Permutation Independent Comparison of Pseudo Boolean Functions

We address the problem of permutation independent comparison of two pseudo Boolean functions given by multiplicative binary moment diagrams (∗Bmds), i. e., the problem of deciding whether there exists a permutation of the input variables such that the two ∗Bmds are equal. The analogous problem has already been investigated for binary decision diagrams (Bdds) in detail [5, 7, 8, 9, 10]. All these methods successfully use signatures which are permutation independent attributes of the input variables. Unfortunately, the signatures for Bdds cannot be applied to ∗Bmds. In this paper, we present signatures for ∗Bmds and prove their efficiency by extensive benchmark computations. In particular we show that the signatures for ∗Bmds are as efficient as signatures for Bdds.