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A137202
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Number of nodes in the BDD for the hidden weighted bit function h_n under the best possible ordering of variables.
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1
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3, 3, 5, 9, 16, 23, 33, 46, 63, 82, 109, 139, 178, 224, 282, 348, 434, 531, 653, 796, 973, 1176, 1433, 1725, 2090
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OFFSET
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1,1
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COMMENTS
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In this problem we don't consider "complement bits" to shorten the BDD.
The best method presently known to find a(n) takes something like 2.5^n steps.
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REFERENCES
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D. E. Knuth, The Art of Computer Programming, Vol. 4A, Section 7.1.4.
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LINKS
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EXAMPLE
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For example, when n=8 the smallest BDD is obtained when one tests first x8 (1 node), then x7 (2 nodes), then x1 (4), then x6 (6), then x2 (9), then x5 (12), then x4 (8), then x3 (2). The total number of nodes is 46, including the two sink nodes.
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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