Invertible operations on a cellular neural network universal machine

This paper is concerned with the invertibility of parallel operations defin able on two-dimensional binary arrays by means of a local Boolean function. In this way, it contributes to the theory of cellular automata and may ope n new potentialities to cellular neural network applications. We provide a theoretically new approach to the invertibility of two-dimensional additive maps which can be used to obtain detailed information on the behaviour of these operations. Other ways to make invertible operations are also investi gated, including local maps which are additive in only one of the terms, an d second-order cellular automata. The discussed techniques yield a rich var iety of invertible operations on infinite and/or finite two-dimensional bin ary arrays. When implemented on CNN Universal Chips, all of these operation s, performed by TeraOPS speed, become subroutines of a 2D analogic algorith m. These operations can be used in 2D cryptography. (C) 1998 John Wiley & S ons, Ltd.