Transformation-based Synthesis of Networks of To oli/Fredkin Gates

Reversible logic has attracted signi cant attention in recent years. It has applications in low power CMOS, quantum computing, nanotechnology, and optical computing. Traditional gates such as AND, OR, and EXOR are not reversible. In fact NOT is the only reversible gate from the traditional set of gates. Several reversible gates have been proposed. Among them are the controlled NOT (also known as the Feynman gate), the To oli gate, and the Fredkin gate. An n-input To oli gate has n-1 control lines which pass through the gate unaltered and a target line on which the value is inverted if all the control lines have value '1'. An n-input Fredkin gate has n-2 control lines which pass through the gate unaltered and two target lines on which the values are swapped if all the control lines have value '1'. A NOT gate is the special case of a To oli gate with no control inputs. Likewise, a SWAP gate is the special case of a Fredkin gate with no control inputs. In this paper, we will review a transformation-based synthesis procedure targeted to To oli gates and show how it can be extended to allow Fredkin gates. This extension results in circuits with fewer gates. The synthesis of reversible logic di ers signi cantly from traditional irreversible logic synthesis approaches. Fan-outs and loops are not permitted due to the target technology. Outputs from one gate are used as inputs to the next gate. This results in a high degree of interdependence among gates. Our algorithm rst nds an initial circuit with no backtracking and minimal look-ahead. We exploit reversibility directly in our synthesis approach. This method always nds a solution. Next we apply a set of template transforms that reduce the size of the circuit. We synthesize all three input, three output reversible functions and compare CCECE 2003 CCGEI 2003, Montreal, May/mai 2003 07803-7781-8/03/$17.00 c 2003 IEEE our results to those obtained previously.