The reversible circuit synthesis problem can be reduced to permutation group. This allows Schreier–Sims algorithm for the strong generating set-finding problem to be used to find tight bounds on the synthesis of 3-bit reversible circuits using the NFFr library. The tight bounds include the maximum and minimum length of 3-bit reversible circuits, the maximum and minimum cost of 3-bit reversible circuits. The analysis shows better results than that found in the literature for the lower bound of the cost. The analysis also shows that there are 2460 universal reversible sub-libraries from the main NFFr library.
Depth-optimized reversible circuit synthesis
