The complexity of language recognition by neural networks

Neural networks are frequently used as adaptive classifiers. This research represents an attempt to measure the 'neural complexity' of any regular set of binary strings, that is, to quantify the size of a recurrent continuous-valued neural network that is needed for correctly classifying the given regular set. Our estimate provides a predictor that is superior to the size of the minimal automaton that was used as an upper bound so far. Moreover, it is easily computable, using techniques from the theory of rational power series in non-commuting variables.