A MAJestic Synthesis Review [Special Section on 2025 IEEE Kirchhoff Award]

This article presents a review of Majority-Inverter Graphs (MIGs) and their practical use in various applications within logic synthesis. MIGs are directed acyclic graphs consisting of three-input majority nodes and regular/complemented edges. They represent a paradigm shift in representing and optimizing logic using only majority (MAJ) and inversion (INV) functions. In this article, we review different optimization algorithms that work on MIGs, including algebraic, Boolean, and exact methods. We also describe different applications of MIGs in logic synthesis: From classical CMOS-based synthesis to their use for theoretical results and emerging technologies.