We present two approaches to the analysis of the relationship between a recurrent neural network (RNN) and the finite state machine M the network is able to exactly mimic. First, the network is treated as a state machine and the relationship between the RNN and M is established in the context of algebraic theory of automata. In the second approach, the RNN is viewed as a set of discrete-time dynamical systems associated with input symbols of M. In particular, issues concerning network...