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Recently, Land and Belew [Phys. Rev. Lett. 74, 5148 (1995)] have shown that no one-dimensional two-state cellular automaton which classifies binary strings according to their densities of 1's and 0's can be constructed. We show that a pair…

comp-gas · Physics 2009-10-30 Henryk Fuks

The density classification problem is the computational problem of finding the majority in a given array of votes in a distributed fashion. It is known that no cellular automaton rule with binary alphabet can solve the density…

Cellular Automata and Lattice Gases · Physics 2016-04-18 Nazim Fatès , Irène Marcovici , Siamak Taati

The density classification task is a famous problem in the theory of cellular automata. It is unsolvable for deterministic automata, but recently solutions for stochastic cellular automata have been found. One of them is a set of stochastic…

Cellular Automata and Lattice Gases · Physics 2019-07-22 Markus Redeker

Suppose each site on a one-dimensional chain with periodic boundary condition may take on any one of the states $0,1,..., n-1$, can you find out the most frequently occurring state using cellular automaton? Here, we prove that while the…

adap-org · Physics 2015-06-24 H. F. Chau , L. W. Siu , K. K. Yan

While binary nearest-neighbour cellar automata (CA) have been studied in detail and from many different angles, the same cannot be said about ternary (three-state) CA rules. We present some results of our explorations of a small subset of…

Cellular Automata and Lattice Gases · Physics 2023-12-18 H. Fukś , R. Procyk

The purpose of the present study is to search one-dimensional Cellular Automata (CA) rules which will solve the density classification task (DCT) perfectly. The mathematical analysis of number conserving functions over binary strings of…

Cellular Automata and Lattice Gases · Physics 2016-07-26 Suryakanta Pal , Sudhakar Sahoo , Birendra Kumar Nayak

The density classification (DC) task, a computation which maps global density information to local density, is studied using one-dimensional non-unitary quantum cellular automata (QCAs). Two approaches are considered: one that preserves the…

Quantum Physics · Physics 2025-01-22 Elisabeth Wagner , Federico Dell'Anna , Ramil Nigmatullin , Gavin K. Brennen

This paper presents solutions to Density Classification Task (DCT) using a variant of Cellular Automata (CA) called Programmable Cellular Automata (PCA). The translation property as well as the density preserving property of fundamental CA…

Cellular Automata and Lattice Gases · Physics 2009-02-17 Sudhakar Sahoo , Pabitra Pal Choudhury , Amita Pal , Birendra Kumar Nayak

We present a probabilistic cellular automaton (CA) with two absorbing states which performs classification of binary strings in a non-deterministic sense. In a system evolving under this CA rule, empty sites become occupied with a…

Cellular Automata and Lattice Gases · Physics 2009-11-10 Henryk Fuks

Given a (finite) string of zeros and ones, we report a way to determine if the number of ones is less than, greater than, or equal to a prescribed number by applying two sets of cellular automaton rules in succession. Thus, we solve the…

adap-org · Physics 2009-10-30 H. F. Chau , K. K. Yan , K. Y. Wan , L. W. Siu

We consider the problem of finding the density of 1's in a configuration obtained by $n$ iterations of a given cellular automaton (CA) rule, starting from disordered initial condition. While this problems is intractable in full generality…

Cellular Automata and Lattice Gases · Physics 2023-12-18 Henryk Fukś , José Manuel Gómez Soto

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…

Statistical Mechanics · Physics 2009-10-30 Kai Nagel , Dietrich E Wolf , Peter Wagner , Patrice Simon

The global majority problem, often referred to as the Density Classification Task, is a classical benchmark in the context of probing the computational capabilities of automata networks. It poses the simple yet challenging problem of…

Discrete Mathematics · Computer Science 2026-03-23 Pedro Paulo Balbi , Kévin Perrot , Marius Rolland , Eurico Ruivo

The Majority (or Density Classification) Problem in Cellular Automata (CA) aims to converge a string of cells to a final homogeneous state which reflects the majority of states present in the initial configuration. The problem is…

Emerging Technologies · Computer Science 2016-06-21 Jeff Jones

We consider the problem of computing a response curve for binary cellular automata -- that is, the curve describing the dependence of the density of ones after many iterations of the rule on the initial density of ones. We demonstrate how…

Cellular Automata and Lattice Gases · Physics 2023-12-18 Henryk Fukś

We investigate number conserving cellular automata with up to five inputs and two states with the goal of comparing their dynamics with diffusion. For this purpose, we introduce the concept of decompression ratio describing expansion of…

Cellular Automata and Lattice Gases · Physics 2023-12-18 Henryk Fukś , Sanchala Abeykoon Mudiyanselage

We consider the problem of computing a response curve for binary cellular automata -- that is, the curve describing the dependence of the density of ones after many iterations of the rule on the initial density of ones. We demonstrate how…

Cellular Automata and Lattice Gases · Physics 2023-12-18 Henryk Fukś , Andrew Skelton

We present analytical results for first-passage processes in a deterministic one-dimensional cellular automaton (CA) model of traffic flow. Starting at time $t=0$ from a random initial state with car density p, at every time step $t\ge 1$…

Statistical Mechanics · Physics 2026-05-20 Ofer Biham , Gilad Hertzberg Rabinovich , Eytan Katzav

This paper presents a novel approach to the description and understanding of two-dimensional binary cellular automata with the Moore neighborhood that preserve the number of active cells. Such dynamical systems are known to successfully…

Dynamical Systems · Mathematics 2025-12-10 B. Wolnik , D. M. Falkiewicz , W. Bołt , A. Rutkowski , B. De Baets

This paper deals with the theory and application of 2-Dimensional, nine-neighborhood, null- boundary, uniform as well as hybrid Cellular Automata (2D CA) linear rules in image processing. These rules are classified into nine groups…

Discrete Mathematics · Computer Science 2008-04-16 Pabitra Pal Choudhury , Birendra Kumar Nayak , Sudhakar Sahoo , Sunil Pankaj Rath
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