Asynchronous dynamics of random Boolean networks

A generalization of neural networks called Boolean networks is considered. Random (n, k)-networks consist of n processors, each connected randomly to k others, computing random k-input Boolean functions. The dynamic behavior of these networks has been studied extensively. The authors examine the asynchronous dynamics of these networks, and prove that convergence to fixpoints is assured for almost all random (n, k)-networks at the limit n → ∞, provided k > log n. The proof of this result lies in random graph theory. They believe it is the first time this branch of mathematics has been used to analyze dynamic behavior of networks.