Related papers: Density of group languages in shift spaces
Recent approaches to cross-lingual word embedding have generally been based on linear transformations between the sets of embedding vectors in the two languages. In this paper, we propose an approach that instead expresses the two…
While natural languages differ widely in both canonical word order and word order flexibility, their word orders still follow shared cross-linguistic statistical patterns, often attributed to functional pressures. In the effort to identify…
In this paper we introduce the geodesic conjugacy language and geodesic conjugacy growth series for a finitely generated group. We study the effects of various group constructions on rationality of both the geodesic conjugacy growth series…
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…
The average uncertainty associated with words is an information-theoretic concept at the heart of quantitative and computational linguistics. The entropy has been established as a measure of this average uncertainty - also called average…
We give an algorithm to construct a translation-invariant transport kernel between ergodic stationary random measures $\Phi$ and $\Psi$ on $\mathbb R^d$, given that they have equal intensities. As a result, this yields a construction of a…
The height of a piecewise-testable language $L$ is the maximum length of the words needed to define $L$ by excluding and requiring given subwords. The height of $L$ is an important descriptive complexity measure that has not yet been…
Surface groups are determined among limit groups by their profinite completions. As a corollary, the set of surface words in a free group is closed in the profinite topology.
The formation of sentences is a highly structured and history-dependent process. The probability of using a specific word in a sentence strongly depends on the 'history' of word-usage earlier in that sentence. We study a simple…
A modal logic that is strong enough to fully characterize the behavior of a system is called expressive. Recently, with the growing diversity of systems to be reasoned about (probabilistic, cyber-physical, etc.), the focus shifted to…
This paper establishes a classification of the critical numbers for restricted sumsets in finite abelian groups, determining them exactly for even-order groups and bounding them for odd-order groups, while revealing a fundamental structural…
The meanings and relationships of words shift over time. This phenomenon is referred to as semantic shift. Research focused on understanding how semantic shifts occur over multiple time periods is essential for gaining a detailed…
We show that, given a word equation over a finitely generated free group, the set of all solutions in reduced words forms an EDT0L language. In particular, it is an indexed language in the sense of Aho. The question of whether a description…
The distances between words calculated in word units are studied and compared with the distributions of the Random Matrix Theory (RMT). It is found that the distribution of distance between the same words can be well described by the…
Using the frequency of keywords is a classic approach in the formal analysis of text, but has the drawback of glossing over the relationality of word meanings. Word embedding models overcome this problem by constructing a standardized and…
How do words change their meaning? Although semantic evolution is driven by a variety of distinct factors, including linguistic, societal, and technological ones, we find that there is one law that holds universally across five major…
Ergodic optimization aims to describe dynamically invariant probability measures that maximize the integral of a given function. The Dyck and Motzkin shifts are well-known examples of transitive subshifts over a finite alphabet that are not…
Word embeddings provide an unsupervised way to understand differences in word usage between discursive communities. A number of recent papers have focused on identifying words that are used differently by two or more communities. But word…
Logic languages based on the theory of rational, possibly infinite, trees have much appeal in that rational trees allow for faster unification (due to the safe omission of the occurs-check) and increased expressivity (cyclic terms can…
In this document we achieve exact and asymptotic enumeration of words, compositions over a finite group, and/or integer compositions characterized by local restrictions and, separately, subsequence pattern avoidance. We also count…