Foreword: asynchronous behavior of cellular automata and discrete models

Abstract

This special issue contains a selection of papers presented at the ‘‘Third International Workshop on Asynchronous Cellular Automata and Asynchronous Discrete Models’’ (ACA 2014), held as a satellite workshop of the 11th International Conference on Cellular Automata for Research and Industry (ACRI 2014) in Krakow (Poland) in September 2014. Six papers were selected and, after an additional review process, five of them have been included in this special issue. They are now presented in an extended and improved form with respect to the already refereed workshop version that appeared in the proceedings of the ACRI 2014 conference. The ACA workshop is devoted to the theme of asynchrony, a hot topic, inside Cellular Automata and other Discrete Models as, for instance, Boolean Networks. Cellular Automata are a well-known formal tool for modeling complex systems; they are considered in many scientific fields and industrial applications. Synchronicity is one of the main features of Cellular Automata evolutions. Indeed, in the most common Cellular Automata framework, all cells are updated simultaneously at each discrete time step by means of a same rule. Recent trends consider the modeling of asynchronous systems based on local and possibly non-uniform interactions. The aim of this workshop is to bring together researchers dealing with the theme of the asynchrony inside Cellular Automata and Discrete Models. Typical, but not exclusive, topics of the workshop are dynamics, complexity and computational issues, emergent properties, models of parallelism and distributed systems, and models of real phenomena. The paper ‘‘Local structure approximation as a predictor of second-order phase transitions in asynchronous cellular automata’’ by Henryk Fukś and Nazim Fates considers aasynchronous elementary cellular automata, that is elementary cellular automata in which each cell independently updates with probability a. By means of an extension of the mean-field approximation technique, the authors study the phase transitions in such automata, i.e., the changes of the dynamical behavior which may occur when the parameter a varies. In the paper ‘‘Supercritical probabilistic cellular automata: How effective is the synchronous updating?’’, PierreYves Louis deals with the issue of quantifying the effectiveness of the parallel updating in probabilistic cellular automata, i.e., cellular automata where the local rule is defined by means of a probability. Two interesting classes of probabilistic cellular automata are considered. An analysis of simulation is presented and shows that the behavior of these classes is nearly asynchronous when transition phase phenomena occur. Boolean Networks model the dynamical interaction of components which take a binary state. They have been & Alberto Dennunzio dennunzio@disco.unimib.it