Related papers: Iterative pushdown automata and hyperbolic contour…

The combinatorial structure of the realization space of the euqilateral pentagon linkage is closely related to a tiling of the hyperbolic plane by right-angled pentagons. In this correspondence lower dimensional faces of the tiling…

We exhibit the construction of a deterministic automaton that, given k > 0, recognizes the (regular) language of k-differentiable words. Our approach follows a scheme of Crochemore et al. based on minimal forbidden words. We extend this…

The aim of this paper is to demonstrate that very many Dehn fillings on a cusped hyperbolic 3-manifold yield a 3-manifold which is irreducible, atoroidal and not Seifert fibred, and which has infinite, word hyperbolic fundamental group. We…

In this paper we study the word problem of groups corresponding to tessellations of the hyperbolic plane. In particular using the Fibonacci technology developed by the second author we show that groups corresponding to the pentagrid or the…

The simulation of deterministic pushdown automata defined over a one-letter alphabet by finite state automata is investigated from a descriptional complexity point of view. We show that each unary deterministic pushdown automaton of size s…

We consider pushdown timed automata (PTAs) that are timed automata (with dense clocks) augmented with a pushdown stack. A configuration of a PTA includes a control state, dense clock values and a stack word. By using the pattern technique,…

We present an architecture for integrating real-time, multimodal input into a computational agent's contextual model. Using a human-avatar interaction in a virtual world, we treat aligned gesture and speech as an ensemble where content may…

Hyperbolic spaces allow for more efficient modeling of complex, hierarchical structures, which is particularly beneficial in tasks involving multi-modal data. Although hyperbolic geometries have been proven effective for language-image…

We consider tilings of Euclidean spaces by polygons or polyhedra, in particular, tilings made by a substitution process, such as the Penrose tilings of the plane. We define an isomorphism invariant related to a subgroup of rotations and…

A turn in a computation of a pushdown automaton is a switch from a phase in which the height of the pushdown store increases to a phase in which it decreases. Given a pushdown or one-counter automaton, we consider, for each string in its…

Boolean programs with multiple recursive threads can be captured as pushdown automata with multiple stacks. This model is Turing complete, and hence, one is often interested in analyzing a restricted class that still captures useful…

Infinite time Turing machines are extended in several ways to allow for iterated oracle calls. The expressive power of these machines is discussed and in some cases determined.

This paper considers finite-automata based algorithms for handling linear arithmetic with both real and integer variables. Previous work has shown that this theory can be dealt with by using finite automata on infinite words, but this…

In Formal Languages and Automata Theory courses, students find understanding nondeterministic finite-state and pushdown automata difficult. In many cases, this means that it is challenging for them to comprehend the operational semantics of…

Timed pushdown automata (TPDA) are an expressive formalism combining recursion with a rich logic of timing constraints. We prove that reachability relations of TPDA are expressible in linear arithmetic, a rich logic generalising Presburger…

With the rapid development of text-to-image generation technology, accurately assessing the alignment between generated images and text prompts has become a critical challenge. Existing methods rely on Euclidean space metrics, neglecting…

The goal of this paper is to exhibit and analyze an algorithm that takes a given closed orientable hyperbolic surface and outputs an explicit Dirichlet domain. The input is a fundamental polygon with side pairings. While grounded in…

Probabilistic B\"uchi Automata (PBA) are randomized, finite state automata that process input strings of infinite length. Based on the threshold chosen for the acceptance probability, different classes of languages can be defined. In this…

We define 2-dimensional topological substitutions. A tiling of the Euclidean plane, or of the hyperbolic plane, is substitutive if the underlying 2-complex can be obtained by iteration of a 2-dimensional topological substitution. We prove…

This paper discusses iterated monodromy groups for transcendental functions. We show that for every post-singularly finite entire transcendental function, the iterated monodromy action can be described by bounded activity automata of a…