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Structural properties of two well-known families of keystream generators, Shrinking Generators and Cellular Automata, have been analyzed. Emphasis is on the equivalence of the binary sequences obtained from both kinds of generators. In…

Cryptography and Security · Computer Science 2010-06-10 Amparo Fúster-Sabater , Dolores de la Gu'\ia-Martínez

Failure to find homogeneous scalar unitary cellular automata (CA) in one dimension led to consideration of only ``approximately unitary'' CA---which motivated our recent proof of a No-go Lemma in one dimension. In this note we extend the…

Quantum Physics · Physics 2009-10-30 David A. Meyer

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

Topological dynamics of cellular automata (CA), inherited from classical dynamical systems theory, has been essentially studied in dimension 1. This paper focuses on 2D CA and aims at showing that the situation is different and more…

Discrete Mathematics · Computer Science 2009-04-29 Mathieu Sablik , Guillaume Theyssier

In this work we provide analytic results of infinite one-dimensional cellular automaton(CA). By realizing symbolic products, we investigate a subclass of infinite CA and prove analytically that within this subclass the only allowed…

Cellular Automata and Lattice Gases · Physics 2009-11-07 Ru-Fen Liu , Chia-Chu Chen

The cellular automata (CA) approach to traffic modeling is extended to allow for spatially homogeneous steady state solutions that cover a two dimensional region in the flow-density plane. Hence these models fulfill a basic postulate of a…

Statistical Mechanics · Physics 2009-11-07 Boris S. Kerner , Sergey L. Klenov , Dietrich E. Wolf

This paper considers interactions between cellular automata and cryptology. It is known that non-linear elementary rule which is correlation-immune don't exist. This results limits the use of cellular automata as pseudo-random generators…

Cryptography and Security · Computer Science 2008-07-16 Bruno Martin

We present a preliminary study of a new class of two-input cellular automata called eventually number-conserving cellular automata characterized by the property of evolving after a finite number of time steps to states whose number of…

Disordered Systems and Neural Networks · Physics 2007-05-23 Nino Boccara

The searching for the stable patterns in the evolution of cellular automata is implemented using stochastic synchronization between the present structures of the system and its precedent configurations. For most of the known evolution rules…

Cellular Automata and Lattice Gases · Physics 2007-05-23 J. R. Sanchez , R. Lopez-Ruiz

Global dynamics of a non-linear Cellular Automata is, in general irregular, asymmetric and unpredictable as opposed to that of a linear CA, which is highly systematic and tractable. In the past efforts have been made to systematize…

Computational Complexity · Computer Science 2008-08-13 Sudhakar Sahoo , Pabitra Pal Choudhury , Mithun Chakraborty

Computing the configuration of any one-dimensional cellular automaton at generation $n$ can be accelerated by constructing and running a composite rule with a radius proportional to $\log n$. The new automaton is the original one, but with…

Computational Complexity · Computer Science 2025-11-04 Joseph Natal , Oleksiy Al-saadi

This paper studies two kinds of simulation between cellular automata: simulations based on factor and simulations based on sub-automaton. We show that these two kinds of simulation behave in two opposite ways with respect to the complexity…

Discrete Mathematics · Computer Science 2010-12-01 Pierre Guillon , Pierre-Etienne Meunier , Guillaume Theyssier

In this paper we provide an analytical study of the theory of multi-valued and fuzzy cellular automata where the fuzziness appears as the result of the application of an underlying multi-valued or continuous logic as opposed to standard…

Logic in Computer Science · Computer Science 2007-06-13 Angelo B. Mingarelli

We consider the parity problem in one-dimensional, binary, circular cellular automata: if the initial configuration contains an odd number of 1s, the lattice should converge to all 1s; otherwise, it should converge to all 0s. It is easy to…

Formal Languages and Automata Theory · Computer Science 2012-08-15 Heater Betel , Pedro P. B. de Oliveira , Paola Flocchini

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

Deep learning techniques have recently demonstrated broad success in predicting complex dynamical systems ranging from turbulence to human speech, motivating broader questions about how neural networks encode and represent dynamical rules.…

Cellular Automata and Lattice Gases · Physics 2020-01-20 William Gilpin

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 (CAs) are fully-discrete dynamical models that have received much attention due to the fact that their relatively simple setup can nonetheless express highly complex phenomena. Despite the model's theoretical maturity and…

Cellular Automata and Lattice Gases · Physics 2025-07-10 Michiel Rollier , Kallil M. C. Zielinski , Aisling J. Daly , Odemir M. Bruno , Jan M. Baetens

We investigate the mean dimension of a cellular automaton (CA for short) with a compact non-discrete space of states. A formula for the mean dimension is established for (near) strongly permutative, permutative algebraic and unit…

Dynamical Systems · Mathematics 2021-05-21 David Burguet , Ruxi Shi

A subset of 10 of the 256 elementary cellular automata (ECA) are implemented as a hash function using an error minimization lossy compression algorithm operating on wrapped 4x4 neighborhood cells. All 256 rules are processed and 10 rules in…

Cellular Automata and Lattice Gases · Physics 2025-06-10 Daniel McKinley