different, and thus effectively inducing different landscapes. In this **work we** will use one type of performance measure based on the fraction of n **initial** configurations that are correctly classified from one sample. We call **standard**
performance **(see also section 2.3) the performance when the sample is drawn**
from a binomial distribution (i.e., each bit is independently drawn with probability 1/**2 of being 0). Standard performance is a hard measure because of**
the predominance in the sample of ICs close to 0.**5 and it has been typically**
employed to measure a CA's capability on the density task.

The standard performance cannot be known perfectly due to random variation of samples of ICs. The fitness function of the landscape is stochatic one which allows population of solutions to drift arround neutral networks. The error of evaluation leads us to define the neutrality of landscape. The ICs are chosen independently, so the fitness value f **of a solution follows a normal law**
N (f, σ(f)
√n
), where σ is the standard deviation of sample of fitness f, and n **is the**
sample size. For binomial sample, σ 2(f) = f(1−f**), the variance of Bernouilli**
trial. Then two neighbors s and s
′
are neutral neighbors (isNeutral(**s, s**
′
**) is**
true) if a t-test accepts the hypothesis of equality of f(s**) and** f(s
′
**) with 95**
percent of confidence (fig. 3). The maximum number of fitness values statistically different for standard performance is 113 for n = 104, 36 for n **= 10**3 and 12 for n **= 10**2.

![0_image_0.png](0_image_0.png)

The DOS of the Majority problem landscape was computed using the uniform random sampling technique. The number of sampled points is 4000 and, among them, the number of solutions with a fitness value equal to 0 is **3979.** Clearly, the space appears to be a difficult one to search since the tail of the distribution to the right is non-existent. Figure 4 shows the DOS obtained using the Metropolis-Hastings technique. This time, over the 4000 solutions sampled, only 176 have a fitness equal to zero, and the DOS clearly shows a more uniform distribution of rules over many different fitness values.