  Reversible logic has applications in various research areas including
low-power design and quantum computation. In this paper, a rule-based
optimization approach for reversible circuits is proposed which uses both
negative and positive control Toffoli gates during the optimization. To this
end, a set of rules for removing NOT gates and optimizing sub-circuits with
common-target gates are proposed. To evaluate the proposed approach, the
best-reported synthesized circuits and the results of a recent synthesis
algorithm which uses both negative and positive controls are used. Our
experiments reveal the potential of the proposed approach in optimizing
synthesized circuits.
