An Experimental Study of Robustness to Asynchronism for Elementary Cellular Automata

Cellular Automata (CA) are a class of discrete dynamical systems that have been widely used to model complex systems in which the dynamics is specified at local cell-scale. Classically, CA are run on a regular lattice and with perfect synchronicity. However, these two assumptions have little chance to truthfully represent what happens at the microscopic scale for physical, biological or social systems. One may thus wonder whether CA do keep their behavior when submitted to small perturbations of synchronicity. This work focuses on the study of one-dimensional (1D) asynchronous CA with two states and nearest-neighbors. We define what we mean by ``the behavior of CA is robust to asynchronism'' using a statistical approach with macroscopic parameters. and we present an experimental protocol aimed at finding which are the robust 1D elementary CA. To conclude, we examine how the results exposed can be used as a guideline for the research of suitable models according to robustness criteria.Comment: Version : Feb 13th, 2004, submitted to Complex System

Modélisation des systèmes complexes

Michel Morvan et Henri Berestycki, directeurs d’études Émergence dans les systèmes complexes : des cas réels aux modèles formels L’émergence dans les systèmes complexes a fait l’objet d’une double interrogation dans ce séminaire mettant en jeu deux points de vue complémentaires. D’un côté, nous avons étudié les phénomènes d’émergence tels qu’ils peuvent être vus par un philosophe. Nous avons tenté de dégager les invariants caractéristiques des situations d’émergence. D’un autre côté, nous nou..

Asynchronism Induces Second Order Phase Transitions in Elementary Cellular Automata

Cellular automata are widely used to model natural or artificial systems. Classically they are run with perfect synchrony, i.e., the local rule is applied to each cell at each time step. A possible modification of the updating scheme consists in applying the rule with a fixed probability, called the synchrony rate. For some particular rules, varying the synchrony rate continuously produces a qualitative change in the behaviour of the cellular automaton. We investigate the nature of this change of behaviour using Monte-Carlo simulations. We show that this phenomenon is a second-order phase transition, which we characterise more specifically as belonging to the directed percolation or to the parity conservation universality classes studied in statistical physics

On the decomposition of stochastic cellular automata

In this paper we present two interesting properties of stochastic cellular automata that can be helpful in analyzing the dynamical behavior of such automata. The first property allows for calculating cell-wise probability distributions over the state set of a stochastic cellular automaton, i.e. images that show the average state of each cell during the evolution of the stochastic cellular automaton. The second property shows that stochastic cellular automata are equivalent to so-called stochastic mixtures of deterministic cellular automata. Based on this property, any stochastic cellular automaton can be decomposed into a set of deterministic cellular automata, each of which contributes to the behavior of the stochastic cellular automaton.Comment: Submitted to Journal of Computation Science, Special Issue on Cellular Automata Application

Robustness of Cellular Automata in the Light of Asynchronous Information Transmission

International audienceCellular automata are classically synchronous: all cells are simultaneously updated. However, it has been proved that perturbations in the updating scheme may induce qualitative changes of behaviours. This paper presents a new type of asynchronism, the beta -synchronism, where cells still update at each time step but where the transmission of information between cells is disrupted randomly. We experimentally study the behaviour of beta-synchronous models. We observe that, although many eff ects are similar to the perturbation of the update, novel phenomena occur. We particularly study phase transitions as an illustration of a qualitative variation of behaviour triggered by continuous change of the disruption probability beta

A guided tour of asynchronous cellular automata

Research on asynchronous cellular automata has received a great amount of attention these last years and has turned to a thriving field. We survey the recent research that has been carried out on this topic and present a wide state of the art where computing and modelling issues are both represented.Comment: To appear in the Journal of Cellular Automat

A statistical approach to the identification of diploid cellular automata based on incomplete observations

In this paper, the identification problem of diploid cellular automata is considered, in which, based on a series of incomplete observations, the underlying cellular automaton rules and the states of missing cell states are to be uncovered. An algorithm for identifying the rule, based on a statistical parameter estimation method using a normal distribution approximation, is presented. In addition, an algorithm for filling the missing cell states is formulated. The accuracy of these methods is examined in a series of computational experiments