Abstract
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.
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