Abstract: We compare a classical CNN architecture for sequence classification involving several convolutional and max-pooling layers against a simple model based on weighted finite state automata (WFA). Each model has its advantages and disadvantages and it is possible that they could be combined. However, we believe that the first research goal should be to investigate and understand how do these two apparently dissimilar models compare in the context of specific natural language processing tasks. This paper is the first step towards that goal. Our experiments with five sequence classification datasets suggest that, despite the apparent simplicity of WFA models and training algorithms, the performance of WFAs is comparable to that of the CNNs.