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A245079
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Number of bipolar Boolean functions, that is, Boolean functions that are monotone or antimonotone in each argument.
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0
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OFFSET
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0,1
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COMMENTS
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A Boolean function is bipolar if and only if for each argument index i, the function is one of: (1) monotone in argument i, (2) antimonotone in argument i, (3) both monotone and antimonotone in argument i.
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REFERENCES
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Richard Dedekind, Über Zerlegungen von Zahlen durch ihre grössten gemeinsamen Theiler, in Fest-Schrift der Herzoglichen Technischen Hochschule Carolo-Wilhelmina, pages 1-40. Vieweg+Teubner Verlag (1897).
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LINKS
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G. Brewka and S. Woltran, Abstract dialectical frameworks, Proceedings of the Twelfth International Conference on the Principles of Knowledge Representation and Reasoning. Pages 102--111. IJCAI/AAAI 2010.
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FORMULA
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a(n) = Sum_{i=1..n}(2^i * C(n,i) * A006126(i)) + 2.
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EXAMPLE
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There are 2 bipolar Boolean functions in 0 arguments, the constants true and false.
All 4 Boolean functions in one argument are bipolar.
For 2 arguments, only equivalence and exclusive-or are not bipolar, 16-2=14.
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CROSSREFS
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KEYWORD
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nonn,hard,more
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AUTHOR
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STATUS
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approved
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