Mod-p decision diagrams: a data structure for multiple-valued functions

Abstract

Multiple-valued decision diagrams (MDDs) give a way of approaching problems by using symbolic variables which are often more naturally associated with the problem statement than the variables obtained by a binary encoding. We present a more general class of MDDs, containing not only branching nodes but also functional nodes, labeled by addition modulo p operation, p-prime, and give algorithms for their manipulation Such decision diagrams have a potential of being more space-efficient than MDDs, However they are not a canonical representation of multiple-valued functions and thus the equivalence test of two Mod-p-DDs is more difficult then the test of two MDDs. To overcome this problem, we design a fast probabilistic equivalence test for Mod-p-DDs that requires time linear in the number of nodes.