Partial Quantifier Elimination

We consider the problem of Partial Quantifier Elimination (PQE). Given formula ∃X[F (X,Y ) ∧G(X,Y )], where F,G are in conjunctive normal form, the PQE problem is to find a formula F ∗(Y ) such that F ∗ ∧ ∃X[G] ≡ ∃X[F ∧G]. We solve the PQE problem by generating and adding to F clauses over the free variables that make the clauses of F with quantified variables redundant in ∃X[F ∧G]. The traditional Quantifier Elimination problem (QE) can be viewed as a degenerate case of PQE where G is empty so all clauses of the input formula with quantified variables need to be made redundant. The importance of PQE is threefold. First, in non-degenerate cases, PQE can be solved more efficiently than QE. Second, many problems are more naturally formulated in terms of PQE rather than QE. Third, an efficient PQE-algorithm will enable new methods of model checking and SAT-solving. We describe a PQE algorithm based on the machinery of dependency sequents and give experimental results showing the promise of PQE.