Synthesis of reversible logic functions using ternary Max-Min algebra

Ternary reversible circuits are normally realized as Toffoli cascades using ternary Galois field sum of products (TGFSOP) expressions. In this work we propose a new method for realization of ternary reversible circuits using ternary Max-Min expressions. The proposed method uses ternary multiple-controlled unary gates to map Max-Min expression into reversible circuit. We also present techniques for realizations of multiple-controlled unary gates using M-S gates at the quantum level. Preliminary results show that the proposed method produces better results than TGFSOP-based method in terms of both quantum cost and ancilla inputs.