Characterisation of the elementary cellular automata in terms of their maximum sensitivity to all possible asynchronous updates
Ruivo
E
L
P
author
Montalva-Medel
M
author
de Oliveira
P
P
B
author
Perrot
K
author
2018
English
Cellular automata are fully-discrete dynamical systems with global behaviour depending upon their locally specified state transitions. They have been extensively studied as models of complex systems as well as objects of mathematical and computational interest. Classically, the local rule of a cellular automaton is iterated synchronously over the entire configuration. However, the question of how asynchronous updates change the behaviour of a cellular automaton has become a major issue in recent years. Here, we analyse the elementary cellular automata rule space in terms of how many different one-step trajectories a rule would entail when taking into account all possible deterministic ways of updating the rule, for one time step, over all possible initial configurations. More precisely, we provide a characterisation of the elementary cellular automata, by means of their one-step maximum sensitivity to all possible update schedules, that is, the property that any change in the update schedule causes the rule's one-step trajectories also to change after one iteration. Although the one-step maximum sensitivity does not imply that the remainder of the time-evolutions will be distinct, it is a necessary condition for that. (C) 2018 Elsevier Ltd. All rights reserved.
Cellular automaton
Asynchronous update
Update digraph
Discrete dynamics
One-step maximum sensitivity
WOS:000442101600024
exported from refbase (show.php?record=910), last updated on Mon, 07 Jan 2019 13:04:45 -0300
text
files/910_Ruivo_etal2018.pdf
10.1016/j.chaos.2018.06.004
Ruivo_etal2018
Chaos Solitons & Fractals
Chaos Solitons Fractals
2018
Pergamon-Elsevier Science Ltd
continuing
periodical
academic journal
113
209
220
0960-0779