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We give a one-dimensional quantum cellular automaton (QCA) capable of simulating all others. By this we mean that the initial configuration and the local transition rule of any one-dimensional QCA can be encoded within the initial…

Quantum Physics · Physics 2008-12-10 Pablo Arrighi , Renan Fargetton , Zizhu Wang

In this work, we investigate the computational aspects of asynchronous cellular automata (ACAs), a modification of cellular automata in which cells update independently, following an asynchronous schedule. We introduce flip automata…

Formal Languages and Automata Theory · Computer Science 2025-10-20 Ivan Baburin , Matthew Cook , Florian Grötschla , Andreas Plesner , Roger Wattenhofer

We present a simple one-dimensional Cellular Automaton (CA) which has the property that an initial state composed of two binary numbers evolves quickly into a final state which is their sum. We call this CA the Adding Cellular Automaton…

Mesoscale and Nanoscale Physics · Physics 2009-10-28 Simon C. Benjamin , Neil F. Johnson

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

The cellular automaton is a widely known model of both reversible and irreversible computations. The family of reversible second-order cellular automata considered in this work is appropriate both for construction of logic gates and…

Cellular Automata and Lattice Gases · Physics 2024-05-10 Alexander Yu. Vlasov

We introduce a scheme to perform universal quantum computation in quantum cellular automata (QCA) fashion in arbitrary subsystem dimension (not necessarily finite). The scheme is developed over a one spatial dimension $N$-element array,…

Quantum Physics · Physics 2010-09-02 G. A. Paz-Silva , G. K. Brennen , J. Twamley

We describe a simple n-dimensional quantum cellular automaton (QCA) capable of simulating all others, in that the initial configuration and the forward evolution of any n-dimensional QCA can be encoded within the initial configuration of…

Quantum Physics · Physics 2010-10-13 Pablo Arrighi , Jonathan Grattage

This work studies some aspects of the computational power of fully asynchronous cellular automata (ACA). We deal with some notions of simulation between ACA and Turing Machines. In particular, we characterize the updating sequences…

Formal Languages and Automata Theory · Computer Science 2011-05-03 Jérôme Chandesris , Alberto Dennunzio , Enrico Formenti , Luca Manzoni

Cellular Automata (CA), as they are presented in the literature, are abstract mathematical models of computation. In this pa- per we present an alternate approach: using the CA as a model or theory of physical systems and devices. While…

Discrete Mathematics · Computer Science 2008-09-11 Donny Cheung , Carlos A. Perez-Delgado

In this paper, we construct a strongly universal cellular automaton on the line with 11 states and the standard neighbourhood. We embed this construction into several tilings of the hyperbolic plane and of the hyperbolic 3D space giving…

Discrete Mathematics · Computer Science 2013-09-09 Maurice Margenstern

Invertible cellular automata are useful as models of physical systems with microscopically revesible dyanmics. There are several well-understood ways to construct them: partitioning rules, second-order rules, and alternating-grid rules. We…

Cellular Automata and Lattice Gases · Physics 2015-09-30 Benjamin Schumacher , Michael D. Westmoreland

A Cellular Automata (CA) is a computing model of complex System using simple rule. In CA the problem space into number of cell and each cell can be one or several final state. Cells are affected by neighbours' to the simple rule. Cellular…

Cryptography and Security · Computer Science 2010-06-15 Debasis Das , Abhishek Ray

While for synchronous deterministic cellular automata there is an accepted definition of reversibility, the situation is less clear for asynchronous cellular automata. We first discuss a few possibilities and then investigate what we call…

Formal Languages and Automata Theory · Computer Science 2012-08-15 Simon Wacker , Thomas Worsch

We show how to perform reversible universal quantum computation on a translationally invariant pure state, using only global operations based on next-neighbor interactions. We do not need not to break the translational symmetry of the state…

Quantum Physics · Physics 2009-11-11 K. G. H. Vollbrecht , J. I. Cirac

In this dissertation, we study two of the global properties of 1-dimensional cellular automata (CAs) under periodic boundary condition, namely, reversibility and randomness. To address reversibility of finite CAs, we develop a mathematical…

Formal Languages and Automata Theory · Computer Science 2019-11-12 Kamalika Bhattacharjee

Physical universality of a cellular automaton was defined by Janzing in 2010 as the ability to implement an arbitrary transformation of spatial patterns. In 2014, Schaeffer gave a construction of a two-dimensional physically universal…

Formal Languages and Automata Theory · Computer Science 2016-02-22 Ville Salo , Ilkka Törmä

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

Parallel algorithms for solving any image processing task is a highly demanded approach in the modern world. Cellular Automata (CA) are the most common and simple models of parallel computation. So, CA has been successfully used in the…

Computer Vision and Pattern Recognition · Computer Science 2014-07-30 Deepak Ranjan Nayak , Prashanta Kumar Patra , Amitav Mahapatra

While the reversibility of multidimensional cellular automata is undecidable and there exists a criterion for determining if a multidimensional linear cellular automaton is reversible, there are only a few results about the reversibility…

Dynamical Systems · Mathematics 2017-05-24 Chih-Hung Chang , Hasan Akın

We describe a class of cellular automata (CAs) that are end-to-end differentiable. DCAs interpolate the behavior of ordinary CAs through rules that act on distributions of states. The gradient of a DCA with respect to its parameters can be…

Discrete Mathematics · Computer Science 2017-09-01 Carlos Martin