Related papers: Syntactic Structures of Regular Languages
Semifields are semirings in which every nonzero element has a multiplicative inverse. A rough classification uses the characteristic of the semifield, that is the isomorphism type of the semifield generated by the two neutral elements. For…
In this paper we develop a structure called Link Algebra, in which we present a Set with two binary operations and an axiom system developed from the study of graph theory and set/antiset theory, sowing main theorems and definitions. Once…
A bialgebra is a structure which is simultaneously an algebra and a coalgebra, such that the algebraic and coalgebraic parts are "compatible". Bialgebras are normally studied over a field or commutative ring. In this paper, we show how to…
This is the second in a series of papers that develops the theory of reflection monoids, motivated by the theory of reflection groups. Reflection monoids were first introduced in arXiv:0812.2789. In this paper we study their presentations…
The fundamental ideas of the definition of solvable and semisimple Bol algebras are given and some related theorems
Orbital semilattices are introduced as bounded semilattices that are, in addition, equipped with an outer multiplication (a semigroup action) and diagonals (a concept borrowed from cylindric algebra), where each semilattice element has a…
This paper discusses SYNTAGMA, a rule based NLP system addressing the tricky issues of syntactic ambiguity reduction and word sense disambiguation as well as providing innovative and original solutions for constituent generation and…
This paper introduces the order-theoretic concept of lattices along with the concept of consistent quantification where lattice elements are mapped to real numbers in such a way that preserves some aspect of the order-theoretic structure.…
This article is an introduction to formal languages from the point of view of combinatorial group theory. Group theoretic applications are included and language classes are defined algebraically.
In this paper, we propose a novel architecture called Composition Attention Grammars (CAGs) that recursively compose subtrees into a single vector representation with a composition function, and selectively attend to previous structural…
We study associative multiplications in semi-simple associative algebras over C compatible with the usual one or, in other words, linear deformations of semi-simple associative algebras over C. It turns out that these deformations are in…
The aim of this article is to study certain categorical-algebraic frameworks for basic homological algebra, introduced in arXiv:2404.15896, with the aim of better understanding the differences between them. We focus on homological…
We describe the basic lattice structures of attractors and repellers in dynamical systems. The structure of distributive lattices allows for an algebraic treatment of gradient-like dynamics in general dynamical systems, both invertible and…
The character theory of finite groups has numerous basic questions that are often already quite involved: enumerating of irreducible characters, their character formulas, point-wise product decompositions, and restriction/induction between…
We consider the lattice of subsemigroups of the general linear group over an Artinian ring containing the group of diagonal matrices and show that every such semigroup is actually a group.
We introduce the concept of basis for a lattice. This basis plays a vital role to determine the completeness and consistency of the lattice. Weighted lattices are introduced and its complexity is formulated. Some axiomatic systems,…
In this paper, the complete algebraic structure of finite semisimple group algebra of a normally monomial group is described. The main result is illustrated by computing the explicit Wedderburn decomposition of finite semisimple group…
We provide a mathematical argument showing that, given a representation of lexical items as functions (wavelets, for instance) in some function space, it is possible to construct a faithful representation of arbitrary syntactic objects in…
This paper includes a reflection on the role of networks in the study of English language acquisition, as well as a collection of practical criteria to annotate free-speech corpora from children utterances. At the theoretical level, the…
Language is highly structured, with syntactic and semantic structures, to some extent, agreed upon by speakers of the same language. With implicit or explicit awareness of such structures, humans can learn and use language efficiently and…