An Anytime Symmetry Detection Algorithm for ROBDDs

Detecting symmetries is crucial to logic synthesis, technology mapping, detecting function equivalence under unknown input correspondence, and ROBDD minimization. State-of-the-art is represented by Mishchenko's algorithm. In this paper we present an efficient anytime algorithm for detecting symmetries in Boolean functions represented as ROBDDs, that output pairs of symmetric variables until a prescribed time bound is exceeded. The algorithm is complete in that given sufficient time it is guaranteed to find all symmetric pairs. The complexity of this algorithm is in O(n^4+n|G|+|G|^3) where n is the number of variables and |G| the number of nodes in the ROBDD, and it is thus competitive with Mishchenko's |G|^3 algorithm in the worst-case since n << |G|. However, our algorithm performs significantly better because the anytime approach only requires lightweight data structure support and it offers unique opportunities for optimization.