The conjunctive complexity of quadratic Boolean functions

Abstract

The minimal number, of conjuctions in monotone circuits for quadratic Boolean functions, i.e. disjunctions of quadratic monomials x i x j, is investigated. Single level circuits which have only one level of conjuctions 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. a quadratic function is defined whose single level complexity is larger than its conjuctive complexity