Lower Bounds for Linearly Transformed OBDDs and FBDDs

Abstract

Linearly transformed ordered binary decision diagrams (LTOBDDs) have been suggested as a generalization of OBDDs for the representation and manipulation of Boolean functions. Instead of variables as in the case of OBDDs, parities of variables may be tested at the nodes of an LTOBDD. By this extension it is possible to represent functions in polynomial size that do not have polynomial size OBDDs, e.g., the characteristic functions of linear codes. In this paper lower bound methods for LTOBDDs and some generalizations of LTOBDDs are presented and applied to explicitly defined functions. By the lower bound results it is possible to compare the set of functions with polynomial size LTOBDDs and their generalizations with the set of functions with polynomial size representations for many other restrictions of BDDs.