Graph-Based Algorithms for Boolean Function Manipulation
IEEE Transactions on Computers
Finding the Optimal Variable Ordering for Binary Decision Diagrams
IEEE Transactions on Computers
Separating the eraser Turing machine classes Le, NLe, co-NLe and Pe
Theoretical Computer Science
Improving the Variable Ordering of OBDDs Is NP-Complete
IEEE Transactions on Computers
Size of ordered binary decision diagrams representing threshold functions
Theoretical Computer Science
Branching programs and binary decision diagrams: theory and applications
Branching programs and binary decision diagrams: theory and applications
Asymptotically optimal bounds for OBDDs and the solution of some basic OBDD problems
Journal of Computer and System Sciences
Computing strongly connected components in a linear number of symbolic steps
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Optimizing OBDDs Is Still Intractable for Monotone Functions
MFCS '98 Proceedings of the 23rd International Symposium on Mathematical Foundations of Computer Science
The Complexity of Equivalence and Containment for Free Single Variable Program Schemes
Proceedings of the Fifth Colloquium on Automata, Languages and Programming
The Complexity of the Optimal Variable Ordering Problems of Shared Binary Decision Diagrams
ISAAC '93 Proceedings of the 4th International Symposium on Algorithms and Computation
Size and Variable Ordering of OBDDs Representing Treshold Functions
COCOON '97 Proceedings of the Third Annual International Conference on Computing and Combinatorics
The Effect of Null-Chains on the Complexity of Contact Schemes
FCT '89 Proceedings of the International Conference on Fundamentals of Computation Theory
On threshold BDDs and the optimal variable ordering problem
COCOA'07 Proceedings of the 1st international conference on Combinatorial optimization and applications
Exact OBDD bounds for some fundamental functions
SOFSEM'08 Proceedings of the 34th conference on Current trends in theory and practice of computer science
On the OBDD complexity of the most significant bit of integer multiplication
TAMC'08 Proceedings of the 5th international conference on Theory and applications of models of computation
On symbolic scheduling independent tasks with restricted execution times
WEA'05 Proceedings of the 4th international conference on Experimental and Efficient Algorithms
| Hi-index | 0.01 |
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.