Majority Logic Synthesis

The majority function 〈xyz〉 evaluates to true, if at least two of its Boolean inputs evaluate to true. The majority function has frequently been studied as a central primitive in logic synthesis applications for many decades. Knuth refers to the majority function in the last volume of his seminal The Art of Computer Programming as “probably the most important ternary operation in the entire universe.” Majority logic synthesis has recently regained significant interest in the design automation community due to nanoemerging technologies which operate based on the majority function. In addition, majority logic synthesis has successfully been employed in CMOS-based applications such as standard cell or FPGA mapping. This tutorial gives a broad introduction into the field of majority logic synthesis. It will review fundamental results and describe recent contributions from theory, practice and applications.