Reversible logic finds many applications, especially in the area of quantum computing. A completely specified n-input, n-output Boolean function is called reversible if it maps each input assignment to a unique output assignment and vice versa. Logic synthesis for reversible functions differs substantially from traditional logic synthesis and is currently an active area of research. The authors present an algorithm and tool for the synthesis of reversible functions. The algorithm uses the positive-polarity Reed-Muller expansion of a reversible function to synthesize the function as a network of Toffoli gates. At each stage, candidate factors, which represent subexpressions common between the Reed-Muller expansions of multiple outputs, are explored in the order of their attractiveness. The algorithm utilizes a priority-based search tree, and heuristics are used to rapidly prune the search space. The synthesis algorithm currently targets the generalized n-bit Toffoli gate library. However, other algorithms exist that can convert an n-bit Toffoli gate into a cascade of smaller Toffoli gates. Experimental results indicate that the authors' algorithm quickly synthesizes circuits when tested on the set of all reversible functions of three variables. Furthermore, it is able to quickly synthesize all four-variable and most five-variable reversible functions that were in the test suite. The authors also present results for some benchmark functions widely discussed in literature and some new benchmarks that the authors have developed. The algorithm is shown to synthesize many, but not all, randomly generated reversible functions of as many as 16 variables with a maximum gate count of 25

A function is reversible if each input vector produces a unique output vector. Reversible functions find applications in low power design, quantum computing, and nanotechnology. Logic synthesis for reversible circuits differs substantially from traditional logic synthesis. In this paper, we present the first practical synthesis algorithm and tool for reversible functions with a large number of inputs. It uses positive-polarity Reed-Muller decomposition at each stage to synthesize the function as a network of Toffoli gates. The heuristic uses a priority queue based search tree and explores candidate factors at each stage in order of attractiveness. The algorithm produces near-optimal results for the examples discussed in the literature. The key contribution of the work is that the heuristic finds very good solutions for reversible functions with a large number of inputs.