相关论文: Classifying Rational Densities Using Two One-Dimen…
We investigate a probabilistic cellular automaton model which has been introduced recently. This model describes single-lane traffic flow on a ring and generalizes the asymmetric exclusion process models. We study the equilibrium properties…
This paper proposes a new pattern of two dimensional cellular automata linear rules that are used for efficient edge detection of an image. Since cellular automata is inherently parallel in nature, it has produced desired output within a…
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…
We show how to construct a deterministic nearest-neighbour cellular automaton (CA) with four states which emulates diffusion on a one-dimensional lattice. The pseudo-random numbers needed for directing random walkers in the diffusion…
In recent years the modelling of traffic flow using methods from statistical physics, especially cellular automata models have allowed simulations of large traffic networks faster than real time. In this paper, we study a probabilistic…
Following work by Hochman and Meyerovitch on multidimensional SFT, we give computability-theoretic characterizations of the real numbers that can appear as the topological entropies of one-dimensional and two-dimensional cellular automata.
As machine learning is increasingly used to help make decisions, there is a demand for these decisions to be explainable. Arguably, the most explainable machine learning models use decision rules. This paper focuses on decision sets, a type…
We propose a four-way classification of two-dimensional semi-totalistic cellular automata that is different than Wolfram's, based on two questions with yes-or-no answers: do there exist patterns that eventually escape any finite bounding…
This paper considers estimation of a univariate density from an individual numerical sequence. It is assumed that (i) the limiting relative frequencies of the numerical sequence are governed by an unknown density, and (ii) there is a known…
The model of cellular automata is fascinating because very simple local rules can generate complex global behaviors. The relationship between local and global function is subject of many studies. We tackle this question by using results on…
We rigorously prove a form of disorder-resistance for a class of one-dimensional cellular automaton rules, including some that arise as boundary dynamics of two-dimensional solidification rules. Specifically, when started from a random…
We propose the characterization of binary cellular automata using a set of behavioral metrics that are applied to the minimal Boolean form of a cellular automaton's transition function. These behavioral metrics are formulated to satisfy…
The emergence of complex behaviors in cellular automata is an area that has been widely developed in recent years with the intention to generate and analyze automata that produce space-moving patterns or gliders that interact in a periodic…
In the parity problem, a given cellular automaton has to classify any initial configuration into two classes according to its parity. Elementary cellular automaton rule 60 can solve the parity problem in periodic boundary conditions with…
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…
This paper designs an efficient two-class pattern classifier utilizing asynchronous cellular automata (ACAs). The two-state three-neighborhood one-dimensional ACAs that converge to fixed points from arbitrary seeds are used here for pattern…
If a cellular automaton (CA) is started with a single ON cell, how many cells will be ON after n generations? For certain "odd-rule" CAs, including Rule 150, Rule 614, and Fredkin's Replicator, the answer can be found by using the…
The basis for most of the ideas mentioned in this paper is the theory of cellular automata. A cellular automata contains a regular grid of cells, with each cell having a pre-defined set of finite states. The initial state is determined at…
Infinite words, also known as streams, hold significant interest in computer science and mathematics, raising the natural question of how their complexity should be measured. We introduce cellular automaton reducibility as a measure of…
Cellular automata have long been celebrated for their ability to generate complex behaviors from simple, local rules, with well-known discrete models like Conway's Game of Life proven capable of universal computation. Recent advancements…