Year: 2022
Type: article
Abstract: We consider the domino problem on Schreier graphs of self-similar groups, and more generally their monadic second-order logic. On the one hand, we prove that if the group is bounded, then the domino problem on the graph is decidable; furthermore, under an ultimate periodicity condition, all its monadic second-order logic is decidable. This covers, for example, the Sierpiński gasket graphs and the Schreier graphs of the Basilica group. On the other hand, we prove undecidability of the domino problem for a class of self-similar groups, answering a question by Barbieri and Sablik, and study some examples including one of linear growth.
Source: Groups Geometry and Dynamics
DOI: 10.4171/ggd/689
Author: Laurent Bartholdi
Institution: Saarland University
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W3097406060