Related papers: Density of group languages in shift spaces
We introduce a family of local models of dynamics based on ``word problems'' from computer science and group theory, for which we can place rigorous lower bounds on relaxation timescales. These models can be regarded either as random…
Motivated by the notion of strong computable type for sets in computable analysis, we define the notion of strong computable type for $G$-shifts, where $G$ is a finitely generated group with decidable word problem. A $G$-shift has strong…
We introduce a method for embedding words as probability densities in a low-dimensional space. Rather than assuming that a word embedding is fixed across the entire text collection, as in standard word embedding methods, in our Bayesian…
We prove that a subset of a virtually free group is rational if and only if the language of geodesic words representing its elements (in any generating set) is rational and that the language of geodesics representing conjugates of elements…
Word embeddings are powerful representations that form the foundation of many natural language processing architectures, both in English and in other languages. To gain further insight into word embeddings, we explore their stability (e.g.,…
Languages vary widely in how meanings map to word forms. These mappings have been found to support efficient communication; however, this theory does not account for systematic relations within word forms. We examine how a restricted set of…
As is the case of many signals produced by complex systems, language presents a statistical structure that is balanced between order and disorder. Here we review and extend recent results from quantitative characterisations of the degree of…
We study packing densities for set partitions, which is a generalization of packing words. We use results from the literature about packing densities for permutations and words to provide packing densities for set partitions. These results…
Languages are continuously undergoing changes, and the mechanisms that underlie these changes are still a matter of debate. In this work, we approach language evolution through the lens of causality in order to model not only how various…
Cross-lingual word embeddings encode the meaning of words from different languages into a shared low-dimensional space. An important requirement for many downstream tasks is that word similarity should be independent of language - i.e.,…
With the widespread application of Large Language Models (LLMs) to various domains, concerns regarding the trustworthiness of LLMs in safety-critical scenarios have been raised, due to their unpredictable tendency to hallucinate and…
We study density estimation for classes of shift-invariant distributions over $\mathbb{R}^d$. A multidimensional distribution is "shift-invariant" if, roughly speaking, it is close in total variation distance to a small shift of it in any…
Ergodic optimization aims to describe dynamically invariant probability measures that maximize the integral of a given function. For a wide class of intrinsically ergodic subshifts over a finite alphabet, we show that the space of…
We discuss recurrence and ergodicity properties of random walks and associated skew products for large classes of locally compact groups and homogeneous spaces. In particular we show that a closed subgroup of a product of finitely many…
We use language theory to study the rational subset problem for groups and monoids. We show that the decidability of this problem is preserved under graph of groups constructions with finite edge groups. In particular, it passes through…
We prove results about subshifts with linear (word) complexity, meaning that $\limsup \frac{p(n)}{n} < \infty$, where for every $n$, $p(n)$ is the number of $n$-letter words appearing in sequences in the subshift. Denoting this limsup by…
Given a finite set of words w1,...,wn independently drawn according to a fixed unknown distribution law P called a stochastic language, an usual goal in Grammatical Inference is to infer an estimate of P in some class of probabilistic…
We consider some questions about formal languages that arise when inverses of letters, words and languages are defined. The reduced representation of a language over the free monoid is its unique equivalent representation in the free group.…
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…
Group languages are regular languages recognized by finite groups, or equivalently by finite automata in which each letter induces a permutation on the set of states. We investigate the separation problem for this class of languages: given…