Approximations by OBDDs and the variable ordering problem
Ordered binary decision diagrams (OBDDs) and their variants are motivated by the need to represent Boolean functions in applications. Research concerning these applications leads also to problems and results interesting from a theoretical point of view. In this paper, methods from communication complexity and information theory are combined to prove that the direct storage access function and the inner product function have the following property. They have linear π-OBDD size for some variable ordering π and, for most variable orderings π′ all functions which approximate them on considerably more than half of the inputs, need exponential π′-OBDD size. These results have implications for the use of OBDDs in experiments with genetic programming.