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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

Several proposed schemes for the physical realization of a quantum computer consist of qubits arranged in a cellular array. In the quantum circuit model of quantum computation, an often complex series of two-qubit gate operations is…

Quantum Physics · Physics 2009-11-10 Gavin K. Brennen , Jamie E. Williams

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

Bijections between sets may be seen as discrete (or crisp) unitary transformations used in quantum computations. So discrete quantum cellular automata are cellular automata with reversible transition functions. This note studies on 1d…

Cellular Automata and Lattice Gases · Physics 2007-05-23 Shuichi Inokuchi , Kazumasa Honda , Hyen Yeal Lee , Tatsuro Sato , Yoshihiro Mizoguchi , Yasuo Kawahara

Neural cellular automata (Neural CA) are a recent framework used to model biological phenomena emerging from multicellular organisms. In these systems, artificial neural networks are used as update rules for cellular automata. Neural CA are…

Neural and Evolutionary Computing · Computer Science 2021-07-13 Alexandre Variengien , Stefano Nichele , Tom Glover , Sidney Pontes-Filho

This paper designs an efficient two-class pattern classifier utilizing asynchronous cellular automata (ACAs). The two-state three-neighborhood one-dimensional ACAs that converge to fixed points from arbitrary seeds are used here for pattern…

Cellular Automata and Lattice Gases · Physics 2016-02-01 Biswanath Sethi , Souvik Roy , Sukanta Das

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 research describes a three dimensional quantum cellular automaton (QCA) which can simulate all other 3D QCA. This intrinsically universal QCA belongs to the simplest subclass of QCA: Partitioned QCA (PQCA). PQCA are QCA of a particular…

Quantum Physics · Physics 2017-08-29 Pablo Arrighi , Jonathan Grattage

We study the notion of limit sets of cellular automata associated with probability measures (mu-limit sets). This notion was introduced by P. Kurka and A. Maass. It is a refinement of the classical notion of omega-limit sets dealing with…

Discrete Mathematics · Computer Science 2007-05-23 Laurent Boyer , Victor Poupet , Guillaume Theyssier

The basis for most of the ideas mentioned in this paper is the theory of cellular automata. A cellular automata contains a regular grid of cells, with each cell having a pre-defined set of finite states. The initial state is determined at…

General Mathematics · Mathematics 2022-10-06 Raghavendra Bhat

Cellular automata, CA for short are continuous maps defined on the set of configurations over a finite alphabet A that commutes with the shift. They are characterized by the existence of local function which determine by local behavior the…

Dynamical Systems · Mathematics 2019-04-30 Rezki Chemlal

In a probabilistic cellular automaton in which all local transitions have positive probability, the problem of keeping a bit of information indefinitely is nontrivial, even in an infinite automaton. Still, there is a solution in 2…

Probability · Mathematics 2024-01-26 Peter Gacs

We show that quantum cellular automata naturally form the degree-zero part of a coarse homology theory. The recent result of Ji and Yang that the space of QCA forms an Omega-spectrum in the sense of algebraic topology is a direct…

K-Theory and Homology · Mathematics 2026-03-27 Matthias Ludewig

Clifford quantum cellular automata (CQCAs) are a special kind of quantum cellular automata (QCAs) that incorporate Clifford group operations for the time evolution. Despite being classically simulable, they can be used as basic building…

Quantum Physics · Physics 2010-01-08 Johannes Gütschow

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,…

Cellular automata (CA) consist of an array of identical cells, each of which may take one of a finite number of possible states. The entire array evolves in discrete time steps by iterating a global evolution G. Further, this global…

Discrete Mathematics · Computer Science 2015-03-18 Pablo Arrighi , Renan Fargetton , Vincent Nesme , Eric Thierry

In addition to the $\lambda$ parameter, we have found another parameter which characterize the class III, class II and class IV patterns more quantitatively. It explains why the different classes of patterns coexist at the same $\lambda$.…

Cellular Automata and Lattice Gases · Physics 2007-05-23 Sunao Sakai , Megumi Kanno

We consider Clifford Quantum Cellular Automata (CQCAs) and their time evolution. CQCAs are an especially simple type of Quantum Cellular Automata, yet they show complex asymptotics and can even be a basic ingredient for universal quantum…

Quantum Physics · Physics 2010-02-01 Johannes Gütschow , Sonja Uphoff , Reinhard F. Werner , Zoltán Zimborás

A small-world cellular automaton network has been formulated to simulate the long-range interactions of complex networks using unconventional computing methods in this paper. Conventional cellular automata use local updating rules. The new…

Cellular Automata and Lattice Gases · Physics 2010-03-26 Xin-She Yang , Young Z. L. Yang

In this paper we identify full list of Elementary Cellular Automata rules which can be simulated using a quantum circuit (there are 22 such rules). For every such rule we present quantum circuit implementing it with $O(N)$ gates.

Quantum Physics · Physics 2025-01-14 Dmytro Fedoriaka