## Section: New Results

### Variant Quantifier Elimination

In [10] , we describe an algorithm (VQE) for a
*variant* of the real quantifier elimination problem (QE). The
variant problem requires the input to satisfy a certain *extra
condition*, and allows the output to be *almost* equivalent
to the input. The motivation/rationale for studying such a variant
QE problem is that many quantified formulas arising in applications
do satisfy the extra conditions. Furthermore, in most applications,
it is sufficient that the output formula is almost equivalent to the
input formula. The main idea underlying the algorithm is to
substitute the repeated projection step of CAD by a single
projection without carrying out a parametric existential decision
over the reals. We find that the algorithm can tackle important and
challenging problems, such as numerical stability analysis of the
widely-used MacCormack's scheme. The problem has been practically
out of reach for standard QE algorithms in spite of many attempts to
tackle it. However the current implementation of VQE can solve it
in about 12 hours.