Related papers: Conjugacy languages in virtual graph products
The study of rational relations is fundamental to the study of formal languages and automata theory. A rational relation is conjugate if each pair of words in the relation is conjugate (or cyclic shifts of each other). The notion of…
We introduce a generalization of the zig-zag product of regular digraphs (directed graphs), which allows us to construct regular digraphs with m ore flexible choices of the degrees. In our generalization, we can control the connectivity of…
We use wreath products to provide criteria for a group to be conjugacy separable or omnipotent. These criteria are in terms of virtual retractions onto cyclic subgroups. We give two applications: a straightforward topological proof of the…
We prove that graph products of sofic groups are sofic, as are graphs of groups for which vertex groups are sofic and edge groups are amenable.
This paper focuses on enhancing human-agent communication by integrating spatial context into virtual agents' non-verbal behaviors, specifically gestures. Recent advances in co-speech gesture generation have primarily utilized data-driven…
The Sierpi\'nski product of graphs generalises the vast and relevant class of Sierpi\'nski-type graphs, and is also related to the classic lexicographic product of graphs. Our first main results are necessary and sufficient conditions for…
We show that the virtual second Betti number of a finitely generated, residually free group $G$ is finite if and only if $G$ is either free, free abelian or the fundamental group of a closed surface. We also prove a similar statement in…
Conversational recommender systems (CRSs) often utilize external knowledge graphs (KGs) to introduce rich semantic information and recommend relevant items through natural language dialogues. However, original KGs employed in existing CRSs…
The present paper is a review of the current state of Graph-Link Theory (graph-links are also closely related to homotopy classes of looped interlacement graphs), dealing with a generalisation of knots obtained by translating the…
Let $G$ be a finitely generated group. We show that for any finite generating set $A$, the language consisting of all geodesics in $Cay(G,A)$ with a contracting property is a regular language. As an application, we show that any finitely…
A theorem of Kontsevich relates the homology of certain infinite dimensional Lie algebras to graph homology. We formulate this theorem using the language of reversible operads and mated species. All ideas are explained using a pictorial…
We provide a pipeline for generating syntax diagrams (also called railroad diagrams) from context free grammars. Syntax diagrams are a graphical representation of a context free language, which we formalize abstractly as a set of mutually…
We discuss various types of Tits Alternative for subgroups of graph products of groups, and prove that, under some natural conditions, a graph product of groups satisfies a given form of Tits Alternative if and only if each vertex group…
The Voynich Manuscript (VMS) exhibits a script of uncertain origin whose grapheme sequences have resisted linguistic analysis. We present a systematic analysis of its grapheme sequences, revealing two complementary structural layers: a…
We consider the problem of exact and inexact matching of weighted undirected graphs, in which a bijective correspondence is sought to minimize a quadratic weight disagreement. This computationally challenging problem is often relaxed as a…
We investigate inflection structure of a synthetic language using Latin as an example. We construct a bipartite graph in which one group of vertices correspond to dictionary headwords and the other group to inflected forms encountered in a…
In this paper, we propose a weak version of quotient for the algebraic action of a group on a variety, which we shall call a pseudo-quotient. They arise when we focus on the purely topological properties of good GIT quotients regardless of…
This study explores two frameworks for co-speech gesture generation, AQ-GT and its semantically-augmented variant AQ-GT-a, to evaluate their ability to convey meaning through gestures and how humans perceive the resulting movements. Using…
We study the geometry of dynamic pairs $(X,\mathcal{V})$ on a manifold $M$, where $X$ is a vector field and $\mathcal{V}$ is a distribution on $M$, both satisfying a regularity condition. Special cases are pairs defined by systems of second…
We study the problem of grammar-constrained context-free language reachability in graphs, focusing on complexity and empirical performance. We present an algorithmic framework for evaluating reachability queries constrained by context-free…