Specification of Decision Diagram Operations

Decision Diagrams (DDs) are a well populated family of data structures, used for efficient representation and manipulation of huge data sets. Typically a given application requires choosing one particular category of DDs, like Binary Decision Diagrams (BDDs) or Data Decision Diagrams (DDDs), and sticking with it. Each category provides a language to specify its operations. For instance, the operation language of BDDs provides if-then-else, apply, etc. We focus on two main kinds of operation languages: BDD-like and DDDlike. They overlap: some operations can be expressed in both kinds of languages, while others are only available in one kind. We propose in this article a critical comparison of BDD-like and DDDlike languages. From the identified problems, we also propose a unified language for DD operations. It covers both BDD-like and DDD-like languages, and even some operations that cannot be expressed in either.