Generalized Symmetries in Boolean Functions: Fast Computation and Application to Boolean Matching

In recent years, the notion of symmetry has been extended from classical symmetries to also include constant cofactor symmetries, single variable symmetries and Kronecker symmetries. All these symmetries form a generalized symmetry scheme. Existing methods to detect generalized symmetries require computing the cofactors for each pair of variables to check certain relationships between the cofactors. In this paper, we present a new algorithm that detects all pairs of symmetric variables in one pass over a multi-output BDD. Experiments on the MCNC benchmarks are encouraging. We also propose a potential application of generalized symmetries in Boolean matching.