"A number of representation schemes have been presented for use within Learning Classifier Systems, ranging from binary encodings to neural networks. This paper presents results from an investigation into using a discrete dynamical system representation within the XCS Learning Classifier System. In particular, asynchronous random Boolean networks are used to represent the traditional condition-action production system rules. It is shown possible to use self-adaptive, open-ended evolution to design an ensemble of such discrete dynamical systems within XCS to solve a number of well-known test problems."

"Consider a large Boolean network with a feed forward structure. Given a probability distribution for the inputs, can one find-possibly small-collections of input nodes that determine the states of most other nodes in the network?…"

"We have shown that there exists a large ensemble of minimal Boolean networks that show reliable and robust dynamics. The networks are minimal in the respect that the number of connections of a node is not larger than necessary for obtaining a desired reliable trajectory. A reliable trajectory is an attractor of the dynamics of the network that does not change when the update schedule is changed or randomized. This means that under parallel update, at each time step only one node changes its state. The reliable trajectories were chosen at random, given a fixed average number of flips per node. High robustness was achieved by using an evolutionary algorithm that modifies the update functions and that accepts only those changes that do not decrease robustness.…"

"…The model is based on the emergent properties of generic genetic networks, it does not refer to specific control circuits and it can therefore hold for a wide class of lineages. The model points to a peculiar role of cellular noise in differentiation, which has never been hypothesized so far, and leads to non trivial predictions which could be subject to experimental testing."