Free Binary Decision Diagram-Based Synthesis of Compact Crossbars for In-Memory Computing

We introduce a new computer-aided design approach based on free binary decision diagrams (FBDDs) for implementing Boolean functions on crossbars using flow-based computing. Our crossbar synthesis procedure uses generalized FBDDs to design crossbars for a Boolean formula such that there is a flow of current from an input nanowire to an output nanowire through the sneak paths in the crossbar if and only if the Boolean formula evaluates to true. Generalized FBDDs are more succinct representations of Boolean formulas than traditional reduced ordered binary decision diagrams (ROBDDs) because they do not require the same variable ordering along all paths of the decision diagram. Our experimental results with the middle bit of a multiplier show that our designs are 69.9% more succinct than flow-based crossbar computing approaches designed using ROBDDs.