^{1,a}, Pierre-Emmanuel Gaillardon

^{1,b}, Robert Wille

^{2,3}and Giovanni De Micheli

^{1,c}

^{1}Integrated Systems Laboratory (LSI), EPFL, Lausanne, Switzerland.

^{a}luca.amaru@epfl.ch

^{b}pierre-emmanuel.gaillardon@epfl.ch

^{c}giovanni.demicheli@epfl.ch

^{2}Integrated Circuit and System Design, Johannes Kepler University, Linz, Austria.

^{3}University of Bremen and DFKI GmbH, Bremen, Germany.

Reversible circuits implement invertible logic functions. They are of great interest to cryptography, coding theory, interconnect design, computer graphics, quantum computing, and many other fields. As for conventional circuits, checking the combinational equivalence of two reversible circuits is an important but difficult (coNP-complete) problem. In this work, we present a new approach for solving this problem significantly faster than the state-of-the-art. For this purpose, we exploit inherent characteristics of reversible computation, namely bi-directional (invertible) execution and the XOR-richness of reversible circuits. Bi-directional execution allows us to create an