Communications of the ACM
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)
Computational limitations on learning from examples
Journal of the ACM (JACM)
Finding the Optimal Variable Ordering for Binary Decision Diagrams
IEEE Transactions on Computers
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
Dynamic variable ordering for ordered binary decision diagrams
ICCAD '93 Proceedings of the 1993 IEEE/ACM international conference on Computer-aided design
Hardness of identifying the minimum ordered binary decision diagram
Discrete Applied Mathematics - Special issue on Boolean functions and related problems
The nonapproximability of OBDD minimization
Information and Computation
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
On the Complexity of Constructing Optimal Ordered Binary Decision Diagrams
MFCS '94 Proceedings of the 19th International Symposium on Mathematical Foundations of Computer Science 1994
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
Some heuristics for generating tree-like FBDD types
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Minimization of decision trees is hard to approximate
Journal of Computer and System Sciences
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Ordered Binary Decision Diagrams (OBDDs) and Free Binary Decision Diagrams (FBDDs) are data structures for Boolean functions. They can efficiently be manipulated if only OBDDs respecting a fixed variable ordering or FBDDs respecting a fixed graph ordering are considered. In this paper, it is shown that the existence of polynomial time approximation schemes for optimizing variable orderings or graph orderings implies NP = P, and so such algorithms are quite unlikely to exist. Similar hardness results are shown for the related problems of computing minimal size OBDDs and FBDDs that are consistent with a given set of examples. The latter result implies that size bounded OBDDs and FBDDs are not PAC-learnable unless NP = RP.