Iterative pushdown automata and hyperbolic contour words

TL;DR

This paper applies iterated pushdown automata to analyze contour words in various hyperbolic tilings across 2D, 3D, and 4D spaces, demonstrating their utility in complex geometric structures.

Contribution

It introduces novel applications of iterated pushdown automata to hyperbolic tilings in multiple dimensions, extending their use beyond traditional contexts.

Findings

Automata effectively recognize contour words in hyperbolic tilings

Extensions to 3D and 4D hyperbolic spaces demonstrated

Potential for analyzing complex geometric structures with automata

Abstract

In this paper, we give an application of iterated pushdown automata to contour words of balls and two other domains in infinitely many tilings of the hyperbolic plane. We also give a similar application for the tiling {5,3,4} of the hyperbolic 3D space and for the tiling {5,3,3,4} of the hyperbolic 4D space as well.