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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

We discovered that certain patterns called injective patterns remain stable during the revolution process, allowing us to create many reversible CA simply by using them to design the revolution rules. By examining injective patterns, we…

Computational Complexity · Computer Science 2023-09-28 Defu Lin , Weilin Chen , Chen Wang , Junchi Ma , Chao Wang

Every Latin square has three attributes that can be even or odd, but any two of these attributes determines the third. Hence the parity of a Latin square has an information content of 2 bits. We extend the definition of parity from Latin…

Combinatorics · Mathematics 2018-01-10 Nevena Francetić , Sarada Herke , Ian M. Wanless

Regarding neighbor balance, we consider natural generalizations of $D$-complete Latin squares and Vatican squares from the finite to the infinite. We show that if $G$ is an infinite abelian group with $|G|$-many square elements, then it is…

Combinatorics · Mathematics 2018-07-24 Anthony B. Evans , Gage N. Martin , Kaethe Minden , M. A. Ollis

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…

Cryptography and Security · Computer Science 2010-05-04 Pino Caballero-Gil , Amparo Fúster-Sabater , Oscar Delgado-Mohatar

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

Every transitive cellular automaton (CA) is sensitive to initial conditions. We study this implication in the more general context of non-uniform cellular automata (NUCA) with finitely many different local update rules assigned to cells. We…

Dynamical Systems · Mathematics 2026-05-22 Supreeti Kamilya , Jarkko Kari , Katariina Paturi

Topological dynamics of cellular automata (CA), inherited from classical dynamical systems theory, has been essentially studied in dimension 1. This paper focuses on higher dimensional CA and aims at showing that the situation is different…

Discrete Mathematics · Computer Science 2009-09-03 Mathieu Sablik , Guillaume Theyssier

Cellular Automata(CA) is a discrete computing model which provides simple, flexible and efficient platform for simulating complicated systems and performing complex computation based on the neighborhoods information. CA consists of two…

Distributed, Parallel, and Cluster Computing · Computer Science 2011-12-12 Debasis Das , Rajiv Misra

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…

Formal Languages and Automata Theory · Computer Science 2009-07-30 Martin Kutrib , Andreas Malcher

In recent work [quant-ph/0405174] by Schumacher and Werner was discussed an abstract algebraic approach to a model of reversible quantum cellular automata (CA) on a lattice. It was used special model of CA based on partitioning scheme and…

Quantum Physics · Physics 2007-05-23 Alexander Yu. Vlasov

A novel two-state, Reversible Cellular Automata (RCA) is described. This three-dimensional RCA is shown to be capable of universal computation. Additionally, evidence is offered that this RCA Is capable of universal construction.

Cellular Automata and Lattice Gases · Physics 2007-05-23 Daniel B. Miller , Edward Fredkin

In this paper we initiate the study of cellular automata on racks. A rack $R$ is a set with a self-distributive binary operation. The rack $R$ acts on the set $A^R$ of configurations from $R$ to a set $A$. We define the cellular automaton…

Group Theory · Mathematics 2018-08-01 Naqeeb ur Rehman , Muhammad Khuram Shahzad

We present results from an experiment similar to one performed by Packard (1988), in which a genetic algorithm is used to evolve cellular automata (CA) to perform a particular computational task. Packard examined the frequency of evolved CA…

adap-org · Physics 2008-02-03 Melanie Mitchell , Peter Hraber , James P. Crutchfield

In this paper, we first present the relation between a transversal in a Latin square with some concepts in its Latin square graph, and give an equivalent condition for a Latin square has an orthogonal mate. The most famous open problem…

Combinatorics · Mathematics 2018-08-17 Adel P. Kazemi , Behnaz Pahlavsay

We show that the sets of $d$-dimensional Latin hypercubes over a non-empty set $X$, with $d$ running over the positive integers, determine an operad which is isomorphic to a sub-operad of the endomorphism operad of $X$. We generalise this…

Combinatorics · Mathematics 2025-08-06 Markus Linckelmann

In this paper we consider cellular automata $(\mathfrak{G},\Phi)$ with algebraic local rules and such that $\mathfrak{G}$ is a topological Markov chain which has a structure compatible to this local rule. We characterize such cellular…

Dynamical Systems · Mathematics 2017-02-15 Marcelo Sobottka

Cellular Automata (CA) are discrete dynamical systems and an abstract model of parallel computation. The limit set of a cellular automaton is its maximal topological attractor. A well know result, due to Kari, says that all nontrivial…

Dynamical Systems · Mathematics 2009-02-10 Pietro Di Lena , Luciano Margara

We discuss the role of classical control in the context of reversible quantum cellular automata. Employing the structure theorem for quantum cellular automata, we give a general construction scheme to turn an arbitrary cellular automaton…

Quantum Physics · Physics 2009-11-11 D. J. Shepherd , T. Franz , R. F. Werner

Let us consider the simplest model of one-dimensional probabilistic cellular automata (PCA). The cells are indexed by the integers, the alphabet is {0, 1}, and all the cells evolve synchronously. The new content of a cell is randomly…

Probability · Mathematics 2012-07-26 Jean Mairesse , Irene Marcovici