Majority-based reversible logic gate

Reversible logic plays an important role in application of adiabatic low power CMOS computing and quantum computing. In this paper we introduce families of reversible gates based on majority and we prove their properties in reversible circuit synthesis. These gates can be used to synthesize reversible circuits of minimum “scratchpad register width ” for arbitrary reversible functions. We show that, given a majority Boolean function f with 2k+1 inputs, f can be implemented by a reversible logic gate with 2k+1 inputs and 2k+1 outputs, i.e., without any constant inputs. The problem is formulated in terms of group theory and solved by using the algebraic software GAP for logic synthesis