Graph-Based Algorithms for Boolean Function Manipulation
IEEE Transactions on Computers
On the complexity of branching programs and decision trees for clique functions
Journal of the ACM (JACM)
Graph driven BDDs—a new data structure for Boolean functions
Theoretical Computer Science
Improving the Variable Ordering of OBDDs Is NP-Complete
IEEE Transactions on Computers
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Efficient Boolean Manipulation with OBDD's Can be Extended to FBDD's
IEEE Transactions on Computers
An Exponential Lower Bound for One-Time-Only Branching Programs
Proceedings of the Mathematical Foundations of Computer Science 1984
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
On the Existence of Polynomial Time Approximation Schemes for OBDD Minimization (Extended Abstract)
STACS '98 Proceedings of the 15th Annual Symposium on Theoretical Aspects of Computer Science
Proof verification and hardness of approximation problems
SFCS '92 Proceedings of the 33rd Annual Symposium on Foundations of Computer Science
Some heuristics for generating tree-like FBDD types
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
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Free Binary Decision Diagrams (FBDDs) axe a data structure for the representation and manipulation of Boolean functions. Efficient algorithms for most of the important operations are known if only FBDDs respecting a fixed graph ordering are considered. However, the size of such an FBDD may strongly depend on the chosen graph ordering and efficient algorithms for computing good or optimal graph orderings are not known. In this paper it is shown that the existence of polynomial time approximation schemes for optimizing graph orderings or for minimizing FBDDs implies NP = P, and so such algorithms axe quite unlikely to exist.