There has been a lot of interest in the use of discrete-time recurrent neural nets (DTRNN) to learn finite-state tasks, with interesting results regarding the induction of simple finite-state machines from input–output strings. Parallel work has studied the computational power of DTRNN in connection with finite-state computation. This article describes a simple strategy to devise stable encodings of finite-state machines in computationally capable discrete-time recurrent neural architectures with sigmoid units and gives a detailed presentation on how this strategy may be applied to encode a general class of finite-state machines in a variety of commonly used first- and second-order recurrent neural networks. Unlike previous work that either imposed some restrictions to state values or used a detailed analysis based on fixed-point attractors, our approach applies to any positive, bounded, strictly growing, continuous activation function and uses simple bounding criteria based on a study of the conditions under which a proposed encoding scheme guarantees that the DTRNN is actually behaving as a finite-state machine.

Recent work has shown that second-order recurrent neural networks (2ORNNs) may be used to infer regular languages. This paper presents a modified version of the real-time recurrent learning (RTRL) algorithm used to train 2ORNNs, that learns the initial state in addition to the weights. The results of this modification, which adds extra flexibility at a negligible cost in time complexity, suggest that it may be used to improve the learning of regular languages when the size of the network is small.