Towards Optimal Logic Representations for Implication-Based Memristive Circuits

Memristive circuits natively perform material implication (IMPLY) operation, IMPLY together with FALSE (by setting a signal of the IMPLY to `0') is a complete set of operators. As one promising approach for in-memory computing, memristive circuits allow for both data-storing and logic-operation. Logic synthesis is essential for the design of emerging technologies. Instead of using well-known logic synthesis data structures to derive an implication logic network, the paper presents an exact synthesis method to obtain an optimal IMPLY logic network, which is a dedicated homogeneous network by using IMPLY as its only logic primitives. By synthesizing all the 256 three-input Boolean functions, the experimental results show 74 of these have better size compared with one-to-one mapping from optimal And-Inverter Graph (AIG) representations.