Related papers: A new universal cellular automaton on the ternary …
Cellular automata are capable of developing complex behaviors based on simple local interactions between their elements. Some of these characteristics have been used to propose and improve meta-heuristics for global optimization; however,…
We prove that many dynamical properties of group cellular automata (i.e., cellular automata defined on any finite group and with global rule which is an endomorphism), including surjectivity, injectivity, sensitivity to initial conditions,…
We study one-dimensional reversible and number-conserving cellular automata (RNCCA) that have both properties of reversibility and number-conservation. In the case of 2-neighbor RNCCA, Garc\'ia-Ramos proved that every RNCCA shows trivial…
In this paper, we look at the following question. We consider cellular automata in the hyperbolic plane and we consider the global function defined on all possible configurations. Is the injectivity of this function undecidable? The problem…
We present a 2-dimensional cellular automaton model for the simulation of pedestrian dynamics. The model is extremely efficient and allows simulations of large crowds faster than real time since it includes only nearest-neighbour…
This paper studies directional dynamics in cellular automata, a formalism previously introduced by the third author. The central idea is to study the dynamical behaviour of a cellular automaton through the conjoint action of its global rule…
We give a one-dimensional quantum cellular automaton (QCA) capable of simulating all others. By this we mean that the initial configuration and the local transition rule of any one-dimensional QCA can be encoded within the initial…
We introduce a novel method of quantum emulation of a classical reversible cellular automaton. By applying this method to a chaotic cellular automaton, the obtained quantum many-body system thermalizes while all the energy eigenstates and…
The cellular automaton is a widely known model of both reversible and irreversible computations. The family of reversible second-order cellular automata considered in this work is appropriate both for construction of logic gates and…
State-of-the-art review of cellular automata, cellular automata for partial differential equations, differential equations for cellular automata and pattern formation in biology and engineering.
The paper proposes a simple formalism for dealing with deterministic, non-deterministic and stochastic cellular automata in a unifying and composable manner. Armed with this formalism, we extend the notion of intrinsic simulation between…
As quantum devices scale to larger and larger sizes, a significant challenge emerges in scaling their coherent controls accordingly. Quantum cellular automata (QCAs) constitute a promising framework that bypasses this control problem:…
We show that a cellular automaton (or shift-endomorphism) on a transitive subshift is either almost equicontinuous or sensitive. On the other hand, we construct a cellular automaton on a full-shift (hence a transitive subshift) that is…
Reversibility of a one-dimensional finite cellular automaton (CA) is dependent on lattice size. A finite CA can be reversible for a set of lattice sizes. On the other hand, reversibility of an infinite CA, which is decided by exploring the…
This article determines and characterizes the minimal number of actuators needed to ensure structural controllability of a linear system under structural alterations that can severe the connection between any two states. We assume that…
The state of structural balance (termed also `Heider balance') of a social network is often discussed in social psychology and sociophysics. In this state, actors at network nodes classify other individuals as enemies or friends. Hence, the…
The properties of two-state nearest-neighbour cellular automata (CA) that are capable of density classification are discussed. It is shown that these CA actually conserve the total density, rather than merely classifying it. This is also…
Cellular automata are a discrete dynamical system which models massively parallel computation. Much attention is devoted to computations with small time complexity for which the parallelism may provide further possibilities. In this paper,…
We investigate the mean dimension of a cellular automaton (CA for short) with a compact non-discrete space of states. A formula for the mean dimension is established for (near) strongly permutative, permutative algebraic and unit…
Cellular automata have long been celebrated for their ability to generate complex behaviors from simple, local rules, with well-known discrete models like Conway's Game of Life proven capable of universal computation. Recent advancements…