Related papers: Morphisms fixing words associated with exchange of…
We study morphisms from certain classes and their action on episturmian words. The first class is $P_{ret}$. In general, a morphism of class $P_{ret}$ can map an infinite word having zero palindromic defect to a word having infinite…
Let $M(A,I)$ be a free partially commutative monoid with involution and $G(A,I)$ be its quotient group, e.g. a right-angled Artin or Coxeter group. Given a system of word equations over $M(A,I)$ with recognizable constraints with input size…
(1) There is a finitely presented group with a word problem which is a uniformly effectively inseparable equivalence relation. (2) There is a finitely generated group of computable permutations with a word problem which is a universal…
Languages continually evolve in response to societal events, resulting in new terms and shifts in meanings. These changes have significant implications for computer applications, including automatic translation and chatbots, making it…
Morphisms, structure preserving maps, are everywhere in Mathematics as useful tools for thinking and problem solving, or as objects to study. Here, we argue that the idea of operations being compatible across two domains goes beyond its…
Linguistic similarity is multi-faceted. For instance, two words may be similar with respect to semantics, syntax, or morphology inter alia. Continuous word-embeddings have been shown to capture most of these shades of similarity to some…
This paper reviews some results regarding symbolic dynamics, correspondence between languages of dynamical systems and combinatorics. Sturmian sequences provide a pattern for investigation of one-dimensional systems, in particular interval…
In this paper, first we use the higher derived brackets to construct an $L_\infty$-algebra, whose Maurer-Cartan elements are $3$-Lie algebra morphisms. Using the differential in the $L_\infty$-algebra that govern deformations of the…
We present three Natural Language Inference (NLI) challenge sets that can evaluate NLI models on their understanding of temporal expressions. More specifically, we probe these models for three temporal properties: (a) the order between…
Dictionary definitions are historically the arbitrator of what words mean, but this primacy has come under threat by recent progress in NLP, including word embeddings and generative models like ChatGPT. We present an exploratory study of…
We revisit once again the connection between three notions of computation: monads, arrows and idioms (also called applicative functors). We employ monoidal categories of finitary functors and profunctors on finite sets as models of these…
First introduced in the study of the Sturmian words, the iterated palindromic closure was recently generalized to pseudopalindromes. This operator allows one to construct words with an infinity of pseudopalindromic prefixes, called…
We show that in the free group of rank 3, given an arbitrary number of automorphisms, the intersection of their fixed subgroups is equal to the fixed subgroup of some other single automorphism.
In English semantic similarity tasks, classic word embedding-based approaches explicitly model pairwise "interactions" between the word representations of a sentence pair. Transformer-based pretrained language models disregard this notion,…
A permutation graph is a graph that can be derived from a permutation, where the vertices correspond to letters of the permutation, and the edges represent inversions. We provide a construction to show that there are infinitely many…
Sturmian words form a family of one-sided infinite words over a binary alphabet that are obtained as a discretization of a line with an irrational slope starting from the origin. A finite version of this class of words called Christoffel…
We introduce a class of sets of words which is a natural common generalization of Sturmian sets and of interval exchange sets. This class of sets consists of the uniformly recurrent tree sets, where the tree sets are defined by a condition…
Compositionality is a widely discussed property of natural languages, although its exact definition has been elusive. We focus on the proposal that compositionality can be assessed by measuring meaning-form correlation. We analyze…
An isomorphism between two hermitian unitals is proved, and used to treat isomorphisms of classical groups that are related to the isomorphism between certain simple real Lie algebras of types A and D (and rank 3).
We consider two graph models of semantic change. The first is a time-series model that relates embedding vectors from one time period to embedding vectors of previous time periods. In the second, we construct one graph for each word: nodes…