English
Related papers

Related papers: Discrete Baker Transformation and Cellular Automat…

200 papers

Cellular automata (CA) are a class of computational models that exhibit rich dynamics emerging from the local interaction of cells arranged in a regular lattice. In this work we focus on a generalised version of typical CA, called graph…

Machine Learning · Computer Science 2021-10-28 Daniele Grattarola , Lorenzo Livi , Cesare Alippi

Cellular automata are discrete dynamical systems that consist of patterns of symbols on a grid, which change according to a locally determined transition rule. In this paper, we will consider cellular automata that arise from polynomial…

Combinatorics · Mathematics 2016-04-13 Bertrand Stone

Cellular automata are dynamical systems defined on lattices and commuting with the Bernoulli shift. In this work, we focus on the spectral properties of D-dimensional cellular automata. We give a characterization of their spectrum from both…

Dynamical Systems · Mathematics 2025-09-03 Nassima Ait Sadi , Rezki Chemlal

In this paper, linear Cellular Automta (CA) rules are recursively generated using a binary tree rooted at "0". Some mathematical results on linear as well as non-linear CA rules are derived. Integers associated with linear CA rules are…

Cellular Automata and Lattice Gases · Physics 2012-09-04 Birendra Kumar Nayak , Sudhakar Sahoo , Sagarika Biswal

We define and study a few properties of a class of random automata networks. While regular finite one-dimensional cellular automata are defined on periodic lattices, these automata networks, called randomized cellular automata, are defined…

Cellular Automata and Lattice Gases · Physics 2009-11-13 Nino Boccara

This work studies Temporally Non-Uniform Cellular Automata (t-NUCAs), a variant of non-uniform cellular automata, which temporally use two rules in a sequence during their evolution. The one-dimensional t-NUCAs, under finite as well as…

Formal Languages and Automata Theory · Computer Science 2026-03-24 Subrata Paul , Sukanta Das

We say that a Cellular Automata (CA) is coalescing when its execution on two distinct (random) initial configurations in the same asynchronous mode (the same cells are updated in each configuration at each time step) makes both…

Cellular Automata and Lattice Gases · Physics 2007-12-13 Jean-Baptiste Rouquier , Michel Morvan

In this paper we present two interesting properties of stochastic cellular automata that can be helpful in analyzing the dynamical behavior of such automata. The first property allows for calculating cell-wise probability distributions over…

Formal Languages and Automata Theory · Computer Science 2015-08-20 Witold Bołt , Jan M. Baetens , Bernard DeBaets

We introduce an efficient cellular automaton for the coagulation-fission process with diffusion 2A->3A, 2A->A in arbitrary dimensions. As the well-known Domany-Kinzel model, it is defined on a tilted hypercubic lattice and evolves by…

Statistical Mechanics · Physics 2009-11-07 Haye Hinrichsen

A wide family of nonlinear sequence generators, the so-called clock-controlled shrinking generators, has been analyzed and identified with a subset of linear cellular automata. The algorithm that converts the given generator into a linear…

Cryptography and Security · Computer Science 2010-05-19 Amparo Fúster-Sabater

We provide a categorical procedure to turn graphs corresponding to state spaces of finite state machines into boolean circuits, leveraging on the fact that boolean circuits can be easily turned into zk-SNARKS. Our circuits verify that a…

Cryptography and Security · Computer Science 2019-09-17 Fabrizio Genovese , Andre Knispel , Joshua Fitzgerald

If X is a discrete abelian group and B a finite set, then a cellular automaton (CA) is a continuous map F:B^X-->B^X that commutes with all X-shifts. If g is a real-valued function on B, then, for any b in B^X, we define G(b) to be the sum…

Dynamical Systems · Mathematics 2009-11-07 Marcus Pivato

Cellular automata can show well known features of quantum mechanics, such as a linear rule according to which they evolve and which resembles a discretized version of the Schroedinger equation. This includes corresponding conservation laws.…

Quantum Physics · Physics 2016-04-25 Hans-Thomas Elze

We study a quantum cellular automaton (QCA) whose time-evolution is defined from global transition function of classical cellular automata (CA). In order to investigate natural transformations from CA to QCA, the present QCA includes CA…

Quantum Physics · Physics 2009-11-11 Norio Inui , Shuichi Inokuchi , Yoshihiro Mizoguchi , Norio Konno

We propose a calibrated two-dimensional cellular automaton model to simulate pedestrian motion behavior. It is a v=4 (3) model with exclusion statistics and random shuffled dynamics. The underlying regular grid structure results in a…

Physics and Society · Physics 2021-04-01 Michael Schultz , Hartmut Fricke

If L=Z^D and A is a finite set, then A^L is a compact space. A cellular automaton (CA) is a continuous transformation F:A^L--> A^L that commutes with all shift maps. A quasisturmian (QS) subshift is a shift-invariant subset obtained by…

Dynamical Systems · Mathematics 2007-05-23 Marcus Pivato

We propose a correspondence between certain multiband linear cellular automata - models of computation widely used in the description of physical phenomena - and endomorphisms of certain algebraic unipotent groups over finite fields. The…

Dynamical Systems · Mathematics 2024-04-22 Jakub Byszewski , Gunther Cornelissen

This paper introduces a hierarchical cellular automaton (HCA)model for simulation of distributed self-organizing control of traffic signals at intersections in road network. The proposed HCA consists of three hierarchy levels that describe…

Systems and Control · Computer Science 2018-10-01 Bartłomiej Płaczek

We study spontaneous symmetry breaking in a one-dimensional driven two-species stochastic cellular automaton with parallel sublattice update and open boundaries. The dynamics are symmetric with respect to interchange of particles. Starting…

Statistical Mechanics · Physics 2009-11-11 Stefan Grosskinsky , Gunter M. Schutz , Richard D. Willmann

Probabilistic cellular automata (CA) provides a classic framework for studying non-equilibrium statistical physics on a lattices. A notable example is the Domany-Kinzel CA, which has been used to investigate the process of directed…

Quantum Physics · Physics 2022-04-26 Ramil Nigmatullin , Elisabeth Wagner , Gavin K. Brennen