Rational Gluing in Edge Replacement Systems

In this paper, we prove the rationality of the gluing relation of edge replacement systems, which were introduced for studying rearrangement groups of fractals. More precisely, we describe an algorithmic procedure for building a finite state automaton that recognizes pairs of equivalent sequences that are glued in the fractal. This fits in recent interest towards the rationality of gluing relations on totally disconnected compact metrizable spaces.