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

Phase Space Invertible Asynchronous Cellular Automata

While for synchronous deterministic cellular automata there is an accepted definition of reversibility, the situation is less clear for asynchronous cellular automata. We first discuss a few possibilities and then investigate what we call phase space invertible asynchronous cellular automata in more detail. We will show that for each Turing machine there is such a cellular automaton simulating it, and that it is decidable whether an asynchronous cellular automaton has this property or not, even in higher dimensions.Comment: In Proceedings AUTOMATA&JAC 2012, arXiv:1208.249

Computational Aspects of Asynchronous CA

This work studies some aspects of the computational power of fully asynchronous cellular automata (ACA). We deal with some notions of simulation between ACA and Turing Machines. In particular, we characterize the updating sequences specifying which are "universal", i.e., allowing a (specific family of) ACA to simulate any TM on any input. We also consider the computational cost of such simulations

A Max-Plus Model of Asynchronous Cellular Automata

This paper presents a new framework for asynchrony. This has its origins in our attempts to better harness the internal decision making process of cellular automata (CA). Thus, we show that a max-plus algebraic model of asynchrony arises naturally from the CA requirement that a cell receives the state of each neighbour before updating. The significant result is the existence of a bijective mapping between the asynchronous system and the synchronous system classically used to update cellular automata. Consequently, although the CA outputs look qualitatively different, when surveyed on "contours" of real time, the asynchronous CA replicates the synchronous CA. Moreover, this type of asynchrony is simple - it is characterised by the underlying network structure of the cells, and long-term behaviour is deterministic and periodic due to the linearity of max-plus algebra. The findings lead us to proffer max-plus algebra as: (i) a more accurate and efficient underlying timing mechanism for models of patterns seen in nature, and (ii) a foundation for promising extensions and applications.Comment: in Complex Systems (Complex Systems Publications Inc), Volume 23, Issue 4, 201

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