Related papers: Density of group languages in shift spaces
We investigate the intersection problem for finite semigroups, which asks for a given set of regular languages, represented by recognizing morphisms to finite semigroups, whether there exists a word contained in their intersection. We…
The title refers to the area of research which studies infinite groups using measure-theoretic tools, and studies the restrictions that group structure imposes on ergodic theory of their actions. The paper is a survey of recent developments…
The notions of concreteness and imageability, traditionally important in psycholinguistics, are gaining significance in semantic-oriented natural language processing tasks. In this paper we investigate the predictability of these two…
In this work, we prove that every SFT, sofic shift, and strongly irreducible shift on locally finite groups has strong dynamical properties. These properties include that every sofic shift is an SFT, every SFT is strongly irreducible, every…
In this paper we explore the connections between the class of Visibly Pushdown Languages ($\mathbf{VPL}$) and the natural sets of words one can associate to a finitely generated group. We show that the word problem of a finitely generated…
Static word embeddings are ubiquitous in computational social science applications and contribute to practical decision-making in a variety of fields including law and healthcare. However, assessing the statistical uncertainty in downstream…
Given a finite group with a generating subset there is a well-established notion of length for a group element given in terms of its minimal length expression as a product of elements from the generating set. Recently, certain quantities…
Human language has a distinct systematic structure, where utterances break into individually meaningful words which are combined to form phrases. We show that natural-language-like systematicity arises in codes that are constrained by a…
In this note we obtain tight bounds on the space-complexity of computing the ergodic measure of a low-dimensional discrete-time dynamical system affected by Gaussian noise. If the scale of the noise is $\varepsilon$, and the function…
Human languages vary widely in how they encode information within circumscribed semantic domains (e.g., time, space, color, human body parts and activities), but little is known about the global structure of semantic information and nothing…
We prove existence of asymptotic entropy of random walks on regular languages over a finite alphabet and we give formulas for it. Furthermore, we show that the entropy varies real-analytically in terms of probability measures of constant…
Statistical regularities in human language have fascinated researchers for decades, suggesting deep underlying principles governing its evolution and information structuring for efficient communication. While Zipf's Law describes the…
We identify a subclass of the regular commutative languages that is closed under the iterated shuffle, or shuffle closure. In particular, it is regularity-preserving on this subclass. This subclass contains the commutative group languages…
We consider Delone sets with finite local complexity. We characterize validity of a subadditive ergodic theorem by uniform positivity of certain weights. The latter can be considered to be an averaged version of linear repetitivity. In this…
We investigate the average-case complexity of decision problems for finitely generated groups, in particular the word and membership problems. Using our recent results on ``generic-case complexity'' we show that if a finitely generated…
In this paper we explore a new hierarchy of classes of languages and infinite words and its connection with complexity classes. Namely, we say that a language belongs to the class $L_k$ if it is a subset of the catenation of $k$ languages…
Let $G$ be a random group in Gromov's density model $G(m,d,L)$ with $d<\tfrac12$. We prove a sharp quantitative constraint on products of conjugates equal to the identity: for every $n\ge1$ and $\varepsilon>0$, with overwhelming probability…
Meaning is the foundation stone of intercultural communication. Languages are continuously changing, and words shift their meanings for various reasons. Semantic divergence in related languages is a key concern of historical linguistics. In…
Weighted automata are nondeterministic automata with numerical weights on transitions. They can define quantitative languages $L$ that assign to each word $w$ a real number $L(w)$. In the case of infinite words, the value of a run is…
We study scale-invariant geometric quantities associated with embedded closed curves in Euclidean three-space, with an emphasis on their behavior under optimization within a fixed knot type. Given a Euclidean-invariant and scale-covariant…