Related papers: Context-free rewriting systems and word-hyperbolic…
An important problem in the theory of finite dynamical systems is to link the structure of a system with its dynamics. This paper contains such a link for a family of nonlinear systems over the field with two elements. For systems that can…
We show that superreflexivity can be characterized in terms of bilipschitz embeddability of word hyperbolic groups. We compare characterizations of superreflexivity in terms of diamond graphs and binary trees. We show that there exist…
For a fixed word hyperbolic group we compare different residual properties related to quasiconvex subgroups.
The hyperedge replacement grammar (HRG) formalism is a natural and well-known generalization of context-free grammars. HRGs inherit a number of properties of context-free grammars, e.g. the pumping lemma. This lemma turns out to be a strong…
Let $M$ be a cancellative and commutative monoid (written additively). The monoid $M$ is atomic if every non-invertible element can be written as a sum of irreducible elements (often called atoms in the literature). Weaker versions of…
A special inverse monoid is one defined by a presentation where all the defining relations have the form $r = 1$. By a result of Ivanov Margolis and Meakin the word problem for such an inverse monoid can often be reduced to the word problem…
Context-free session types provide a typing discipline for recursive structured communication protocols on bidirectional channels. They overcome the restriction of regular session type systems to tail recursive protocols. This extension…
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…
Hyperbolic spaces have proven to be suitable for modeling data of hierarchical nature. As such we use the Poincare ball to embed sentences with the goal of proving how hyperbolic spaces can be used for solving Textual Entailment. To this…
Context modeling has a pivotal role in open domain conversation. Existing works either use heuristic methods or jointly learn context modeling and response generation with an encoder-decoder framework. This paper proposes an explicit…
This monograph is an updated and extended version of the author's PhD thesis. It consists of an introductory text followed by two separate parts which are loosely related but may be read independently of each other. In Part I we analyze…
There is a wealth of results in the literature on the thermodynamic formalism for potentials that are, in some sense, "hyperbolic". We show that for a sufficiently regular one-dimensional map satisfying a weak hyperbolicity assumption,…
We describe a procedure which verifies that a group given by generators and relators is word-hyperbolic. This procedure always works with a group which is word-hyperbolic, provided there is sufficient memory and time devoted to the problem.…
The paper presents algebraic and logical developments. From the algebraic viewpoint, we introduce Monadic Equational Systems as an abstract enriched notion of equational presentation. From the logical viewpoint, we provide Equational…
We show that any product of bushy hyperbolic spaces has a unique coarse median structure, and that having a unique coarse median structure is a property closed under relative hyperbolicity. As a consequence, in contrast with the case of…
We obtain a criterion for quasiconvexity of a subgroup of an amalgamated free product of two word hyperbolic groups along a virtually cyclic subgroup. The result provides a method of constructing new word hyperbolic group in class (Q), that…
Cross-lingual word embeddings can be applied to several natural language processing applications across multiple languages. Unlike prior works that use word embeddings based on the Euclidean space, this short paper presents a simple and…
In this paper we continue the analysis of non-diagonalisable hyperbolic systems initiated in \cite{GarJRuz, GarJRuz2}. Here we assume that the system has discontinuous coefficients or more in general distributional coefficients.…
Previously, Reynolds showed that any irreducible nonsurjective endomorphism can be represented by an irreducible immersion on a finite graph. We give a new proof of this and also show a partial converse holds when the immersion has…
Let $V$ be a finite graph and let $\phi:V\rightarrow V$ be an irreducible train track map whose mapping torus has word-hyperbolic fundamental group $G$. Then $G$ acts freely and cocompactly on a CAT(0) cube complex.