25 citations · 44 across the 6 of their papers we have counts for
6 papers
The domino problem on groups of polynomial growth
Alexis Ballier, Maya Stein
We characterize the virtually nilpotent finitely generated groups (or, equivalently by Gromov's theorem, groups of polynomial growth) for which the Domino Problem is decidable: The…
Structuring multi-dimensional subshifts
Alexis Ballier, Emmanuel Jeandel
We study two relations on multi-dimensional subshifts: A pre-order based on the patterns configurations contain and the Cantor-Bendixson rank. We exhibit several structural propert…
Universality in symbolic dynamics constrained by Medvedev degrees
Alexis Ballier
We define a weak notion of universality in symbolic dynamics and, by generalizing a proof of Mike Hochman, we prove that this yields necessary conditions on the forbidden patterns…
Limit sets of stable Cellular Automata
Alexis Ballier
We study limit sets of stable cellular automata standing from a symbolic dynamics point of view where they are a special case of sofic shifts admitting a steady epimorphism. We pro…
Computing (or not) Quasi-Periodicity Functions of Tilings
Alexis Ballier, Emmanuel Jeandel
We know that tilesets that can tile the plane always admit a quasi-periodic tiling [4, 8], yet they hold many uncomputable properties [3, 11, 21, 25]. The quasi-periodicity functio…
Structural aspects of tilings
Alexis Ballier, Bruno Durand, Emmanuel Jeandel
In this paper, we study the structure of the set of tilings produced by any given tile-set. For better understanding this structure, we address the set of finite patterns that each…