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On the Behavior of Substitution-based Reversible Circuit Synthesis Algorithms: Investigation and Improvement

In this paper, the behavior of substitution-based reversible circuit synthesis methods is studied. We analyze one of the most recent search-based synthesis algorithms to improve its quality by adding some new non-trivial substitutions. Furthermore, it is shown that the order of factor substitution affects the depth of search tree significantly. In addition, we consider the number of terms in positive polarity Reed-Muller (PPRM) expansions during factor substitution to show that some local increases in the number of terms may lead to better final synthesis results. Besides, the behavior of depth-first search (DFS) and breadth-first search (BFS) synthesis algorithms are investigated. It is demonstrated that BFS has more effects on the quality of results and sometimes leads to shorter runtime. Based on these properties, a new hybrid DFS/BFS synthesis algorithm is proposed. Our experiments show the efficiency of this algorithm