A Simple Cellular Automation that Solves the Density and Ordering Problems

Cellular automata (CA) are discrete, dynamical systems that perform computations in a distributed fashion on a spatially extended grid. The dynamical behavior of a CA may give rise to emergent computation, referring to the appearance of global information processing capabilities that are not explicitly represented in the system's elementary components nor in their local interconnections.1 As such, CAs o?er an austere yet versatile model for studying natural phenomena, as well as a powerful paradigm for attaining ?ne-grained, massively parallel computation. An example of such emergent computation is to use a CA to determine the global density of bits in an initial state con?guration. This problem, known as density classi?cation, has been studied quite intensively over the past few years. In this short communication we describe two previous versions of the problem along with their CA solutions, and then go on to show that there exists yet a third version | which admits a simple solution

Evolution of Asynchronous Cellular Automata

One of the prominent features of the Cellular Automata (CA) model is its synchronous mode of operation, meaning that all cells are updated simultaneously. but this feature is far from being realistic from a biological point of view as well as from a computational point of view. Past research has mainly concentrated on studying Asynchronous CAs in themselves, trying to determine what behaviours were an "artifact" of the global clock. In this paper, I propose to evolve Asynchronous CAs that compute successfully one of the well-studied task for regular CSs: The synchronisation task. As I will show evolved solutions are both unexpected and best for uncertain criteria

An Evolving Ontogenetic Cellular System for Better Adaptiveness

In this paper, we present an original cellular system named Phuon. The main motivation behind this project is to go beyond classical cellular systems, such as cellular automata (CA). CA often lack adaptability and turn out to be very brittle in uncertain environment. The idea here is to add ontogeny to cellularity, growth and development being means of adaptation and thus robustness. However, we do not wish to develop yet another cellular system for the sake of it. What we are seeking in the long term is a developmental system for problem solving. This global aim enticed us into finding a way to map a desired global behavior of the system to the local behavior of a cell. Quite naturally a peculiar brand of genetic programming was used for that purpose. The results are still preliminary but in our view they already validate some of the hypotheses behind this work

Evolution of asynchronous Cellular Automata: finding the good compromise

One of the prominent features of the Cellular Automata (CA) model is its synchronous mode of operation, meaning that all cells are updated simultaneously. But this feature is far from being realistic from a biological point of view as well as from a computational point of view. Past research has mainly concentrated on studying Asynchronous CAs in themselves, trying to determine what behaviors were an "artifact" of the global clock. In this paper, I propose to evolve Asynchronous CAs that compute successfully one of the well-studied task for regular CAs: The synchronization task. As I will show evolved solutions are both unexpected and best for certain criteria than a perfect solution. The model used is fully asynchronous. Each cell has the same probability pf of not updating its state at each step

Necessary Conditions for Density Classification by Cellular Automata

Classifying the initial configuration of a binary-state cellular automaton (CA) as to whether it contains a majority of 0s or 1s-the so-called density-classification problem-has been studied over the past decade by researchers wishing to glean an understanding of how locally interacting systems compute global properties. In this paper we prove two necessary conditions that a CA must satisfy in order to classify density: (1) the density of the initial configuration must be conserved over time, and (2) the rule table must exhibit a density of 0.5

Evolving Asynchronous and Scalable Non-uniform Cellular Automata

We have previously shown that non-uniform cellular automata (CA) can be evolved to perform computational tasks, using the cellular programming algorithm. In this paper we focus on two novel issues, namely, the evolution of asynchronous CAs, and the scalability of evolved synchronous systems. We find that asynchrony presents a more difficult case for evolution though good CAs can still be attained. We describe an empirically derived scaling procedure by which successful CAs of any size may be obtained from a particular evolved system. Our motivation for this study stems in part from our desire to attain realistic systems that axe more amenable to implementation as “evolving ware,” evolware

Designing Cellular Automata Using a Parallel Evolutionary Algorithm

We have previously shown that non-uniform Cellular Automata (CA) can be evolved to perform computational tasks, using the cellular programming evolutionary algorithm. In this paper we focus on two novel issues, namely the evolution of asynchronous CAs, and the fault tolerance of our evolved systems. We find that asynchrony presents a more difficult case for evolution though good CAs can still be attained. We show that our evolved systems exhibit graceful degradation in performance, able to tolerate a certain level of faults. Our motivation for this study stems in part by our desire to attain realistic systems that are more amenable to implementation as 'evolving ware', evolware