Spectral Transforms for Large Boolean Functions with Applications to Technology Mapping

The Walsh transform has numerous applications in computer-aided design, but the usefulness of these techniques in practice has been limited by the size of the boolean functions that can be transformed. Currently available techniques limit the functions to less than 20 variables. In this paper, we show how to compute concise representations of the Walsh transform for functions with several hundred variables. We have applied our techniques to boolean technology mapping and, in certain cases, we obtained a speed up of as much as 50% for the matching phase.