5 papers · 1 filter
Medvedev degrees of subshifts on groups
Sebastián Barbieri, Nicanor Carrasco-Vargas
The Medvedev degree of a subshift is a dynamical invariant of computable origin that can be used to compare the complexity of subshifts that contain only uncomputable configuration…
A general framework for quasi-isometries in symbolic dynamics beyond groups
Sebastián Barbieri, Nicolás Bitar
We introduce an algebraic structure which encodes a collection of countable graphs through a set of states, generators and relations. These structures, which we call blueprints, ca…
A remark on inverse limits of effective subshifts
Sebastián Barbieri, Leo Poirier
We show that, for every finitely generated group with decidable word problem and undecidable domino problem, there exists a sequence of effective subshifts whose inverse limit is n…
The automorphism group of a strongly irreducible subshift on a group
Sebastián Barbieri, Nicanor Carrasco-Vargas, Paola Rivera-Burgos
We study the automorphism group of a non-trivial strongly irreducible subshift on an arbitrary infinite group and generalize classical results of Ry…
Cellular automata, percolation and dynamical dichotomies
Sebastián Barbieri, Felipe GarcÃa-Ramos, Siamak Taati
We establish a connection between percolation on the Cayley graphs of a group and the dynamical diversity of cellular automata on that group. Specifically, we demonstrate that Gilm…