相关论文: Limit Measures for Affine Cellular Automata, II
Classical Cellular Automata (CCAs) are a powerful computational framework widely used to model complex systems driven by local interactions. Their simplicity lies in the use of a finite set of states and a uniform local rule, yet this…
We present a probabilistic cellular automaton (CA) with two absorbing states which performs classification of binary strings in a non-deterministic sense. In a system evolving under this CA rule, empty sites become occupied with a…
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…
We study lattice spin systems and analyze the evolution of Gaussian concentration bounds (GCB) under the action of probabilistic cellular automata (PCA), which serve as discrete-time analogues of Markovian spin-flip dynamics. We establish…
We prove that topologically isomorphic linear cellular automaton shifts are algebraically isomorphic. Using this, we show that two distinct such shifts cannot be isomorphic. We conclude that the automorphism group of a linear cellular…
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…
In [6], a constraint on invariant measures of bi-permutative cellular automata has been observed: fixed values at the positive indices determine almost-surely a uniform conditional probability on the subset of values of positive conditional…
Let $A$ be a unital AH-algebra and let $\alpha\in Aut(A)$ be an automorphism. A necessary condition for $A\rtimes_{\alpha}\Z$ being embedded into a unital simple AF-algebra is the existence of a faithful tracial state. If in addition, there…
A soliton cellular automaton associated with crystals of symmetric tensor representations of the quantum affine algebra U'_q(A^{(1)}_M) is introduced. It is a crystal theoretic formulation of the generalized box-ball system in which…
We classify quantum cellular automata whose cells are qubits, on hypercubic lattices $\mathbb Z^s$, with the von Neumann neighborhood scheme, in terms of realizability as finite-depth quantum circuits. We show the most general structure of…
Cellular automata (CA) are dynamical systems on symbolic configurations on the lattice. They are also used as models of massively parallel computers. As dynamical systems, one would like to understand the effect of small random…
A new class of automata networks is defined. Their evolution rules are determined by a probability measure p on the set of all integers Z and an indicator function I_A on the interval [0,1]. It is shown that any cellular automaton rule can…
The phase diagram of the coupled sine circle map lattice shows spatio-temporal intermittency of two distinct types: spatio-temporal intermittency of the directed percolation (DP) class, and spatial intermittency which does not belong to…
We introduce and study cellular automata whose cell spaces are left-homogeneous spaces. Examples of left-homogeneous spaces are spheres, Euclidean spaces, as well as hyperbolic spaces acted on by isometries; uniform tilings acted on by…
We consider a probabilistic cellular automaton (PCA) of evaporation-deposition on the one-dimensional lattice having $n$ sites with periodic boundary conditions, in which each site, during each epoch, can be in one of two states: $0$ and…
This article surveys some theoretical aspects of Cellular Automata (CAs) research. In particular, we discuss on maximal length CA. An n-cell CA is a maximal length CA, if all the configurations except one form a single cycle. There is a…
We construct a cellular automaton (CA) model that describes the movement of a particle in a disordered system. The mathematical properties of the CA model were examined by varying the configuration of grid and determining the number of…
Cyclic cellular automata (CCA) are models of excitable media. Started from random initial conditions, they produce several different kinds of spatial structure, depending on their control parameters. We introduce new tools from information…
In previous works, hexagonal cellular automata (CA) have been studied as a variation of the famous Game of Life CA, mainly for spiral phenomena simulations; where the most interesting constructions are related to the Belousov-Zhabotinsky…
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…