Related papers: Minimal subshifts with a language pivot property
We construct a minimal dynamical system of mean dimension equal to $1$, which can be embedded in the shift action on the Hilbert cube $[0,1]^\mathbb{Z}$. This clarifies a seemingly plausible impression about embedding possibility in…
Neural machine translation (NMT) models typically operate with a fixed vocabulary, but translation is an open-vocabulary problem. Previous work addresses the translation of out-of-vocabulary words by backing off to a dictionary. In this…
We use some of the largest order statistics of the random projections of a reference signal to construct a binary embedding that is adapted to signals correlated with such signal. The embedding is characterized from the analytical…
For finite reflection groups of types A and B, we determine the diameter of the graph whose vertices are reduced words for the longest element and whose edges are braid relations. This is deduced from a more general theorem that applies to…
An edit distance is a metric between words that quantifies how two words differ by counting the number of edit operations needed to transform one word into the other one. A word f is said isometric with respect to an edit distance if, for…
Two results on palindromicity of bi-infinite words in a finite alphabet are presented. The first is a simple, but efficient criterion to exclude palindromicity of minimal sequences and applies, in particular, to the Rudin-Shapiro sequence.…
We improve the upper bounds (in terms of $n$) in [9] and [13] on the minimal number of elements required to generate a minimally transitive permutation group of degree $n$.
The Hamming graph $H(n,q)$ is the graph whose vertices are the words of length $n$ over the alphabet $\{0,1,\ldots,q-1\}$, where two vertices are adjacent if they differ in exactly one coordinate. The adjacency matrix of $H(n,q)$ has $n+1$…
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…
A function on a discrete group is weakly combable if its discrete derivative with respect to a combing can be calculated by a finite state automaton. A weakly combable function is bicombable if it is Lipschitz in both the left and right…
We construct a minimal subshift \((X^{*},\sigma)\) that serves as an open proximal extension of its maximal equicontinuous factor. We establish that every point in this subshift is multiply recurrent minimal. This work solves an open…
Given any oriented link diagram, one can construct knot invariants using skein relations. Usually such a skein relation contains three or four terms. In this paper, the author introduces several new ways to smooth a crossings, and uses a…
We study the commutative positive varieties of languages closed under various operations: shuffle, renaming and product over one-letter alphabets.
For every $n\ge 3$ we determine the minimum number of edges of graph with $n$ vertices such that for any non edge $xy$ there exits a hamiltonian cycle containing $xy$.
The primary research questions of this paper center on defining the amount of context that is necessary and/or appropriate when investigating the relationship between language model probabilities and cognitive phenomena. We investigate…
In the setting of minimal local grammar-based coding, the input string is represented as a grammar with the minimal output length defined via simple symbol-by-symbol encoding. This paper discusses four contributions to this field. First, we…
In this note, we give a construction that provides a tight lower bound of mn-1 for the length of the shortest word in the intersection of two regular languages with state complexities m and n.
We study the fractal structure of language, aiming to provide a precise formalism for quantifying properties that may have been previously suspected but not formally shown. We establish that language is: (1) self-similar, exhibiting…
In this paper we study underlying graphs corresponding to a set of halving lines. We establish many properties of such graphs. In addition, we tighten the upper bound for the number of halving lines.
We bound the change in entropy incurred by an irreducible subshift of finite type upon perturbing it by forbidding a pair of admissible words. Lind has proven such bounds in the one-word case, and we adapt his methods. In particular, we…