On the OBDD complexity of threshold functions and the variable ordering problem : Extended abstract

Abstract

Ordered binary decision diagrams (OBDDs) are one of the most common dynamic data structures for Boolean functions. Among the many areas of application are verification, model checking, computer aided design, relational algebra, and symbolic graph algorithms. Threshold functions are the basic functions for discrete neural networks and are used as building blocks in the design of symbolic graph algorithms. In this paper the first exponential lower bound on the size of a more general model than OBDDs and the first nontrivial asymptotically optimal bound on the OBDD size for a threshold function are presented. Furthermore, if the number of different weights is a constant it is shown that computing an optimal variable order for multiple output threshold functions is NP-hard whereas for single output function the problem is solvable in deterministic polynomial time. © Springer-Verlag Berlin Heidelberg 2009.