Related papers: A Language Hierarchy of Binary Relations
We analyse the pseudofinite monadic second order theory of words over a fixed finite alphabet. In particular we present an axiomatisation of this theory, working in a one-sorted first order framework. The analysis hinges on the fact that…
We study the P versus NP problem through properties of functions and monoids, continuing the work of [3]. Here we consider inverse monoids whose properties and relationships determine whether P is different from NP, or whether injective…
A certain analysis of all possible associative binary operations on N is presented. This is equivalent with an analysis of all possible monoid structures on N. Several results and a conjecture in this regard are given.
The number of possible methods of generalizing binary classification to multi-class classification increases exponentially with the number of class labels. Often, the best method of doing so will be highly problem dependent. Here we present…
We present an example of two countable $\omega$-categorical structures, one of which has a finite relational language, whose endomorphism monoids are isomorphic as abstract monoids, but not as topological monoids -- in other words, no…
We show that the word problem for braided monoidal categories is at least as hard as the unknotting problem. As a corollary, so is the word problem for Gray categories. We conjecture that the word problem for Gray categories is decidable.
A double category is constructed from a `fattened' version of a given category, motivated in part by a context of parallel transport. We also study monoidal structures on the underlying category and on the fattened category.
We develop layered monoidal theories -- a generalisation of monoidal theories combining formal descriptions of a system at different levels of abstraction. Via their representation as string diagrams, monoidal theories provide a graphical…
This paper investigates biases of Large Language Models (LLMs) through the lens of grammatical gender. Drawing inspiration from seminal works in psycholinguistics, particularly the study of gender's influence on language perception, we…
Diagrammatically speaking, grammatical calculi such as pregroups provide wires between words in order to elucidate their interactions, and this enables one to verify grammatical correctness of phrases and sentences. In this paper we also…
Learning word embeddings using distributional information is a task that has been studied by many researchers, and a lot of studies are reported in the literature. On the contrary, less studies were done for the case of multiple languages.…
In this article we provide a new perspective on the word problem of a group by using languages of nested words. These were introduced by Alur and Madhusudan as a way to model programming languages such as HTML. We demonstrate how a class of…
In this paper, we continue the research on the power of contextual grammars with selection languages from subfamilies of the family of regular languages. We investigate various comet-like types of languages and compare such language…
This paper studies the classes of semigoups and monoids with context-free and deterministic context-free word problem. First, some examples are exhibited to clarify the relationship between these classes and their connection with the…
Let $f(x)$ be a monic polynomial over $\mathbb{Q}$ with complex roots $\alpha_1,\dots,\alpha_n$. Linear relations among them and $1$ over $\mathbb{Q}$ play an important role when we study the distribution of roots modulo a prime. We study…
Different semantic interpretation tasks such as text entailment and question answering require the classification of semantic relations between terms or entities within text. However, in most cases it is not possible to assign a direct…
In the general context of presentations of monoids, we study normalisation processes that are determined by their restriction to length-two words. Garside's greedy normal forms and quadratic convergent rewriting systems, in particular those…
A binary relation over a free monoid is synchronous if it can be recognized by a synchronous automaton that reads its two tapes simultaneously. We consider the case where the free monoid is generated by a single element (which makes it…
We prove that the closure of the one-sided Dyck language in a free monoid is a two-sided Dyck language.
Human language can be described as a complex network of linked words. In such a treatment, each distinct word in language is a vertex of this web, and neighboring words in sentences are connected by edges. It was recently found (Ferrer and…