3,734 research outputs found
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
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
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
A Survey of Cellular Automata: Types, Dynamics, Non-uniformity and Applications
Cellular automata (CAs) are dynamical systems which exhibit complex global
behavior from simple local interaction and computation. Since the inception of
cellular automaton (CA) by von Neumann in 1950s, it has attracted the attention
of several researchers over various backgrounds and fields for modelling
different physical, natural as well as real-life phenomena. Classically, CAs
are uniform. However, non-uniformity has also been introduced in update
pattern, lattice structure, neighborhood dependency and local rule. In this
survey, we tour to the various types of CAs introduced till date, the different
characterization tools, the global behaviors of CAs, like universality,
reversibility, dynamics etc. Special attention is given to non-uniformity in
CAs and especially to non-uniform elementary CAs, which have been very useful
in solving several real-life problems.Comment: 43 pages; Under review in Natural Computin
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