Related papers: Hard Asymptotic Sets for One-Dimensional Cellular …
We show that the set of strictly temporally periodic points of cellular automata with almost equicontinuous points is dense in the topological support of the measure. This extends a result of Lena, Margara and Dennunzio about the density of…
In this paper, we prove that there is a strongly universal cellular automaton in the dodecagrid, the tessellation {5,3,4} of the hyperbolic 3D-space, with five states which is rotation invariant. This improves a previous paper of the author…
The notions of universality and completeness are central in the theories of computation and computational complexity. However, proving lower bounds and necessary conditions remains hard in most of the cases. In this article, we introduce…
Let $G$ be a group and let $A$ be a finite-dimensional vector space over an arbitrary field $K$. We study finiteness properties of linear subshifts $\Sigma \subset A^G$ and the dynamical behavior of linear cellular automata $\tau \colon…
A simple mathematical expression for the universal map for cellular automata is found in closed form with the help of a digit function, whose most basic properties are established. This result is found after proving a theorem on the…
In this paper, we study a class of cellular automata (CA) called stable cellular automata (SCA) that preserve stability by reflection, modulo-recurrent, and richness. After applying these automata to Sturmian words, we determine some of…
We show that the automorphism group of a one-dimensional full shift (the group of reversible cellular automata) does not satisfy the Tits alternative. That is, we construct a finitely-generated subgroup which is not virtually solvable yet…
This article introduces new tools to study self-organisation in a family of simple cellular automata which contain some particle-like objects with good collision properties (coalescence) in their time evolution. We draw an initial…
Following work by Hochman and Meyerovitch on multidimensional SFT, we give computability-theoretic characterizations of the real numbers that can appear as the topological entropies of one-dimensional and two-dimensional cellular automata.
This paper studies complexity of recognition of classes of bounded configurations by a generalization of conventional cellular automata (CA) -- finite dynamic cellular automata (FDCA). Inspired by the CA-based models of biological and…
Relation between global transition function and local transition function of a homogeneous one dimensional cellular automaton (CA) is investigated for some standard transition functions. It could be shown that left shift and right shift CA…
We introduce languages of higher-dimensional automata (HDAs) and develop some of their properties. To this end, we define a new category of precubical sets, uniquely naturally isomorphic to the standard one, and introduce a notion of event…
We introduce the entropy rate of multidimensional cellular automata. This number is invariant under shift-commuting isomorphisms; as opposed to the entropy of such CA, it is always finite. The invariance property and the finiteness of the…
While for synchronous deterministic cellular automata there is an accepted definition of reversibility, the situation is less clear for asynchronous cellular automata. We first discuss a few possibilities and then investigate what we call…
In a probabilistic cellular automaton in which all local transitions have positive probability, the problem of keeping a bit of information indefinitely is nontrivial, even in an infinite automaton. Still, there is a solution in 2…
We study two categories of cellular automata. First, for any group $G$, we consider the category $\mathcal{CA}(G)$ whose objects are configuration spaces of the form $A^G$, where $A$ is a set, and whose morphisms are cellular automata of…
The complexity of cellular automata is traditionally measured by their computational capacity. However, it is difficult to choose a challenging set of computational tasks suitable for the parallel nature of such systems. We study the…
Cellular Automata (CA), as they are presented in the literature, are abstract mathematical models of computation. In this pa- per we present an alternate approach: using the CA as a model or theory of physical systems and devices. While…
A simple mechanism for the emergence of complexity in cellular automata out of predictable dynamics is described. This leads to unfold the concept of conditional predictability for systems whose trajectory can only be piecewise known. The…
The simulation of deterministic pushdown automata defined over a one-letter alphabet by finite state automata is investigated from a descriptional complexity point of view. We show that each unary deterministic pushdown automaton of size s…