Related papers: Inverse problems of symbolic dynamics
Sofic shifts are symbolic dynamical systems defined by the set of bi-infinite sequences on an edge-labeled directed graph, called a presentation. We study the computational complexity of an array of natural decision problems about…
We give an introduction to the "stable algebra of matrices" as related to certain problems in symbolic dynamics. We consider this stable algebra (especially, shift equivalence and strong shift equivalence) for matrices over general rings as…
We extend the classical Ostrowski numeration systems, closely related to Sturmian words, by allowing a wider range of coefficients, so that possible representations of a number $n$ better reflect the structure of the associated Sturmian…
This survey paper is aimed to describe a relatively new branch of symbolic dynamics which we call Arithmetic Dynamics. It deals with explicit arithmetic expansions of reals and vectors that have a "dynamical" sense. This means precisely…
Rauzy-type dynamics are group actions on a collection of combinatorial objects. The first and best known example concerns an action on permutations, associated to interval exchange transformations (IET) for the Poincar\'e map on compact…
In this paper, we explore applications of combinatorics on words across various domains, including data compression, error detection, cryptographic protocols, and pseudorandom number generation. The examination of the theoretical…
Distributional semantics provides multi-dimensional, graded, empirically induced word representations that successfully capture many aspects of meaning in natural languages, as shown in a large body of work in computational linguistics;…
Symbolic perturbations offer a novel approach for influencing neural representations without requiring direct modification of model parameters. The recursive regeneration of symbolic structures introduces structured variations in latent…
In the following article, we construct an interaction model (a variant of the SIR-model) of general language change. In the context of language change it is desirable to deduce the long-term behaviour of the corresponding dynamical system…
Irreducible interval exchange transformations are studied with regard to whirly property, a condition for non-trivial spatial factor. Uniformly whirly transformation is defined and to be further studied. An equivalent condition is…
In this paper we study how certain families of aperiodic infinite words can be used to produce aperiodic pseudorandom number generators (PRNGs) with good statistical behavior. We introduce the \emph{well distributed occurrences} (WELLDOC)…
In the paper the notion of {\em Rauzy scheme} is introduced. From Rauzy graph Rauzy Scheme can be obtaining by uniting sequence of vertices of ingoing and outgoing degree 1 by arches. This notion is a tool to describe Rauzy graph behavior.…
A graph $G=(V,E)$ is word-representable if there exists a word $w$ over the alphabet $V$ such that letters $x$ and $y$ alternate in $w$ if and only if $xy\in E$. For integers $n>k>0 $, the shift graph $G(n,k)$ is the graph whose vertex set…
A binary word is Sturmian if the occurrences of each letter are balanced, in the sense that in any two factors of the same length, the difference between the number of occurrences of the same letter is at most 1. In digital geometry,…
We consider infinite sequences of superstable orbits (cascades) generated by systematic substitutions of letters in the symbolic dynamics of one-dimensional nonlinear systems in the logistic map universality class. We identify the…
Gradual semantics with abstract argumentation provide each argument with a score reflecting its acceptability, i.e. how "much" it is attacked by other arguments. Many different gradual semantics have been proposed in the literature, each…
The decimal expansion real numbers, familiar to us all, has a dramatic generalization to representation of dynamical system orbits by symbolic sequences. The natural way to associate a symbolic sequence with an orbit is to track its history…
We introduce a new dynamic vocabulary for language models. It can involve arbitrary text spans during generation. These text spans act as basic generation bricks, akin to tokens in the traditional static vocabularies. We show that, the…
Let $d\in\mathbb{Z}$ and $p_i$ be an integral polynomial with $p_i(0)=0,1\leq i\leq d$. It is shown that if $S$ is thickly syndetic in $\mathbb{Z}$, then $\{(m,n)\in\mathbb{Z}^2:m+p_i(n),m+p_2(n),\ldots,m+p_d(n)\in S\}$ is thickly syndetic…
The problem we consider is the following: Given an infinite word $w$ on an ordered alphabet, construct the sequence $\nu_w=(\nu[n])_n$, equidistributed on $[0,1]$ and such that $\nu[m]<\nu[n]$ if and only if $\sigma^m(w)<\sigma^n(w)$, where…