  We consider the problem of Partial Quantifier Elimination (PQE). Given
formula exists(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* & exists(X)[G] is
logically equivalent to exists(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. The traditional Quantifier
Elimination problem (QE) is a special 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 twofold. First, many problems are more
naturally formulated in terms of PQE rather than QE. Second, in many cases PQE
can be solved more efficiently than QE. We describe a PQE algorithm based on
the machinery of dependency sequents and give experimental results showing the
promise of PQE.
