A simplification algorithm for reversible logic network of positive/negative control gates

Templates for Positive and Negative Control Toffoli Networks

“…In [2], the authors defined positive/negative control Toffoli gates as PNC gates and proposed new merging, moving, and splitting rules and an algorithm for PNC gates. A deletion rule is defined as if two adjacent PNC gates have the same control and target bits, then the two gates can be deleted.…”

“…A child gate can be obtained by merging the parent gate and the other child gate. These rules are defined as merging rules [2]. Alternatively, a parent gate can be split into its two child gates or a child gate can be split into its parent gate and its brother gate.…”

“…Alternatively, a parent gate can be split into its two child gates or a child gate can be split into its parent gate and its brother gate. This is defined as splitting rules [2]. If the target bit of one gate is not the control of the other gate or two gates have the same target bit then the position of these two gates can be interchanged which is known as a moving rule.…”

“…If the target bit of one gate is not the control of the other gate or two gates have the same target bit then the position of these two gates can be interchanged which is known as a moving rule. A simplification algorithm utilizing the above deletion, merging, splitting, and moving rules was proposed in [2].…”

“…In another paper [5], the authors defined two MCT gates as adjacent gates if they have targets on the same line and differ in only one line with respect to the control connections. These adjacent gates are defined as brother (child) gates in [2] and are depicted in Figure 3.7. If two MCT gates have targets on the same line and differ in two control lines, then they are defined as distance-2 gates.…”