On the influence of the variable ordering for algorithmic learning using OBDDs

OBDDs with a fixed variable ordering are used successfully as data structure in experiments with learning heuristics based on examples. In this paper, it is shown that, for some functions, it is necessary to develop an algorithm to learn also a good OBDD variable ordering. There are functions with the following properties. They have OBDDs of linear size for optimal variable orderings. But for all but a small fraction of all variable orderings one needs large size to represent a list of randomly chosen examples. These properties are shown for simple functions like the multiplexer and the inner product.