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Characterization of Threshold Functions
Unateness Monotonicity and Asummability
8 other sections not shown
1-realizable 2-monotonic assignment of weights Boolean function complementary function consider contradiction convex sets corresponding denote electronic Comput Equation example exists expressed F of n function F function realized function-input FXjXk given function hyperplane I.E.E.E. Trans I.R.E. Trans input variables integral realization irredundant normal disjunctive isobaric functions l)-cube linearly separable m-tuples majority gate maximal vertices maximum allowable sensitivities minimal realization minimal-integral realization minimum number minterm n variables n-cube normal disjunctive form number of threshold obtained output pairwise unateness permutation prime implicant product-of-sum form proof q.e.d. corollary q.e.d. theorem realization of F realization of threshold reduced functions set of inequalities shown in Fig single threshold successive higher ordering switching function symmetric function testing and realization three-input majority gate threshold function threshold logic elements threshold value unate functions University of Ottawa vertex of F vertices in F weight vector Xj and xk