Decision diagrams are often used for efficient representation of discrete functions in terms of needed storage space and processing time. In this paper, we propose an XML (Extensible Markup Language) based standard for the structural description of various types of decision diagrams. The proposed standard describes elements of the structure common to various types of decision diagrams. It also provides facilities for storing additional information, specific to particular types of decision diagrams. Properties of XML enable us to define a standard that is flexible enough to be applicable to various existing types of decision diagrams as well as new types that could be defined in the future. The existence of such a standard permits efficient storage and exchange of data in decision diagram form between various software systems. In this way, it supports benchmarking, testing and verification of various procedures using decision diagrams as a basic data structure.

This paper presents a group theoretic approach to the design of Decision diagrams (DDs) with increased functionality of nodes. Basic characteristics of DDs determine their applications, and thus, the optimization of DDs with respect to different characteristics is an important task. Increased functionality of nodes provides for optimization of DDs. In this paper, the methods for optimization of binary DDs by pairing of variables are interpreted as the optimization of DDs by changing the domain group for the represented functions. Then, it is pointed out that, for Abelian groups, the increased functionality of nodes by using larger subgroups may improve some of the characteristics of DDs at the price of other characteristics. With this motivation, we proposed the use of non-Abelian groups for the domain of represented functions by taking advantages from basic features of their group representations. At the same time, the present methods for optimization of DDs, do not offer any criterion or efficient algorithm to choose among a variety of possible different DDs for an assumed domain group. Therefore, we propose Fourier DDs on non-Abelian groups to exploit the reduced cardinality of the Fourier spectrum on these groups.