Abstract

Pollack (1991) demonstrated that second-order recurrent neural networks can act as dynamical recognizers for formal languages when trained on positive and negative examples, and observed both phase transitions in learning and IFS-like fractal state sets. Follow-on work focused mainly on the extraction and minimization of a finite state automaton (FSA) from the trained network. However, such networks are capable of inducing languages which are not regular, and therefore not equivalenttoany FSA. Indeed, it may be simpler for a small network to fit its training data by inducing such a non-regular language. But when is the network's language not regular? In this paper, using a low dimensional network capable of learning all the Tomita data sets, we present an empirical method for testing whether the language induced by the network is regular or not. We also provide a detailed "-machine analysis of trained networks for both regular and non-regular languages.

Citations