The multiple variable order problem for binary decision diagrams: theory and practical application

Reduced Ordered Binary Decision Diagrams (ROBDDs) gained widespread use in logic design verification, test generation, fault simulation, and logic synthesis. Since the size of an ROBDD heavily depends on the variable order used, there is a strong need to find variable orders that minimize the number of nodes in an ROBDD. In certain applications we have to cope with ROBDDs with different variable orders, whereas further manipulations of these ROBDDs require common variable orders. In this paper we give a theoretical background for this "Multiple Variable Order problem". Moreover we solve the problem to transform ROBDDs with different variable orders into a good common variable order using dynamic variable ordering techniques.