TY - JOUR

T1 - Characterisation of the elementary cellular automata in terms of their maximum sensitivity to all possible asynchronous updates

AU - Ruivo, Eurico L.P.

AU - Montalva-Medel, Marco

AU - P.B. de Oliveira, Pedro

AU - Perrot, Kévin

N1 - Funding Information:
This work was partially supported by FONDECYT Iniciación 11150827 (M.M-M.), P.P.B.O. thanks CNPq and K.P. thanks ECOS-C16E01, PACA project FRI-2015_01134 and PEPS JCJC INS2I project CGETA.
Publisher Copyright:
© 2018 Elsevier Ltd

PY - 2018/8

Y1 - 2018/8

N2 - 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.

AB - 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.

KW - Asynchronous update

KW - Cellular automaton

KW - Discrete dynamics

KW - One-step maximum sensitivity

KW - Update digraph

UR - http://www.scopus.com/inward/record.url?scp=85048852106&partnerID=8YFLogxK

U2 - 10.1016/j.chaos.2018.06.004

DO - 10.1016/j.chaos.2018.06.004

M3 - Article

AN - SCOPUS:85048852106

VL - 113

SP - 209

EP - 220

JO - Chaos, Solitons and Fractals

JF - Chaos, Solitons and Fractals

SN - 0960-0779

ER -