Characterization and synthesis of classical reversible circuits

Abstract

Irreversible circuits were transformed into their equivalent reversible circuits. The resulting reversible circuits were optimized using a synthesis method proposed by Miller, Maslov, and Dueck, and a line reduction algorithm proposed by Wille, Soeken, and Drechsler. The application of the line-reduction algorithm reduced the number of circuit lines from 5 to 4. The effect of the line-reduction algorithm on the matrix representation of the original circuit was shown to preserve the reversibility of the function. It was also shown that only the matrix representation of a circuit or cascade of gates is needed to determine the operation of its n successive applications, which may be useful in length reduction of reversible circuits.