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2014 ; 21
(9
): 699-708
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Probabilistic cellular automata
#MMPMID24999557
Agapie A
; Andreica A
; Giuclea M
J Comput Biol
2014[Sep]; 21
(9
): 699-708
PMID24999557
show ga
Cellular automata are binary lattices used for modeling complex dynamical
systems. The automaton evolves iteratively from one configuration to another,
using some local transition rule based on the number of ones in the neighborhood
of each cell. With respect to the number of cells allowed to change per
iteration, we speak of either synchronous or asynchronous automata. If randomness
is involved to some degree in the transition rule, we speak of probabilistic
automata, otherwise they are called deterministic. With either type of cellular
automaton we are dealing with, the main theoretical challenge stays the same:
starting from an arbitrary initial configuration, predict (with highest accuracy)
the end configuration. If the automaton is deterministic, the outcome simplifies
to one of two configurations, all zeros or all ones. If the automaton is
probabilistic, the whole process is modeled by a finite homogeneous Markov chain,
and the outcome is the corresponding stationary distribution. Based on our
previous results for the asynchronous case-connecting the probability of a
configuration in the stationary distribution to its number of zero-one
borders-the article offers both numerical and theoretical insight into the
long-term behavior of synchronous cellular automata.
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