5 research outputs found
The conjunctive complexity of quadratic Boolean functions
AbstractThe minimal number, of conjuctions in monotone circuits for quadratic Boolean functions, i.e. disjunctions of quadratic monomials xixj, 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 complexit
Proving Finite Satisfiability of Deductive Databases
It is shown how certain refutation methods can be extended into semi-decision
procedures that are complete for both unsatisfiability and finite satisfiability. The proposed extension
is justified by a new characterization of finite satisfiability. This research was motivated
by a database design problem: Deduction rules and integrity constraints in definite databases
have to be finitely satisfiabl