Inversions Optimization in XOR-Majority Graphs with an Application to QCA

Inversions are indispensable to build a logically complete Boolean system. However, the implementations of inversion in some nanotechnologies are expensive than the other logical operations. Therefore, the inversions optimization is of paramount interest for high-performance nanotechnology circuit design. Recently, XOR-Majority Graphs (XMGs) are used as logic representations for advanced logic synthesis. To this end, we propose an XMG optimization technique to rewrite the complemented edges while not changing its shape. The optimizations consider both majority-of-three (MAJ) nodes and exclusive-OR (XOR) nodes by using inverter propagations. The experimental results on EPFL benchmark suites show our method can achieve an average reduction of 17.3% number of inversions, which brings up to 9.8% area improvement for the implementation using Quantum-dot Cellular Automata (QCA) circuits.