39 citations · 100 across the 11 of their papers we have counts for
12 papers
The expressiveness of quasiperiodic and minimal shifts of finite type
Bruno Durand, Andrei Romashchenko
We study multidimensional minimal and quasiperiodic shifts of finite type. We prove for these classes several results that were previously known for the shifts of finite type in ge…
On the expressive power of quasiperiodic SFT
Bruno Durand, Andrei Romashchenko
In this paper we study the shifts, which are the shift-invariant and topologically closed sets of configurations over a finite alphabet in . The minimal shifts are th…
Quasiperiodicity and non-computability in tilings
Bruno Durand, Andrei Romashchenko
We study tilings of the plane that combine strong properties of different nature: combinatorial and algorithmic. We prove existence of a tile set that accepts only quasiperiodic an…
Aperiodic tilings and entropy
Bruno Durand, Guilhem Gamard, Anael Grandjean
In this paper we present a construction of Kari-Culik aperiodic tile set - the smallest known until now. With the help of this construction, we prove that this tileset has positive…
1D Effectively Closed Subshifts and 2D Tilings
Durand Bruno, Alexander Shen, Andrei Romashchenko
Michael Hochman showed that every 1D effectively closed subshift can be simulated by a 3D subshift of finite type and asked whether the same can be done in 2D. It turned out that t…
Effective closed subshifts in 1D can be implemented in 2D
Bruno Durand, Andrei Romashchenko, Alexander Shen
In this paper we use fixed point tilings to answer a question posed by Michael Hochman and show that every one-dimensional effectively closed subshift can be implemented by a local…