Multiple-valued decision diagrams with symmetric variable nodes

Symmetry is an important property of logic functions. In this paper, we introduce symmetric variable nodes, and investigate how they can be used to advantage in decision diagrams. We consider totally-symmetric and partially-symmetric functions as well as functions with partial symmetries. The identification of symmetric variable nodes is investigated as is the uniqueness of the resulting representation. A principal advantage of the new node type is that it often reduces the depth of the decision diagram. We consider the effect this has on the circuits that can be directly identified from decision diagrams.