In this paper finite automata are treated as general discrete dynamical systems from the viewpoint of systems theory. The unconditional on-line identification of an unknown finite automaton is the problem considered. A generalized architecture of recurrent neural networks with a corresponding on-line learning scheme is proposed as a solution to the problem. An on-line rule-extraction algorithm is further introduced. The architecture presented, the on-line learning scheme and the on-line rule-extraction method are tested on different, strongly connected automata, ranging from a very simple example with two states only to a more interesting and complex one with 64 states; the results of both training and extraction processes are very promising.