Automatic implementation of totalistic cellular automata through polynomial cellular neural networks

The learning procedures of cellular automata and cellular neural networks are not trivial tasks. They have been addressed previously with several techniques such as genetic algorithms, although they are computationally costly. As a contribution in the area of polynomial cellular neural networks, in this paper we present a novel method to determine automatically the optimum order of the polynomial term, and the generalized system of equations for a polynomial cellular neural network that implements any totalistic cellular automata behavior. Such advances can be coupled with a quadratic programming algorithm in order to radically boost training performance and dispense human intervention.