Online Testing of Ternary Reversible Multiple-Controlled Unary Gate Circuits
Recently a synthesis method for ternary reversible circuit using Max-Min algebra has been introduced, which synthesizes the circuit as a cascade of multiple-controlled unary gates. It has been shown that this method outperforms the previous TGFSOP-based method in terms of both quantum cost and number of ancilla inputs. We propose two techniques for online testing of ternary reversible circuits synthesized using multiple-controlled unary gates, one for testing a single line fault and another for testing a single fault of any fault model. For this purpose, we propose two new ternary reversible gates, namely a modified Feynman gate and extended multiple-controlled unary gates. We show realizations of these gates using elementary unary and M-S gates. In both the online testable circuits, one pre-fix and another post-fix circuit are added to the original circuit. For online testing of a single line fault, the multiple-controlled unary gates of the original circuit are replaced by their corresponding extended multiple-controlled unary gates. For online testing of a single fault of any fault model, for each multiple-controlled unary gate of the original circuit, we add an additional multiple-controlled unary gate with different target operation. We experimented with 24 benchmark logic functions of up to five variables. For online testing of a single line fault, on average the proposed technique requires 29.77% quantum cost overhead. For online testing of a single fault of any fault model, on average the proposed technique requires 123.94% quantum cost overhead.
Keywords: Line fault, missing gate fault, missing control fault, online testing, ternary reversible circuit, ternary extended multiple-controlled unary gates, ternary modified Feynman gate