We define a notion of equivalence for designs containing black boxes. Using this notion, we describe a sound and complete methodology for optimizing designs containing black boxes, i.e. components whose functionality is not known; these arise naturally in the course of hierarchical design. Keywords: Hierarchical Logic Synthesis, Black Boxes, Don't Cares 1 Introduction The advent of modern VLSI CAD tools has radically changed the process of designing digital systems. The first CAD tools automated the final stages of design, such as placement and routing. As the low level steps became better understood, the focus shifted to the higher stages. In particular logic synthesis, the science of optimizing gate level designs for measures such ...