Several algorithms have been proposed for the synthesis of reversible circuits. In this paper, a cycle-based synthesis algorithm for reversible logic, based on the NCT library, has been proposed. In other words, direct implementation of a single 3-cycle, a pair of 3-cycles and a pair of 2-cycles have been explored and used to propose an efficient Toffoli-based synthesis algorithm for reversible circuits. The synthesis algorithm decomposes a given large cycle into a set of single 3-cycles, pairs of 3-cycles and pair of 2-cycles and synthesizes the resulted cycles directly. Our experimental results show that the proposed synthesis algorithm can outperform the available 2-cycle-based approach about 34% on average. In addition, several discussions for the generalization of the proposed method to the 2 m -cycles are given.

Abstract-In this paper, a new non-search based synthesis algorithm for reversible circuits is proposed. Compared with the widely used search-based methods, our algorithm is guarantied to produce a result and can lead to a solution with much fewer steps. To evaluate the proposed method, several circuits taken from the literature are used. The experimental results corroborate the expected findings.