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This work introduces a new problem, named as, affinity classification problem which is a generalization of the density classification problem. To solve this problem, we introduce temporally stochastic cellular automata where two rules are…

Formal Languages and Automata Theory · Computer Science 2022-07-13 Kamalika Bhattacharjee , Subrata Paul , Sukanta Das

Probing the ability of automata networks to solve decision problems has received a continuous attention in the literature, and specially with the automata reaching the answer by distributed consensus, i.e., their all taking on a same state,…

Discrete Mathematics · Computer Science 2025-10-24 Eurico Ruivo , Pedro Paulo Balbi , Kévin Perrot , Marco Montalva-Medel , Eric Goles

The density classification task is to determine which of the symbols appearing in an array has the majority. A cellular automaton solving this task is required to converge to a uniform configuration with the majority symbol at each site. It…

Probability · Mathematics 2015-03-30 Siamak Taati

While the surjectivity of the global map in two-dimensional cellular automata (2D CA) is undecidable in general, in specific cases one can often decide if the rule is surjective or not. We attempt to classify as many 2D CA as possible by…

Cellular Automata and Lattice Gases · Physics 2012-08-06 Henryk Fukś , Andrew Skelton

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…

comp-gas · Physics 2007-05-23 N. Sukumar

We investigate the density classification task (DCT) -- determining the majority bit in a one-dimensional binary lattice -- within a quantum cellular automaton (CA) framework. While there is no one-dimensional two-state, radius $r \geq 1$,…

Quantum Physics · Physics 2025-10-09 Pedro C. S. Costa , Yuval R. Sanders , Pedro Paulo Balbi , Gavin K. Brennen

We consider the problem of finding response curves for a class of binary two-dimensional cellular automata with $L$-shaped neighbourhood. We show that the dependence of the density of ones after an arbitrary number of iterations, on the…

Cellular Automata and Lattice Gases · Physics 2011-08-09 Henryk Fukś , Andrew Skelton

We investigate a cellular automaton (CA) model of traffic on a bi-directional two-lane road. Our model is an extension of the one-lane CA model of {Nagel and Schreckenberg 1992}, modified to account for interactions mediated by passing, and…

Statistical Mechanics · Physics 2009-10-31 Patrice Simon , Howard A Gutowitz

We propose a four-way classification of two-dimensional semi-totalistic cellular automata that is different than Wolfram's, based on two questions with yes-or-no answers: do there exist patterns that eventually escape any finite bounding…

Cellular Automata and Lattice Gases · Physics 2010-09-02 David Eppstein

Consider an infinite graph with nodes initially labeled by independent Bernoulli random variables of parameter p. We address the density classification problem, that is, we want to design a (probabilistic or deterministic) cellular…

Probability · Mathematics 2011-11-22 Ana Busic , Nazim Fates , Jean Mairesse , Irene Marcovici

We study a two-dimensional cellular automaton (CA), called Diffusion Rule (DR), which exhibits diffusion-like dynamics of propagating patterns. In computational experiments we discover a wide range of mobile and stationary localizations…

Formal Languages and Automata Theory · Computer Science 2015-05-13 Genaro J. Martinez , Andrew Adamatzky , Harold V. McIntosh

We have determined families of two-dimensional deterministic totalistic cellular automaton rules whose stationary density of active sites exhibits a period two in time. Each family of deterministic rules is characterized by an ``average…

adap-org · Physics 2015-06-24 Nino Boccara , Michel Roger

The rule 184 fuzzy cellular automaton is regarded as a mathematical model of traffic flow because it contains the two fundamental traffic flow models, the rule 184 cellular automaton and the Burgers equation, as special cases. We show that…

Pattern Formation and Solitons · Physics 2020-04-14 Kohei Higashi , Junkichi Satsuma , Tetsuji Tokihiro

The objective is to find a Cellular Automata rule that can form a 2D point pattern with a maximum number of points (1-cells). Points are not allowed to touch each other, they have to be separated by 0-cells, and every 0-cell can find at…

Computational Geometry · Computer Science 2022-02-15 Rolf Hoffmann

We propose a stochastic cellular-automaton model for two-lane traffic flow based on the misanthrope process in one dimension. The misanthrope process is a stochastic process allowing for an exact steady-state solution; hence we have an…

Cellular Automata and Lattice Gases · Physics 2011-06-22 Masahiro Kanai

We introduce density dependence of the cell size in cellular-automaton models for traffic flow, which allows a more precise correspondence between real-world phenomena and what observed in simulation. Also, we give an explicit calibration…

Cellular Automata and Lattice Gases · Physics 2015-05-18 Masahiro Kanai

To advance our understanding of Quantum Cellular Automata in problem solving through parallel and distributed computing, this research quantized the density classification problem and adopted the Quantum Particle Automata (QPA) to solve the…

Quantum Physics · Physics 2015-01-27 Tina Yu , Radel Ben-Av

We analyze the steady-state flow as a function of the initial density for a class of deterministic cellular automata rules (``traffic rules'') with periodic boundary conditions [H. Fuks and N. Boccara, Int. J. Mod. Phys. C 9, 1 (1998)]. We…

Cellular Automata and Lattice Gases · Physics 2007-05-23 Janne V. Kujala , Tuomas J. Lukka

Modeling and control of agent-based models is twice cursed by the dimensionality of the problem, as both the number of agents and their state space dimension can be large. Even though the computational barrier posed by a large ensemble of…

Optimization and Control · Mathematics 2025-07-16 Giacomo Albi , Sara Bicego , Dante Kalise

Cellular automata (CA) dynamics are ordered in terms of two global parameters, computable {\sl a priori} from the description of rules. While one of them (activity) has been used before, the second one is new; it estimates the average…

adap-org · Physics 2009-10-22 P. -M. Binder