how these orders are mapped onto different meanings. We test the hypothesis that, despite these…
In classification problems, especially those that categorize data into a large number of classes, the classes often naturally follow a hierarchical structure. That is, some classes are likely to share similar structures and features. Those…
We study the language-theoretic properties of the word problem, in the sense of Duncan & Gilman, of weakly compressible monoids, as defined by Adian & Oganesian. We show that if $\mathcal{C}$ is a reversal-closed super-$\operatorname{AFL}$,…
Eilenberg's variety theorem, a centerpiece of algebraic automata theory, establishes a bijective correspondence between varieties of languages and pseudovarieties of monoids. In the present paper this result is generalized to an abstract…
The Eilenberg correspondence relates varieties of regular languages to pseudovarieties of finite monoids. Various modifications of this correspondence have been found with more general classes of regular languages on one hand and classes of…
We consider the problem of learning a certain type of lexical semantic knowledge that can be expressed as a binary relation between words, such as the so-called sub-categorization of verbs (a verb-noun relation) and the compound noun phrase…
In this article we undertake a study of extension complexity from the perspective of formal languages. We define a natural way to associate a family of polytopes with binary languages. This allows us to define the notion of extension…
We study the action of monads on categories equipped with several monoidal structures. We identify the structure and conditions that guarantee that the higher monoidal structure is inherited by the category of algebras over the monad.…
The use of monoids in the study of word languages recognized by finite-state automata has been quite fruitful. In this work, we look at the same idea of "recognizability by finite monoids" for other monoids. In particular, we attempt to…
In this work we consider monoids as algebras with an associative binary operation and the nullary operation that fixes the identity element. We found an example of two varieties of monoids with finite subvariety lattices such that their…
When using a third language to construct a bilingual dictionary, it is necessary to discriminate equivalencies from inappropriate words derived as a result of ambiguity in the third language. We propose a method to treat this by utilizing…
In the first part of this survey, we present classical notions arising in combinatorics on words: growth function of a language, complexity function of an infinite word, pattern avoidance, periodicity and uniform recurrence. Our…
We introduce regular languages of morphisms in free monoidal categories, with their associated grammars and automata. These subsume the classical theory of regular languages of words and trees, but also open up a much wider class of…