Related papers: Topology Inspired Problems for Cellular Automata, …
The Besicovitch pseudodistance measures the relative size of the set of points where two functions take different values; the quotient space modulo the induced equivalence relation is endowed with a natural metric. We study the behavior of…
The Besicovitch pseudo-metric is a shift-invariant pseudo-metric on the set of infinite sequences, that enjoys interesting properties and is suitable for studying the dynamics of cellular automata. They correspond to the asymptotic behavior…
Cellular automata, CA for short are continuous maps defined on the set of configurations over a finite alphabet A that commutes with the shift. They are characterized by the existence of local function which determine by local behavior the…
We investigate some general properties of algebraic cellular automata, i.e., cellular automata over groups whose alphabets are affine algebraic sets and which are locally defined by regular maps. When the ground field is assumed to be…
Topological dynamics of cellular automata (CA), inherited from classical dynamical systems theory, has been essentially studied in dimension 1. This paper focuses on 2D CA and aims at showing that the situation is different and more…
Cellular automata represent physical systems where both space and time are discrete, and the associated physical quantities assume a limited set of values. While previous research has applied cellular automata in modeling chemical,…
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.
Topological dynamics of cellular automata (CA), inherited from classical dynamical systems theory, has been essentially studied in dimension 1. This paper focuses on higher dimensional CA and aims at showing that the situation is different…
We study the problem of sequentializing a cellular automaton without introducing any intermediate states, and only performing reversible permutations on the tape. We give a decidable characterization of cellular automata which can be…
The thesis presents the subject of synthetic topology, especially with relation to metric spaces. A model of synthetic topology is a categorical model in which objects possess an intrinsic topology in a suitable sense, and all morphisms are…
The search for symmetry as an unusual yet profoundly appealing phenomenon, and the origin of regular, repeating configuration patterns have long been a central focus of complexity science and physics. To better grasp and understand symmetry…
Cellular automata are discrete dynamical systems and a model of computation. The limit set of a cellular automaton consists of the configurations having an infinite sequence of preimages. It is well known that these always contain a…
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…
We discuss cellular automata over arbitrary finitely generated groups. We call a cellular automaton post-surjective if for any pair of asymptotic configurations, every pre-image of one is asymptotic to a pre-image of the other. The well…
Directed Algebraic Topology studies spaces equipped with a form of direction, to include models of non-reversible processes. In the present extension we also want to cover critical processes, indecomposable and unstoppable. The first part…
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…
Finite automata were used to determine multiple addresses in number systems and to find topological properties of self-affine tiles and finite type fractals. We join these two lines of research by axiomatically defining automata which…
We introduce and study cellular automata whose cell spaces are left-homogeneous spaces. Examples of left-homogeneous spaces are spheres, Euclidean spaces, as well as hyperbolic spaces acted on by isometries; uniform tilings acted on by…
We study discrete dynamical systems through the topological concepts of limit set, which consists of all points that can be reached arbitrarily late, and asymptotic set, which consists of all adhering values of orbits. In particular, we…
Cellular automata are a set of computational models in discrete space that have a discrete time evolution defined by neighbourhood rules. They are used to simulate many complex systems in physics and science in general. In this work,…