  Hopfield attractor networks are robust distributed models of human memory,
but lack a general mechanism for effecting state-dependent attractor
transitions in response to input. We propose construction rules such that an
attractor network may implement an arbitrary finite state machine (FSM), where
states and stimuli are represented by high-dimensional random vectors, and all
state transitions are enacted by the attractor network's dynamics. Numerical
simulations show the capacity of the model, in terms of the maximum size of
implementable FSM, to be linear in the size of the attractor network for dense
bipolar state vectors, and approximately quadratic for sparse binary state
vectors. We show that the model is robust to imprecise and noisy weights, and
so a prime candidate for implementation with high-density but unreliable
devices. By endowing attractor networks with the ability to emulate arbitrary
FSMs, we propose a plausible path by which FSMs could exist as a distributed
computational primitive in biological neural networks.
