相关论文: Classifying Rational Densities Using Two One-Dimen…

For many cellular automata, it is possible to express the state of a given cell after $n$ iterations as an explicit function of the initial configuration. We say that for such rules the solution of the initial value problem can be obtained.…

Defining the density flow of perturbations moving at a given speed for cellular automata, we establish equalities and inequalities between the measurable entropy of a cellular automaton and the measurable entropy of its associated shift.

This paper presents a classification of Cellular Automata rules based on its properties at the nth iteration. Elaborate computer program has been designed to get the nth iteration for arbitrary 1-D or 2-D CA rules. Studies indicate that the…

We consider random boolean cellular automata on the integer lattice, i.e., the cells are identified with the integers from 1 to $N$. The behaviour of the automaton is mainly determined by the support of the random variable that selects one…

We investigate a cellular automaton (CA) model of traffic on a bi-directional two-lane road. Our model is an extension of the one-lane CA model of {Nagel and Schreckenberg 1992}, modified to account for interactions mediated by passing, and…

Introducing the notion of a rational system of measure preserving transformations and proving a recurrence result for such systems, we give sufficient conditions in order a subset of rational numbers to contain arbitrary long arithmetic…

We investigate number conserving cellular automata with up to five inputs and two states with the goal of comparing their dynamics with diffusion. For this purpose, we introduce the concept of decompression ratio describing expansion of…

This paper studies complexity of recognition of classes of bounded configurations by a generalization of conventional cellular automata (CA) -- finite dynamic cellular automata (FDCA). Inspired by the CA-based models of biological and…

We discuss example of an elementary cellular automaton for which the density of ones decays toward its limiting value as a power of the number of iterations $n$. Using the fact that this rule conserves the number of blocks 10 and that…

This paper considers the problem of specifying a simple approximating density function for a given data set (x_1,...,x_n). Simplicity is measured by the number of modes but several different definitions of approximation are introduced. The…

Given a natural number $k\ge 2$ and a $k$-automatic set $S$ of natural numbers, we show that the lower density and upper density of $S$ are recursively computable rational numbers and we provide an algorithm for computing these quantities.…

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…

We compare several definitions for number-conserving cellular automata that we prove to be equivalent. A necessary and sufficient condition for \cas to be number-conserving is proved. Using this condition, we give a linear-time algorithm to…

We propose a novel density based numerical method for uncertainty propagation under certain partial differential equation dynamics. The main idea is to translate them into objects that we call cellular probabilistic automata and to evolve…

We study the fixed points of outer-totalistic cellular automata on sparse random regular graphs. These can be seen as constraint satisfaction problems, where each variable must adhere to the same local constraint, which depends solely on…

In this paper, linear Cellular Automta (CA) rules are recursively generated using a binary tree rooted at "0". Some mathematical results on linear as well as non-linear CA rules are derived. Integers associated with linear CA rules are…

This is a study of localised structures in one-dimensional cellular automata, with the elementary cellular automaton Rule 54 as a guiding example. A formalism for particles on a periodic background is derived, applicable to all…

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…

Estimating the ratio of two probability densities from finitely many samples, is a central task in machine learning and statistics. In this work, we show that a large class of kernel methods for density ratio estimation suffers from error…

We systematically study the boundaries of one-dimensional, 2-color cellular automata depending on 4 cells, begun from simple initial conditions. We determine the exact growth rates of the boundaries that appear to be reducible. Morphic…