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We present a hybrid recurrent neural networks architecture inspired by hidden Markov models. We train the architecture to model dynamical systems such as deterministic finite automaton using a genetic training algorithm. We then use a machine learning approach for the extraction of deterministic finite automaton; we apply a generalisation of the Trakhtenbrot-Barzdin algorithm to extract DFAs in symbolic form using the string labelling assigned by the trained network. The results demonstrate that the approach successfully extracts the correct deterministic equivalent automaton for strings much longer than the longest string in the training set. Thus, our hybrid recurrent neural network architecture inspired by hidden Markov models can train and represent an important class of discrete dynamical systems.