相关论文: Discrete Baker Transformation and Cellular Automat…
In a recent paper Sutner proved that the first-order theory of the phase-space $\mathcal{S}_\mathcal{A}=(Q^\mathbb{Z}, \longrightarrow)$ of a one-dimensional cellular automaton $\mathcal{A}$ whose configurations are elements of…
A necessary and sufficient condition for a one-dimensional q-state n-input cellular automaton rule to be number-conserving is established. Two different forms of simpler and more visual representations of these rules are given, and their…
A natural architecture for nanoscale quantum computation is that of a quantum cellular automaton. Motivated by this observation, in this paper we begin an investigation of exactly unitary cellular automata. After proving that there can be…
The classical dynamical systems model of continuous stirred tank reactors (CSTR) in which a first order chemical reaction takes place is reformulated in terms of stochastic cellular automata by extending previous works of Seyborg (1997) and…
Using the concept of the Boolean derivative we study damage spreading for one dimensional elementary cellular automata and define their maximal Lyapunov exponent. A random matrix approximation describes quite well the behavior of…
Linear quantum cellular automata were introduced recently as one of the models of quantum computing. A basic postulate of quantum mechanics imposes a strong constraint on any quantum machine: it has to be unitary, that is its time evolution…
We present a diagrammatic method to build up sophisticated cellular automata (CAs) as models of complex physical systems. The diagrams complement the mathematical approach to CA modeling, whose details are also presented here, and allow CAs…
A two-state, three-dimensional, deterministic, reversible cellular automaton is shown to be capable of approximately circular orbits, wavelike undulations, and particle-like configurations that decay in accordance with a half-life law.
We derive a set of algorithms for simulating the diffusion-limited growth of faceted crystals using local cellular automata. This technique has been shown to work well in reproducing realistic crystal morphologies, and the present work…
A quantum cellular automaton (QCA) is an abstract model consisting of an array of finite-dimensional quantum systems that evolves in discrete time by local unitary operations. Here we propose a simple coarse-graining map, where the spatial…
We derive a class of cellular automata for the Schr\"odinger Hamiltonian, including scalar and vector potentials. It is based on a multi-split of the Hamiltonian, resulting in a multi-step unitary evolution operator in discrete time and…
We extend the usual definition of cellular automaton on a group in order to deal with a new kind of cellular automata, like cellular automata in the hyperbolic plane and we explore some properties of these cellular automata. This definition…
We study the problem of sequentializing a cellular automaton without introducing any intermediate states, and only performing reversible permutations on the tape. We give a decidable characterization of cellular automata which can be…
In this paper we present a theoretical analysis of a recently proposed two-dimensional Cellular Automata model for traffic flow in cities with the novel ingredient of turning capability. Numerical simulations of this model show that there…
We present a family of one-dimensional cellular automata modeling the diffusion of an innovation in a population. Starting from simple deterministic rules, we construct models parameterized by the interaction range and exhibiting a…
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 are investigated towards their ability to compute transductions, that is, to transform inputs into outputs. The families of transductions computed are classified with regard to the time allowed to process the input and to…
The use of buried dopants to construct quantum-dot cellular automata is investigated as an alternative to conventional electronic devices for information transport and elementary computation. This provides a limit in terms of…
We present a one dimensional reversible block cellular automaton, where the time evolution is dictated by a period 3 cycle of update rules. At each time step a subset of the cells is updated using a four site rule with two control bits and…
We study the classification of cellular-automaton update rules into Wolfram's four classes. We start with the notion of the input entropy of a spatiotemporal block in the evolution of a cellular automaton, and build on it by introducing two…