An algebra of asynchronous logic networks

Abstract

In this article we develop the algebraic properties of asynchronous logic networks and apply them to propose a new approach to network composition. The traditional methods of network composition produce compositions whose dimension is higher than the dimension of the components. A typical example of such a method is Miller's theorem [I] which specifies a technique for combining semimodular networks. A characteristic of our approach is that the dimension of the network produced by composition is not greater than the dimension of each of thecomponent networks. Binary operations of network intersection and union and unary operations of inversion and complementation are described. The main laws and properties of the algebra of asynchronous logic networks areconsidered, and in particular it is proved that the set of asynchronous logic networks of equal dimension with the operations of intersection, union, and complementation form a Boolean algebra. The generator system of this algebra is investigated. Methods are proposed for transformation of asynchronous logic networks based on algebraic composition (intersection or union) of the given network and some standard network.