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pro vyhledávání: '"37B50"'
We study tiling spaces in the diffeological context. We prove some basic diffeological properties for tiling spaces and analyze two different fiber bundle structures of one-dimensional tiling spaces over the irrational torus. We use the diffeological
Externí odkaz:
http://arxiv.org/abs/2404.00508
Autor:
Phung, Xuan Kien
We establish several extensions of the well-known Garden of Eden theorem for non-uniform cellular automata over the full shifts and over amenable group universes. In particular, our results describe quantitatively the relations between the partial pr
Externí odkaz:
http://arxiv.org/abs/2304.00661
We study an abstract group of reversible Turing machines. In our model, each machine is interpreted as a homeomorphism over a space which represents a tape filled with symbols and a head carrying a state. These homeomorphisms can only modify the tape
Externí odkaz:
http://arxiv.org/abs/2303.17270
In this article we discuss potential Markov partitions for three different Wang tile protosets. The first partition is for the order-24 aperiodic Wang tile protoset that was recently shown in the Ph.D. thesis of H. Jang to encode all tilings by the P
Externí odkaz:
http://arxiv.org/abs/2302.13516
Autor:
Béaur, Pierre, Kari, Jarkko
Many decision problems concerning cellular automata are known to be decidable in the case of algebraic cellular automata, that is, when the state set has an algebraic structure and the automaton acts as a morphism. The most studied cases include fini
Externí odkaz:
http://arxiv.org/abs/2301.11133
Autor:
Kari, Jarkko
A d-dimensional configuration c : Z^d -> A is a coloring of the d-dimensional infinite grid by elements of a finite alphabet A \subseteq Z. The configuration c has an annihilator if a non-trivial linear combination of finitely many translations of c
Externí odkaz:
http://arxiv.org/abs/2301.06868
Publikováno v:
J. Math. Phys. 63 (2022) 082702:1-13
The direct product of two Fibonacci tilings can be described as a genuine stone inflation rule with four prototiles. This rule admits various modifications, which lead to 48 different inflation rules, known as the direct product variations. They all
Externí odkaz:
http://arxiv.org/abs/2203.07743
Autor:
Rieck, Yo'av
D. B. Cohen, C. Goodman-Strauss, and the author proved that a hyperbolic group admits an "SA SFT" if and only if it has at most one end. This paper has two distinct parts: the first is a conversation explaining what an SA SFT is and how they may be o
Externí odkaz:
http://arxiv.org/abs/2202.00212
Autor:
Kumar, Prashant, Sharma, Puneet
\begin{abstract} In this paper, we investigate a shift arising from graph $G$. We prove that any $k$-dimensional shift of finite type can be generated through a $k$-dimensional graph. We investigate the structure of the shift space using the generati
Externí odkaz:
http://arxiv.org/abs/2112.14079
We say that a finitely generated group $\Gamma$ is (dynamically) self-simulable if every effectively closed action of $\Gamma$ on a closed subset of $\{\mathtt{0},\mathtt{1}\}^{\mathbb{N}}$ is the topological factor of a $\Gamma$-subshift of finite t
Externí odkaz:
http://arxiv.org/abs/2104.05141