Heuristic Minimization of Synchronous Relations

SynchronousBoolean relations can represent sequential don’t care information in synchronous systems. These allow greater flexibility in expressing don’t care information than ordinary Boolean relations. Synchronous relations can be used to specify sequential designs both at the finite state machine level as well as at the level of combinational elements and latches. The main objective of this paper is to present a heuristic approach to find a minimal implementation for a given synchronous relation. We also show that the synchronous relation formulation can also be used to find a minimal sum-of-products form which implements a function compatible with an arbitrary set of Boolean relations.