In this paper, the authors present solutions to embedded large irreversible functions, which are considered a problem in reversible circuit synthesis. The main contributions include three algorithms for determining the number of additional lines of large irreversible functions (one heuristic cube-based algorithm and two exact cube-based and binary decision diagram (BDD)-based ones) and two algorithms for embedding large irreversible functions (one exact cube-based algorithm and one heuristic BDD-based algorithm). The details are described in sections 5 and 6.

Since most Boolean functions of practical interest are irreversible, such functions are embedded into reversible ones prior to synthesis. Determining an efficient embedding for large irreversible functions is an open research problem that affects the synthesis performance for reversible logic. This paper provides algorithms that enable embedding of functions containing up to hundreds of variables, although efficient embedding of irreversible functionality has been restricted to very small functions.

Some experimental results using these algorithms are illustrated in section 7. Instead of implementing these proposed functions as circuits and showing the performance as gate count, maximum of frequency, latency, and power/energy consumption, the authors list experimental results as the number of additional lines. The reason is explained in this section.

In conclusion, the algorithms are novel. The implementation and evaluation are thorough and indeed show that the algorithms can be used effectively for compact embeddings of functions containing a large number of variables.