Learning Picture Languages Using Dimensional Reduction

One-dimensional (string) formal languages and their learning have been studied in considerable depth. However, the knowledge of their two-dimensional (picture) counterpart, which retains similar importance, is lacking. We investigate the problem of learning formal two-dimensional picture languages by applying learning methods for one-dimensional (string) languages. We formalize the transcription process from a two-dimensional input picture into a string and propose a few adaptations to it. These proposals are then tested in a series of experiments, and their outcomes are compared. Finally, these methods are applied to a practical problem and an automaton for recognizing a part of the MNIST dataset is learned. The obtained results show improvements in the topic and the potential to use the learning of automata in fitting problems.