Related papers: A sequential solution to the density classificatio…
We discuss example of an elementary cellular automaton for which the density of ones decays toward its limiting value as a power of the number of iterations $n$. Using the fact that this rule conserves the number of blocks 10 and that…
Cellular Automata (CA) are common and most simple models of parallel computations. Edge detection is one of the crucial task in image processing, especially in processing biological and medical images. CA can be successfully applied in…
In this paper, we develop a new cellular automata-based linear model for several nonlinear pseudorandom number generators with practical applications in symmetric cryptography. Such a model generates all the solutions of linear binary…
The transport and chemical reactions of solutes are modelled as a cellular automaton in which molecules of different species perform a random walk on a regular lattice and react according to a local probabilistic rule. The model describes…
Using FSA and the construction algorithm, we generated a list of surjective span 6 cellular automata as a modest sample for our FDense program. We wanted to experimentally quantify Mike Boyle's conjecture which states that the jointly…
This study focuses on an extended model of a standard cellular automaton (CA) that includes an extra index consisting of a radius that defines a perception area for each cell in addition to the radius defined by the CA rule. Extended…
We add small random perturbations to a cellular automaton and consider the one-parameter family $(F_\epsilon)_{\epsilon>0}$ parameterized by $\epsilon$ where $\epsilon>0$ is the level of noise. The objective of the article is to study the…
We propose a novel density based numerical method for uncertainty propagation under certain partial differential equation dynamics. The main idea is to translate them into objects that we call cellular probabilistic automata and to evolve…
We present a new analytical description of the cellular automaton model for single-lane traffic. In contrast to previous approaches we do not use the occupation number of sites as dynamical variable but rather the distance between…
In this paper we study the statistical properties of a reversible cellular automaton in two out-of-equilibrium settings. In the first part we consider two instances of the initial value problem, corresponding to the inhomogeneous quench and…
Given $iid$ observations from an unknown absolute continuous distribution defined on some domain $\Omega$, we propose a nonparametric method to learn a piecewise constant function to approximate the underlying probability density function.…
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…
Computing the configuration of any one-dimensional cellular automaton at generation $n$ can be accelerated by constructing and running a composite rule with a radius proportional to $\log n$. The new automaton is the original one, but with…
We study qualitative properties of two-dimensional freezing cellular automata with a binary state set initialized on a random configuration. If the automaton is also monotone, the setting is equivalent to bootstrap percolation. We explore…
Determining properties of an arbitrary binary sequence is a challenging task if only local processing is allowed. Among these properties, the determination of the parity of 1s by distributed consensus has been a recurring endeavour in the…
We prove that a random automaton with $n$ states and any fixed non-singleton alphabet is synchronizing with high probability (modulo an unpublished result about unique highest trees of random graphs). Moreover, we also prove that the…
Cellular automata are one-dimensional arrays of interconnected interacting finite automata. We investigate one of the weakest classes, the real-time one-way cellular automata, and impose an additional restriction on their inter-cell…
Microscopic modeling of multi-lane traffic is usually done by applying heuristic lane changing rules, and often with unsatisfying results. Recently, a cellular automaton model for two-lane traffic was able to overcome some of these problems…
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…
We consider two relatively natural topologizations of the set of all cellular automata on a fixed alphabet. The first turns out to be rather pathological, in that the countable space becomes neither first-countable nor sequential. Also,…