Application of Permutation Group Theory in Reversible Logic Synthesis

This paper discusses various applications of permutation group theory in the synthesis of reversible logic circuits, consisting of Toffoli gates with negative control lines. First asymptotically optimal synthesis algorithm is described. An algorithm for the gate complexity reduction, based on equivalent replacements of gates compositions, is introduced. New approach for combining group theory based synthesis algorithms with Reed-Muller spectra based synthesis algorithms is described. Experimental results are presented to show that the proposed synthesis techniques allows to reduce input lines count, the gate complexity or the quantum cost of a reversible circuit, implementing a known benchmark specification.