Fast computation of symmetries in Boolean functions

Symmetry detection in completely specified Boolean functions is important for several applications in logic synthesis, technology mapping, BDD minimization, and testing. This paper presents a new algorithm to detect four basic types of two-variable symmetries. The algorithm detects all pairs of symmetric variables in one pass over the shared BDD of the multi-output function. The worst-case complexity of this method is cubic in the number of BDD nodes but, on typical logic synthesis benchmarks, the complexity appears to be linear. The computation is particularly efficient when the functions have multiple symmetries or no symmetries. Experiments show that the algorithm is faster than other known methods, and in some cases achieves a speed-up of several orders of magnitude.