Exact Synthesis of Toffoli Gate Circuits with Negative Control Lines

The development of synthesis approaches for reversible circuits is an active research area. Besides heuristic methods, also exact synthesis received significant attention. Here, circuits realizing the desired functions e.g. with a minimal number of gates are determined. However, so far exact synthesis considering Toffoli gate circuits with positive control lines only has been considered. In this paper, we are extending the scope of exact synthesis by additionally considering negative control lines in the circuits to be synthesized. For this purpose, we propose and evaluate a SAT-based synthesis method. Our experiments show that incorporating negative control lines leads to smaller circuits with respect to the number of gates. Furthermore, in some cases even the run-time of the synthesis can be improved.