Conjugate symmetry

—Conjugate symmetry is an entirely new approach to symmetric Boolean functions that can be used to extend existing methods for handling symmetric functions to a much wider class of functions. These are functions that currently appear to have no symmetries of any kind. Such symmetries occur widely in practice. In fact, we show that even the simplest circuits exhibit conjugate symmetry. To demonstrate the effectiveness of conjugate symmetry we modify an existing simulation algorithm, the hyperlinear algorithm, to take advantage of conjugate symmetry. This algorithm can simulate symmetric functions faster than non-symmetric ones, but due to the rarity of symmetric functions, this optimization is only of limited benefit. Because the standard benchmark circuits contain many symmetries it is possible to simulate these circuits faster than is possible with the fastest known event-driven algorithm. The detection and exploitation of conjugate symmetries makes use of GF(2) matrices. It is likely that conjugate symmetry and GF(2) will find applications in many other areas of EDA.