Any 2-asummable bipartite function is weighted threshold |
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Authors: | Javier Herranz |
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Institution: | Dept. Matemàtica Aplicada IV, Universitat Politècnica de Catalunya, C. Jordi Girona 1-3, 08034 Barcelona, Spain |
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Abstract: | Possible characterizations of which positive boolean functions are weighted threshold were studied in the 60s and 70s. It is known that a boolean function is weighted threshold if and only if it is k-asummable for every value of k. Furthermore, for some particular subfamilies of functions (those with up to eight variables, and graph functions), it is known that a function is weighted threshold if and only if it is 2-asummable.In this work we prove that bipartite functions also satisfy this property: a bipartite function is weighted threshold if and only if it is 2-asummable. In a bipartite function the set of variables can be partitioned in two classes, such that all the variables in the same class play exactly the same role in the function. |
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Keywords: | Weighted threshold boolean functions Bipartite functions 2-asummability |
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