Ternary Max-Min Algebra for Representation of Reversible Logic Functions

Ternary reversible logic functions are generally represented as ternary Galois field sum of products (TGFSOP) expressions and the TGFSOP expressions are mapped to reversible circuits using cascades of Feynman and Toffoli gates. Although a ternary logic function with a large number of variables can be minimized as a TGFSOP expression, the process is computationally expensive and the resulting reversible circuit tends to have a high quantum cost and ancilla inputs. To overcome these limitations, in this work we propose a new method of representing ternary reversible logic functions as Max of Min-terms (Max-Min) expressions, which can be mapped to a reversible circuit using multiple-controlled unary gates requiring lower quantum cost and fewer ancilla inputs. We propose a map-based minimization method for Max-Min expressions of up to four variables focusing on restrictions of the reversible circuit mapping technique.