Quantifier elimination via clause redundancy

Abstract

We consider the problem of existential quantifier elimination for Boolean formulas in conjunctive normal form. Recently we presented a new method for solving this problem based on the machinery of Dependency sequents (D-sequents). The essence of this method is to add to the quantified formula implied clauses until all the clauses with quantified variables become redundant. A D-sequent is a record of the fact that a set of quantified variables is redundant in some subspace. In this paper, we introduce a quantifier elimination algorithm based on a new type of D-sequents called clause D-sequents that express redundancy of clauses rather than variables. Clause D-sequents significantly extend our ability to introduce and algorithmically exploit redundancy, as our experimental results show.