Related papers: Cellular Automata are Generic
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…
A probabilistic cellular automaton for cargo transport is presented that generalizes the totally asymmetric exclusion process with a defect from continuous time to parallel dynamics. It appears as an underlying principle in cellular…
This talk advocates intrinsic universality as a notion to identify simple cellular automata with complex computational behavior. After an historical introduction and proper definitions of intrinsic universality, which is discussed with…
Cellular Automata(CA) is a discrete computing model which provides simple, flexible and efficient platform for simulating complicated systems and performing complex computation based on the neighborhoods information. CA consists of two…
We introduce a novel framework of reservoir computing, that is capable of both connectionist machine intelligence and symbolic computation. Cellular automaton is used as the reservoir of dynamical systems. Input is randomly projected onto…
It is shown that irreversible classical cellular automata can be performed by quantum algorithm using additional ancilla registers. The algorithm for cellular automata states analysis has been proposed. This algorithm is based on the…
The theory of cellular automata in operational probabilistic theories is developed. We start introducing the composition of infinitely many elementary systems, and then use this notion to define update rules for such infinite composite…
We say that a Cellular Automata (CA) is coalescing when its execution on two distinct (random) initial configurations in the same asynchronous mode (the same cells are updated in each configuration at each time step) makes both…
Particle-like objects are observed to propagate and interact in many spatially extended dynamical systems. For one of the simplest classes of such systems, one-dimensional cellular automata, we establish a rigorous upper bound on the number…
Neural Cellular Automata (NCA) represent a powerful framework for modeling biological self-organization, extending classical rule-based systems with trainable, differentiable (or evolvable) update rules that capture the adaptive…
This study aims at finding a method for constructing molecular dynamics like models using the formalism of cellular automata for fast simulation of fluid dynamic systems (including compressible phenomena). In as much as the results…
In mathematics and engineering, control theory is concerned with the analysis of dynamical systems through the application of suitable control inputs. One of the prominent problems in control theory is controllability which concerns the…
Emergent processes in complex systems such as cellular automata can perform computations of increasing complexity, and could possibly lead to artificial evolution. Such a feat would require scaling up current simulation sizes to allow for…
We introduce a quantum cellular automaton that achieves approximate phase-covariant cloning of qubits. The automaton is optimized for 1-to-2N economical cloning. The use of the automaton for cloning allows us to exploit different foliations…
In this paper we study the dynamics of 1- and 2- dimensional cellular automata, using a 2-adic representation of the states, we give a simple graphical technique for finding periodic solutions. We also study the continuity properties of the…
We extend a previously introduced semi-analytical representation of a decomposition of CA dynamics in arbitrary dimensions and neighborhood schemes via the use of certain universal maps in which CA rule vectors are derivable from the…
This paper describes a new concept of cellular automaton (CA). XCA consists of a set of arcs (edges) that correspond to cells in CA. At a particular time, the arcs are connected to a directed graph. With each time step, the arcs exchange…
I outline a possible logical path from the formulation of physics of classical mechanics to "abstract" systems like cellular automata. The goal of this article is that of illustrating why physicists often study extremely simplified models,…
Many computer models such as cellular automata and artificial neural networks have been developed and successfully applied. However, in some cases, these models might be restrictive on the possible solutions or their solutions might be…
For an arbitrary group $G$ and arbitrary set $A$, we define a monoid structure on the set of all uniformly continuous functions $A^G\to A$ and then we show that it is naturally isomorphic to the monoid of cellular automata $\mathrm{CA}(G,…