ORDER BETWEEN LOGIC NETWORKS AND STABLE NEURAL NETWORKS

摘要

A logic network is a network of binary logic functions, which may be expressed as a higher-order neural network. We consider asynchronous operation mode and characterize stable networks through corresponding Lyapunov functions. We distinguish a special type of Lyapunov functions called pure and reveal their properties with relation to ordinary Lyapunov functions. We also introduce some order relations among logic functions and among logic networks, which play a crucial role in characterizing the existence condition of Lyapunov function in general for logic networks.