相关论文: Information content in formal languages
The motivation for this thesis was to recast quantum self-testing [MY98,MY04] in operational terms. The result is a category-theoretic framework for discussing the following general question: How do different implementations of the same…
Today with Big Data and data lakes, we are faced of a mass of data that is very difficult to manage it manually. The protection of personal data in this context requires an automatic analysis for data discovery. Storing the names of…
A unified theory of language combines a Bayesian cognitive linguistic model of language processing, with the proposal that language evolved by sexual selection for the display of intelligence. The theory accounts for the major facts of…
Given a language, which in this article is a set of strings of some fixed length, we study the problem of producing its elements by a procedure in which each position has its own local rule. We introduce a way of measuring how much…
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.
Regular expressions are commonly understood in terms of their denotational semantics, that is, through formal languages -- the regular languages. This view is inductive in nature: two primitives are equivalent if they are constructed in the…
Documents in scientific newspapers are often marked by attitudes and opinions of the author and/or other persons, who contribute with objective and subjective statements and arguments as well. In this respect, the attitude is often…
This paper proposes a definition of recognizable transducers over monads and comonads, which bridges two important ongoing efforts in the current research on regularity. The first effort is the study of regular transductions, which extends…
These are lecture notes on the algebraic approach to regular languages. The classical algebraic approach is for finite words; it uses semigroups instead of automata. However, the algebraic approach can be extended to structures beyond…
The set of distances of a monoid or of a domain is the set of all $d \in \mathbb N$ with the following property: there are irreducible elements $u_1, \ldots, u_k, v_1, \ldots, v_{k+d}$ such that $u_1 \cdot \ldots \cdot u_k = v_1 \cdot…
Recently, researchers started to pay attention to the detection of temporal shifts in the meaning of words. However, most (if not all) of these approaches restricted their efforts to uncovering change over time, thus neglecting other…
Let $\mathcal{R}=(R,\oplus,\leq,0)$ be an algebraic structure, where $\oplus$ is a commutative binary operation with identity $0$, and $\leq$ is a translation-invariant total order with least element $0$. Given a distinguished subset…
Oftentimes the elements of a ring or semigroup $H$ can be written as finite products of irreducible elements, say $a=u_1 \cdot \ldots \cdot u_k = v_1 \cdot \ldots \cdot v_{\ell}$, where the number of irreducible factors is distinct. The set…
This paper is the first in a series whose goal is to develop a fundamentally new way of constructing theories of physics. The motivation comes from a desire to address certain deep issues that arise when contemplating quantum theories of…
Traditionally, formal languages are defined as sets of words. More recently, the alternative coalgebraic or coinductive representation as infinite tries, i.e., prefix trees branching over the alphabet, has been used to obtain compact and…
Given a metric pair $(X,A)$, i.e. a metric space $X$ and a distinguished closed set $A \subset X$, one may construct in a functorial way a pointed pseudometric space $\mathcal{D}_\infty(X,A)$ of persistence diagrams equipped with the…
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.
By virtue of linguistic compositionality, few syntactic rules and a finite lexicon can generate an unbounded number of sentences. That is, language, though seemingly high-dimensional, can be explained using relatively few degrees of…
This paper concerns the compactness and separability properties of the normed Boolean algebras (N.B.A.) with respect to topology generated by a distance equal to the square root of a measure of symmetric difference between two elements. The…
In ancient Greek mathematics, magnitudes such as lengths were strictly distinguished from numbers. In modern quantity calculus, a distinction is made between quantities and scalars that serve as measures of quantities. It can be argued that…