@Article{MendonçaSimõ:2018:DeClPe,
author = "Mendon{\c{c}}a, J. Ricardo G. and Sim{\~o}es, Rolf Ezequiel de
Oliveira",
affiliation = "{Universidade de S{\~a}o Paulo (USP)} and {Instituto Nacional de
Pesquisas Espaciais (INPE)}",
title = "Density classification performance and ergodicity of the
Gacs-Kurdyumov-Levin cellular automaton model IV",
journal = "Physical Review E",
year = "2018",
volume = "98",
number = "1",
pages = "e012135",
month = "July",
abstract = "Almost four decades ago, Gacs, Kurdyumov, and Levin introduced
three different cellular automata to investigate whether
one-dimensional nonequilibrium interacting particle systems are
capable of displaying phase transitions, and, as a byproduct, they
introduced the density classification problem (the ability to
classify arrays of symbols according to their initial density) in
the cellular automata literature. Their model II became a
well-known model in theoretical computer science and statistical
mechanics. The other two models, however, did not receive much
attention. Here we characterize the density classification
performance of Gacs, Kurdyumov, and Levin's model IV, a four-state
cellular automaton with three absorbing states-only two of which
are attractive-by numerical simulations. We show that model IV
compares well with its sibling model II in the density
classification task: the additional states slow down the
convergence to the majority state but confer a slight advantage in
classification performance. We also show that, unexpectedly,
initial states diluted in one of the nonclassifiable states are
more easily classified. The performance of model IV under the
influence of noise was also investigated, and we found signs of an
ergodic-nonergodic phase transition at some small finite positive
level of noise, although the evidence is not entirely conclusive.
We set an upper bound on the critical point for the transition, if
any.",
doi = "10.1103/PhysRevE.98.012135",
url = "http://dx.doi.org/10.1103/PhysRevE.98.012135",
issn = "1539-3755",
language = "en",
targetfile = "mendonca_density.pdf",
urlaccessdate = "04 jun. 2024"
}