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A Brain-Computer Interface (BCI) is an interface that directly analyzes brain activity to transform user intentions into commands. Many known techniques use the P300 event-related potential by extracting relevant features from the EEG signal and feeding those features into a classifier. In these approaches, feature extraction becomes the key point, and doing it by hand can be at the same time cumbersome and suboptimal. In this paper we face the issue of feature extraction by using a genetic algorithm able to retrieve the relevant aspects of the signal to be classified in an automatic fashion. We have applied this algorithm to publicly available data sets (a BCI competition) and data collected in our lab, obtaining with a simple logistic classifier results comparable to the best algorithms in the literature. In addition, the features extracted by the algorithm can be interpreted in terms of signal characteristics that are contributing to the success of classification, giving new insights for brain activity investigation.