Automata, groups, limit spaces, and tilings Academic Article

abstract

• We explore the connections between automata, groups, limit spaces of self-similar actions, and tilings. In particular, we show how a group acting "nicely" on a tree gives rise to a self-covering of a topological groupoid, and how the group can be reconstructed from the groupoid and its covering. The connection is via finite-state automata. These define decomposition rules, or self-similar tilings, on leaves of the solenoid associated with the covering. 2005 Elsevier Inc. All rights reserved.

authors

• Nekrashevych, Volodymyr

published proceedings

• Journal of Algebra

author list (cited authors)

• Bartholdi, L., Henriques, A. G., & Nekrashevych, V. V.

citation count

• 5

complete list of authors

• Bartholdi, Laurent||Henriques, André G||Nekrashevych, Volodymyr V

publication date

• January 2006

publisher

• Elsevier  Publisher

published in

• Journal of Algebra  Journal

keywords

• 20e08; 37b10
• Math.gr

Digital Object Identifier (DOI)

• 10.1016/j.jalgebra.2005.10.022

start page

• 629

end page

• 663

volume

• 305

issue

• 2

URL

• http://dx.doi.org/10.1016/j.jalgebra.2005.10.022