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accomplish the task any longer. Clearly, the propagation of transversal signals
is more and more hindered as the automaton becomes more noisy.
(a)
(b)
(c)
Fig.6.
Typical behavior of the EvCA CA under probabilistic updating. The density
ρ
0
is 0.416 and the probabilities of fault
p
f
in (a), (b), and (c) are, respectively, 0,
0.001 and 0.01.
The following figure 7 shows the same evolution for the best evolved asyn-
chronous CA using the uniform choice update policy. The visual inspection al-
ready confirms that the CA is much less perturbed by random noise in the rules.
Even relatively high levels of faults do not prevent the CA from recovering and
finding the correct classification in many cases. This is clearly due to the fact
that asynchronous CAs were evolved in a noisy environment (the randomness as-
sociated with the sequential update order) and thus, to some extent, this allows
them to cope better with errors.
Although the previous examples are single cases, they are typical of what
happens. The following figure 8 shows an histogram of the ratio of the success
rate of the best evolved synchronous CA and of two evolved asynchronous CAs
as a function of the fault probability, with respect to the unperturbed versions.
Each CA has been tested on 1000 IC. The ranking is relative, since we only kept
the successful runs of the unperturbed automata to calculate the ratio. One sees
clearly that, already for
p
f
=1
.
0
×
10
−
4
, the synchronous CA starts to degrade,
while both asynchronous versions maintain good performance, especially the
uniform choice one, for values of
p
f
up to the order of 10
−
3
.
In the case of intermittent faults, we have tested 1000 IC for each of a number
of probability values of cell inactivity. We have used three CA rules: the best
evolved synchronous CA (EvCA [6]), the GKL rule, and the best evolved uniform
choice asynchronous automaton. The results are reported in figure 9. We observe
that for low values of the fault probability the three rules are almost equivalent
in that they keep a very good level of performance. However, as soon as the
