Abstract
The minimal number of conjunctions in monotone circuits for quadratic Boolean functions, i.e. disjunctions of quadratic monomials xi xj, is investigated. Single level circuits which have only one level of conjunctions are compared with arbitrary monotone circuits. The computation of the single level complexity is shown to be NP complete. For almost all quadratic functions almost optimal circuits can be computed in polynomial time. The single level conjecture is disproved, i.e. some quadratic function is defined whose single level complexity is larger than its conjunctive complexity.KeywordsBoolean FunctionQuadratic FunctionSingle LevelComplete Bipartite GraphMonotone FormulaThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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