On the size of (generalized) OBDDs for threshold functions

doi:10.1016/j.ipl.2009.01.005

Information Processing Letters

Volume 109, Issue 10, 30 April 2009, Pages 499-503

https://doi.org/10.1016/j.ipl.2009.01.005 Get rights and content

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 hardware verification, model checking, and symbolic graph algorithms. Threshold functions are the basic functions for discrete neural networks and are used as building blocks in the design of some 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.

References (16)

B. Bollig et al.
Asymptotically optimal bounds for OBDDs and the solution of some basic OBDD problems
Journal of Computer and System Sciences
(2000)
K. Hosaka et al.
Size of ordered binary decision diagrams representing threshold functions
Theoretical Computer Science
(1997)
M. Krause et al.
Separating the eraser Turing machine classes $L_{e}$ , $N L_{e}$ , co- $N L_{e}$ and $P_{e}$
Theoretical Computer Science
(1991)
D. Sieling et al.
NC-algorithms for operations on binary decision diagrams
Parallel Processing Letters
(1993)
P. Woelfel
Symbolic topological sorting with OBDDs
Journal of Discrete Algorithms
(2006)
M. Behle
On threshold BDDs and the optimal variable ordering problem
B. Bollig et al.
Exact OBDD bounds for some fundamental functions
R.E. Bryant
Graph-based algorithms for Boolean function manipulation
IEEE Trans. Comput.
(1986)

There are more references available in the full text version of this article.

Cited by (3)

Yet harder knapsack problems
2011, Theoretical Computer Science
Already 30 years ago, Chvátal has shown that some instances of the zero-one knapsack problem cannot be solved in polynomial time using a particular type of branch-and-bound algorithms based on relaxations of linear programs together with some rudimentary cutting-plane arguments as bounding rules. We extend this result by proving an exponential lower bound in a more general class of branch-and-bound and dynamic programming algorithms which are allowed to use memoization and arbitrarily powerful bound rules to detect and remove subproblems leading to no optimal solution.
On the Minimization of (Complete) Ordered Binary Decision Diagrams
2016, Theory of Computing Systems
On the complexity of some ordering problems
2014, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

View full text

On the size of (generalized) OBDDs for threshold functions

Abstract

Journal of Computer and System Sciences

Theoretical Computer Science

Theoretical Computer Science

Parallel Processing Letters

Journal of Discrete Algorithms

On threshold BDDs and the optimal variable ordering problem

Exact OBDD bounds for some fundamental functions

Graph-based algorithms for Boolean function manipulation

IEEE Trans. Comput.