## 1 Introduction  
Brain-computer interfaces (BCI) provide a way for their users to control devices by basically interpreting their brain activity [1]. BCI have enormous potential for improving quality of life, particularly for those who have been affected by neurological disorders that partially or fully impede their motor capacities. In severe conditions such as complete locked-in syndrome (CLIS), patients are unable to willfully control movements of the eye or any other body part. In such cases, BCI based on only auditory cues are a viable option for establishing a communication channel [2]. BCI can be seen as module-based devices, where at least two essential parts can be recognized: the brain activity recording module and the brain activity classification one. To record brain activity, electroencephalography (EEG)-based technologies are often used because they are noninvasive, portable, produce accurate readings and are affordable compared with other methods [3; 4; 5]. Within the EEG readings, we can find some recognizable patterns, the P300 event-related potential (ERP) being of particular interest. The P300 is a positive deflection that can be observed in the brain activity of a subject, and it can be elicited via cue presentation following the oddball paradigm, an experimental setting in which sequences of regular cues are interrupted by irregular ones in order to evoke recognizable patterns within the brain activity of the subject. The P300 occurs between 250 and 700 ms after the presentation of an irregular cue in an experimental setting in which the participant is asked to attend to a particular cue (an irregular one in the oddball paradigm). The P300 has been exploited in many ways to produce a number of functional applications [6; 7]. Although the specific technology used for recording the brain activity is closely tied to the final performance of the classifier used, [8; 9] demonstrated that training and motivation have a positive and visible impact on the shape and appearance of the P300. Experimental setups using EEG and the P300 have been widely used in the development of BCI [10; 11; 12; 13]. For data classification, machine learning models such as artificial neural networks (ANN) and support vector machines (SVM) have not only been used widely but have also produced satisfactory results in many BCI applications [14; 15; 16; 17; 18]. In recent years, the implementation of convolutional neural networks (CNN) for classification purposes in tasks such as image and speech recognition has been successful [19; 20]. As a result, CNN have become an increasing topic of focus in various research fields, especially those involving multidimensional data. The CNN topology enables dimensional reduction of the input while also extracting relevant features for classification. For BCI, CNN have successfully been used for rapid serial visual presentation (RSVP) tasks [21], as well as for navigation in a virtual environment [22]. CNN consist of an arrangement of layers where the input goes through a convolution and a sub-sampling process called pooling, generating in this way features and reducing the size of the needed connections. In the work of [15], which serves as a major inspiration and reference for the present study, the authors advise against the use of CNN models that mix data from multiple dimensions during the processes of the convolution layer for classification purposes in BCI. However, for our research, we found that considering data from both the time and space domains for the pooling process of the convolution layer results in better CNN classification accuracy. Additionally, we tested pool processes with and without overlapping to assess whether this difference in processing impacts CNN performance. These overlapping approaches were explored for image classification in the work of [23], who reported better performance in the overlapping case, and with respect to speech-related tasks in [24], who found no difference between the approaches and stated that it might depend strictly on the data being used.